ltpda: m-toolbox/classes/@ao/xfit.m annotate

annotate m-toolbox/classes/@ao/xfit.m @ 45:a59cdb8aaf31 database-connection-manager

Merge

author	Daniele Nicolodi <nicolodi@science.unitn.it>
date	Tue, 06 Dec 2011 19:07:22 +0100
parents	f0afece42f48
children

rev	line source
0 f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1 % XFIT fit a function of x to data.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	4 % DESCRIPTION: XFIT performs a non-linear fit of a function of x to data.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	5 % smodels fitting is also supported.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	6 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	7 % ALGORITHM: XFIT does a chi-squared minimization by means of different
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	8 % algorithms (see details in the default plist). Covariance matrix is also
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	9 % computed from the Fisher's Information Matrix. In case the Information
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	10 % Matrix is not positive-definite, uncertainties will not be stored in the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	11 % output.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	12 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	13 % CALL: b = xfit(a, pl)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	14 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	15 % INPUTS: a - input AO to fit to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	16 % pl - parameter list (see below)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	17 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	18 % OUTPUTs: b - a pest object containing the best-fit parameters,
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	19 % goodness-of-fit reduced chi-squared, fit degree-of-freedom
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	20 % covariance matrix and uncertainties. Additional
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	21 % quantities, like the Information Matrix, are contained
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	22 % within the procinfo. The best-fit model can be evaluated
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	23 % from pest\eval.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	24 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	25 % <a href="matlab:utils.helper.displayMethodInfo('ao', 'xfit')">Parameters Description</a>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	26 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	27 % EXAMPLES:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	28 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	29 % % 1) Fit to a frequency-series
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	30 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	31 % % Create a frequency-series
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	32 % datapl = plist('fsfcn', '0.01./(0.0001+f) + 5*abs(randn(size(f))) ', 'f1', 1e-5, 'f2', 5, 'nf', 1000, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	33 % 'xunits', 'Hz', 'yunits', 'N/Hz');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	34 % data = ao(datapl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	35 % data.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	36 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	37 % % Do fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	38 % fitpl = plist('Function', 'P(1)./(P(2) + Xdata) + P(3)', ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	39 % 'P0', [0.1 0.01 1]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	40 % params = xfit(data, fitpl)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	41 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	42 % % Evaluate model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	43 % BestModel = eval(params,plist('type','fsdata','xdata',data,'xfield','x'));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	44 % BestModel.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	45 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	46 % % Display results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	47 % iplot(data,BestModel)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	48 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	49 % % 2) Fit to a noisy sine-wave
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	50 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	51 % % Create a noisy sine-wave
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	52 % fs = 10;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	53 % nsecs = 500;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	54 % datapl = plist('waveform', 'Sine wave', 'f', 0.01, 'A', 0.6, 'fs', fs, 'nsecs', nsecs, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	55 % 'xunits', 's', 'yunits', 'm');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	56 % sw = ao(datapl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	57 % noise = ao(plist('tsfcn', '0.01*randn(size(t))', 'fs', fs, 'nsecs', nsecs));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	58 % data = sw+noise;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	59 % data.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	60 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	61 % % Do fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	62 % fitpl = plist('Function', 'P(1).sin(2piP(2).Xdata + P(3))', ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	63 % 'P0', [1 0.01 0]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	64 % params = xfit(data, fitpl)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	65 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	66 % % Evaluate model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	67 % BestModel = eval(params,plist('type','tsdata','xdata',sw,'xfield','x'));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	68 % BestModel.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	69 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	70 % % Display results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	71 % iplot(data,BestModel)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	72 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	73 % % 3) Fit an smodel of a straight line to some data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	74 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	75 % % Create a noisy straight-line
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	76 % datapl = plist('xyfcn', '2.33 + 0.1x + 0.01randn(size(x))', 'x', 0:0.1:10, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	77 % 'xunits', 's', 'yunits', 'm');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	78 % data = ao(datapl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	79 % data.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	80 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	81 % % Model to fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	82 % mdl = smodel('a + b*x');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	83 % mdl.setXvar('x');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	84 % mdl.setParams({'a', 'b'}, {1 2});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	85 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	86 % % Fit model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	87 % fitpl = plist('Function', mdl, 'P0', [1 1]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	88 % params = xfit(data, fitpl)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	89 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	90 % % Evaluate model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	91 % BestModel = eval(params,plist('xdata',data,'xfield','x'));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	92 % BestModel.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	93 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	94 % % Display results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	95 % iplot(data,BestModel)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	96 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	97 % % 4) Fit a chirp-sine firstly starting from an initial guess (quite close
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	98 % % to the true values) (bad convergency) and secondly by a Monte Carlo
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	99 % % search (good convergency)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	100 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	101 % % Create a noisy chirp-sine
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	102 % fs = 10;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	103 % nsecs = 1000;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	104 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	105 % % Model to fit and generate signal
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	106 % mdl = smodel(plist('name', 'chirp', 'expression', 'A.sin(2pi(f + f0.t).*t + p)', ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	107 % 'params', {'A','f','f0','p'}, 'xvar', 't', 'xunits', 's', 'yunits', 'm'));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	108 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	109 % % signal
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	110 % s = mdl.setValues({10,1e-4,1e-5,0.3});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	111 % s.setXvals(0:1/fs:nsecs-1/fs);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	112 % signal = s.eval;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	113 % signal.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	114 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	115 % % noise
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	116 % noise = ao(plist('tsfcn', '1*randn(size(t))', 'fs', fs, 'nsecs', nsecs));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	117 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	118 % % data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	119 % data = signal + noise;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	120 % data.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	121 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	122 % % Fit model from the starting guess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	123 % fitpl_ig = plist('Function', mdl, 'P0',[8,9e-5,9e-6,0]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	124 % params_ig = xfit(data, fitpl_ig);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	125 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	126 % % Evaluate model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	127 % BestModel_ig = eval(params_ig,plist('xdata',data,'xfield','x'));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	128 % BestModel_ig.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	129 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	130 % % Display results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	131 % iplot(data,BestModel_ig)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	132 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	133 % % Fit model by a Monte Carlo search
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	134 % fitpl_mc = plist('Function', mdl, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	135 % 'MonteCarlo', 'yes', 'Npoints', 1000, 'LB', [8,9e-5,9e-6,0], 'UB', [11,3e-4,2e-5,2*pi]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	136 % params_mc = xfit(data, fitpl_mc)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	137 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	138 % % Evaluate model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	139 % BestModel_mc = eval(params_mc,plist('xdata',data,'xfield','x'));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	140 % BestModel_mc.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	141 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	142 % % Display results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	143 % iplot(data,BestModel_mc)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	144 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	145 % % 5) Multichannel fit of smodels
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	146 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	147 % % Ch.1 data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	148 % datapl = plist('xyfcn', '0.1x + 0.01randn(size(x))', 'x', 0:0.1:10, 'name', 'channel 1', ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	149 % 'xunits', 'K', 'yunits', 'Pa');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	150 % a1 = ao(datapl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	151 % % Ch.2 data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	152 % datapl = plist('xyfcn', '2.5x + 0.1sin(2pix) + 0.01*randn(size(x))', 'x', 0:0.1:10, 'name', 'channel 2', ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	153 % 'xunits', 'K', 'yunits', 'T');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	154 % a2 = ao(datapl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	155 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	156 % % Model to fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	157 % mdl1 = smodel('a*x');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	158 % mdl1.setXvar('x');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	159 % mdl1.setParams({'a'}, {1});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	160 % mdl1.setXunits('K');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	161 % mdl1.setYunits('Pa');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	162 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	163 % mdl2 = smodel('bx + asin(2pix)');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	164 % mdl2.setXvar('x');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	165 % mdl2.setParams({'a','b'}, {1,2});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	166 % mdl2.setXunits('K');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	167 % mdl2.setYunits('T');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	168 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	169 % % Fit model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	170 % params = xfit(a1,a2, plist('Function', [mdl1,mdl2]));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	171 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	172 % % evaluate model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	173 % b = eval(params, plist('index',1,'xdata',a1,'xfield','x'));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	174 % b.setName('fit Ch.1');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	175 % r = a1-b;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	176 % r.setName('residuals');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	177 % iplot(a1,b,r)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	178 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	179 % b = eval(params, plist('index',2,'xdata',a2,'xfield','x'));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	180 % b.setName('fit Ch.2');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	181 % r = a2-b;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	182 % r.setName('residuals');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	183 % iplot(a2,b,r)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	184 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	185 % <a href="matlab:utils.helper.displayMethodInfo('ao', 'xfit')">Parameters Description</a>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	186 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	187 % VERSION: $Id: xfit.m,v 1.83 2011/05/12 07:46:29 mauro Exp $
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	188 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	189 % HISTORY: 17-09-2009 G. Congedo
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	190 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	191 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	192
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	193 function varargout = xfit(varargin)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	194
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	195 % global variables
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	196 global Pidx Ydata weights modelFuncs dFcns hFcns lb ub Nch Ndata estimator
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	197
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	198
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	199 % Check if this is a call for parameters
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	200 if utils.helper.isinfocall(varargin{:})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	201 varargout{1} = getInfo(varargin{3});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	202 return
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	203 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	204
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	205 import utils.const.*
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	206 utils.helper.msg(msg.PROC3, 'running %s/%s', mfilename('class'), mfilename);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	207
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	208 % Collect input variable names
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	209 in_names = cell(size(varargin));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	210 for ii = 1:nargin,in_names{ii} = inputname(ii);end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	211
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	212 % Collect all AOs and plists
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	213 [as, ao_invars] = utils.helper.collect_objects(varargin(:), 'ao', in_names);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	214 pl = utils.helper.collect_objects(varargin(:), 'plist', in_names);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	215
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	216 if nargout == 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	217 error('### xfit cannot be used as a modifier. Please give an output variable.');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	218 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	219
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	220 % combine plists
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	221 pl = parse(pl, getDefaultPlist());
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	222
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	223 % Extract necessary parameters
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	224 targetFcn = pl.find('Function');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	225 P0 = pl.find('P0');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	226 % ADDP = pl.find('ADDP');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	227 userOpts = pl.find('OPTSET');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	228 weights = pl.find('WEIGHTS');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	229 FitUnc = pl.find('FitUnc');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	230 UncMtd = pl.find('UncMtd');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	231 linUnc = pl.find('LinUnc');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	232 FastHess = pl.find('FastHess');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	233 SymDiff = pl.find('SymDiff');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	234 SymGrad = pl.find('SymGrad');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	235 SymHess = pl.find('SymHess');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	236 DiffOrder = pl.find('DiffOrder');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	237 lb = pl.find('LB');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	238 ub = pl.find('UB');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	239 MCsearch = pl.find('MonteCarlo');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	240 Npoints = pl.find('Npoints');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	241 Noptims = pl.find('Noptims');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	242 % SVDsearch = pl.find('SVD');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	243 % nSVD = pl.find('nSVD');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	244 Algorithm = pl.find('Algorithm');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	245 % AdpScale = pl.find('AdpScale');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	246 % only for function handle fitting
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	247 pnames = pl.find('pnames');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	248 % pvalues = pl.find('pvalues');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	249 estimator = pl.find('estimator');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	250
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	251 % Convert yes/no, true/false, etc. to booleans
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	252 FitUnc = utils.prog.yes2true(FitUnc);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	253 linUnc = utils.prog.yes2true(linUnc);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	254 FastHess = utils.prog.yes2true(FastHess);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	255 SymDiff = utils.prog.yes2true(SymDiff);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	256 MCsearch = utils.prog.yes2true(MCsearch);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	257 % SVDsearch = utils.prog.yes2true(SVDsearch);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	258 % AdpScale = utils.prog.yes2true(AdpScale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	259
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	260 % Check the fitting algorithm
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	261 % AlgoCheck = ~strcmpi(Algorithm,'fminsearch') & ~strcmpi(Algorithm,'fminunc') & ~isempty(Algorithm);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	262
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	263 if isempty(Algorithm)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	264 Algorithm = 'fminsearch';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	265 utils.helper.msg(msg.IMPORTANT, 'using %s as the fitting algorithm', upper(Algorithm));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	266 elseif ischar(Algorithm)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	267 Algorithm = lower(Algorithm);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	268 switch Algorithm
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	269 case 'fminsearch'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	270 utils.helper.msg(msg.IMPORTANT, 'using %s as the fitting algorithm', upper(Algorithm));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	271 Algorithm = 'fminsearch';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	272 case 'fminunc'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	273 if exist('fminunc','file')==2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	274 utils.helper.msg(msg.IMPORTANT, 'using %s as the fitting algorithm', upper(Algorithm));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	275 Algorithm = 'fminunc';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	276 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	277 error('### you must install Optimization Toolbox in order to use %s', upper(Algorithm))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	278 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	279 case 'fmincon'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	280 if exist('fmincon','file')==2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	281 utils.helper.msg(msg.IMPORTANT, 'using %s as the fitting algorithm', upper(Algorithm));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	282 Algorithm = 'fmincon';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	283 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	284 error('### you must install Optimization Toolbox in order to use %s', upper(Algorithm))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	285 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	286 case 'patternsearch'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	287 if exist('patternsearch','file')==2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	288 utils.helper.msg(msg.IMPORTANT, 'using %s as the fitting algorithm', upper(Algorithm));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	289 Algorithm = 'patternsearch';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	290 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	291 error('### you must install Genetic Algorithm and Direct Search Toolbox in order to use %s', upper(Algorithm))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	292 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	293 case 'ga'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	294 if exist('ga','file')==2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	295 utils.helper.msg(msg.IMPORTANT, 'using %s as the fitting algorithm', upper(Algorithm));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	296 Algorithm = 'ga';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	297 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	298 error('### you must install Genetic Algorithm and Direct Search Toolbox in order to use %s', upper(Algorithm))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	299 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	300 case 'simulannealbnd'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	301 if exist('simulannealbnd','file')==2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	302 utils.helper.msg(msg.IMPORTANT, 'using %s as the fitting algorithm', upper(Algorithm));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	303 Algorithm = 'simulannealbnd';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	304 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	305 error('### you must install Genetic Algorithm and Direct Search Toolbox in order to use %s', upper(Algorithm))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	306 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	307 otherwise
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	308 error('### unknown fitting algorithm')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	309 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	310 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	311 error('### unknown format for ALGORITHM parameter')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	312 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	313
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	314 % Estimator
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	315 if isempty(estimator)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	316 estimator = 'chi2';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	317 elseif ~strcmp(estimator,{'chi2','abs','log','median'})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	318 error('### unknown name of the estimator')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	319 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	320
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	321
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	322 % Data we will fit to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	323 Xdata = as.x;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	324 Ydata = as.y;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	325 % dYdata = as.dy;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	326
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	327 % Number of data point per each channel
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	328 Ndata = numel(as(1).x);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	329
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	330 % Number of channels
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	331 Nch = numel(as);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	332 multiCh = Nch-1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	333
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	334 % Number of models
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	335 if all(isa(targetFcn, 'smodel'))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	336 Nmdls = numel(targetFcn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	337 elseif iscell(targetFcn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	338 Nmdls = numel(targetFcn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	339 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	340 Nmdls = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	341 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	342
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	343 % consistency check on the data units
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	344 Xunits = as.xunits;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	345 % Xunits = as(1).xunits.strs;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	346 if Nch>1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	347 XunitsCheck = Xunits(1).strs;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	348 for kk=2:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	349 if ~strcmp(Xunits(kk).strs,XunitsCheck)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	350 error('### in multi-channel fitting the xunits of all data objects must be the same')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	351 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	352 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	353 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	354 Xunits = as(1).xunits;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	355 Yunits = as.yunits;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	356
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	357 % consistency check on the inputs
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	358
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	359 if isempty(targetFcn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	360 error('### please specify at least a model');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	361 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	362
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	363 if Nch~=Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	364 error('### number of data channels and models do not match')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	365 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	366
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	367 for kk=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	368 if any(numel(as(kk).x)~=Ndata)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	369 error('### the number of data is not self-consistent: please check that all channels have the same length')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	370 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	371 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	372
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	373 for kk=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	374 for kkk=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	375 if any(Xdata(:,kk)~=Xdata(:,kkk))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	376 error('### in multi-channel fitting the x-field of all data objects must be the same')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	377 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	378 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	379 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	380
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	381 cellMdl = iscell(targetFcn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	382
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	383 if multiCh
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	384 if cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	385 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	386 if ~isa(targetFcn{kk}, 'function_handle')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	387 error('### please use a cell array of function handles')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	388 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	389 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	390 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	391 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	392 if ~isa(targetFcn(kk), 'smodel')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	393 error('### multi-channel fitting is only possible with smodels')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	394 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	395 if isempty(targetFcn(kk).expr)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	396 error('### please specify a target function for all smodels');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	397 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	398 if ~isempty(targetFcn(kk).values) & size(targetFcn(kk).values)~=size(targetFcn(kk).params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	399 error('### please give an initial value for each parameter')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	400 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	401 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	402 if ~isempty(P0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	403 error('in multi-channel fitting the initial values for the parameters must be within each smodel')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	404 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	405 checkExistAllParams = 0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	406 for kk=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	407 checkExistAllParams = checkExistAllParams + ~isempty(targetFcn(kk).values);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	408 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	409 if checkExistAllParams==0 && ~MCsearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	410 error('### please give initial values for all parameters or use Monte Carlo instead')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	411 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	412 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	413 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	414
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	415 % check P0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	416 if isempty(P0) && ~MCsearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	417 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	418 if isa(targetFcn(kk), 'smodel') && isempty(targetFcn(kk).values)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	419 error('### please give initial values for all parameters or use Monte Carlo instead')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	420 elseif ischar(targetFcn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	421 error('### please give initial values for all parameters or use Monte Carlo instead')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	422 % elseif cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	423 % error('### please give initial values for all parameters or use Monte Carlo instead')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	424 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	425 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	426 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	427
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	428 % Extract anonymous functions
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	429
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	430 if multiCh
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	431
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	432 if ~cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	433 % concatenate models and parameters
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	434 [params,mdl_params,Pidx] = cat_mdls(targetFcn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	435 else%if iscell(P0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	436 [params,mdl_params,Pidx] = cat_mdls_cell(targetFcn, pnames);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	437 % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	438 % params = pnames;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	439 % Pidx = cell(1,Nch);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	440 % mdl_params = pnames;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	441 % for ii=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	442 % Pidx{ii} = ones(1,numel(pnames));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	443 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	444 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	445
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	446 % create the full initial value array
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	447 if ~MCsearch && ~cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	448 P0 = zeros(1,numel(params));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	449 for ii=1:numel(params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	450 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	451 for jj=1:numel(targetFcn(kk).params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	452 if strcmp(params{ii},targetFcn(kk).params{jj})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	453 P0(ii) = targetFcn(kk).values{jj};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	454 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	455 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	456 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	457 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	458 elseif cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	459 if isempty(P0)% \|\| ~iscell(pvalues)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	460 error('### please give initial values')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	461 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	462 if isempty(pnames) \|\| ~iscell(pnames)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	463 error('### please give parameter names in a cell array')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	464 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	465 if size(P0)~=size(pnames)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	466 error('### the size of pnames and pvalues does not match')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	467 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	468 % P0 = zeros(1,numel(params));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	469 % for ii=1:numel(P0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	470 % P0(ii) = pvalues{ii};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	471 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	472 if iscell(P0) && ~MCsearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	473 for ii=1:numel(P0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	474 if isempty(P0{ii})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	475 error('### please give initial values for all parameters or use Monte Carlo instead');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	476 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	477 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	478 for ii=1:numel(params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	479 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	480 for jj=1:numel(pnames{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	481 if strcmp(params{ii},pnames{kk}{jj})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	482 P0new(ii) = P0{kk}(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	483 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	484 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	485 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	486 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	487 P0 = P0new;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	488 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	489 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	490
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	491 if all(isa(targetFcn,'smodel'))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	492 % anonymous fcns
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	493 modelFuncs = cell(1,Nch);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	494 for kk=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	495 targetFcn(kk).setXvals(Xdata(:,kk));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	496 modelFuncs{kk} = targetFcn(kk).fitfunc;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	497 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	498 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	499 % if cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	500 % for kk=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	501 % modelFuncs{kk} = targetFcn{kk};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	502 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	503 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	504
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	505 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	506
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	507 % Check parameters
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	508 if isempty(P0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	509 if isa(targetFcn, 'smodel')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	510 P0 = [targetFcn.values{:}];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	511 elseif isempty(P0) && ~MCsearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	512 error('### please give initial values for all parameters or use Monte Carlo instead');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	513 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	514 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	515 if size(P0)~=[1 numel(P0)]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	516 P0 = P0';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	517 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	518
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	519 % convert input regular expression to anonymous function only for
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	520 % single-channel fitting
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	521 % create anonymouse function from user input expression
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	522 if ischar(targetFcn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	523 checkFcn = regexp(targetFcn, 'Xdata');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	524 if isempty(checkFcn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	525 error('### when using a string expression for the input model, the independent variable must be named as Xdata')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	526 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	527 % tfunc = eval(['@(P,Xdata,ADDP) (',targetFcn,')']);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	528 tfunc = eval(['@(P,Xdata) (',targetFcn,')']);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	529 % now create another anonymous function that only depends on the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	530 % parameters
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	531 % modelFunc = @(x)tfunc(x, Xdata, ADDP);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	532 modelFuncs{1} = @(x)tfunc(x, Xdata);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	533 elseif isa(targetFcn,'smodel')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	534 targetFcn.setXvals(Xdata);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	535 modelFuncs{1} = targetFcn.fitfunc;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	536 % elseif isa(targetFcn,'function_handle')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	537 % modelFunc = targetFcn;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	538 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	539
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	540 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	541
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	542 if cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	543 for kk=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	544 modelFuncs{kk} = targetFcn{kk};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	545 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	546 % if ~multiCh
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	547 % modelFunc = modelFuncs{1};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	548 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	549 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	550
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	551
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	552
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	553 % check lb and ub
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	554
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	555 % constrained search or not
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	556 conSearch = ~isempty(lb) \|\| ~isempty(ub);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	557
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	558 if MCsearch \|\| conSearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	559 if isempty(lb) \|\| isempty(ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	560 error('### please give LB and UB')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	561 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	562 if multiCh && (~iscell(lb) \|\| ~iscell(ub))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	563 error('### in multi-channel fitting upper and lower bounds must be cell array')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	564 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	565 if size(lb)~=size(ub) % \| size(lb)~=size(P0) \| size(ub)~=size(P0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	566 error('### LB and UB must be of the same size');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	567 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	568 if multiCh && numel(lb)~=Nch && numel(ub)~=Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	569 error('### in multi-channel fitting LB and UB must be cell array whose number of elements is equal to the number of models');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	570 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	571 if ~multiCh && ~all(lb<=ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	572 error('### UB must me greater equal to LB');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	573 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	574 if multiCh
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	575 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	576 if numel(lb{kk})~=numel(mdl_params{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	577 error('### please give the proper number of values for LB for each model')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	578 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	579 if numel(ub{kk})~=numel(mdl_params{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	580 error('### please give the proper number of values for UB for each model')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	581 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	582 if ~all(lb{kk}<=ub{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	583 error('### UB must me greater equal to LB for all parameters and models');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	584 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	585 if size(lb{kk})~=[1 numel(lb{kk})]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	586 lb{kk} = lb{kk}';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	587 ub{kk} = ub{kk}';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	588 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	589 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	590 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	591 if ~multiCh
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	592 if size(lb)~=[1 numel(lb)]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	593 lb = lb';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	594 ub = ub';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	595 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	596 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	597 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	598
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	599
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	600 % create the full bounds array
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	601 if (MCsearch \|\| conSearch) && multiCh && ~cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	602 lb_full = zeros(1,numel(params));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	603 ub_full = zeros(1,numel(params));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	604 for ii=1:numel(params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	605 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	606 for jj=1:numel(targetFcn(kk).params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	607 if strcmp(params{ii},targetFcn(kk).params{jj})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	608 lb_full(ii) = lb{kk}(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	609 ub_full(ii) = ub{kk}(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	610 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	611 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	612 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	613 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	614 lb = lb_full;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	615 ub = ub_full;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	616 elseif (MCsearch \|\| conSearch) && multiCh && cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	617 lb_full = zeros(1,numel(params));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	618 ub_full = zeros(1,numel(params));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	619 for ii=1:numel(params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	620 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	621 for jj=1:numel(mdl_params{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	622 if strcmp(params{ii},mdl_params{kk}(jj))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	623 lb_full(ii) = lb{kk}(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	624 ub_full(ii) = ub{kk}(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	625 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	626 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	627 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	628 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	629 lb = lb_full;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	630 ub = ub_full;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	631 % elseif cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	632 % lb = lb;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	633 % ub = ub;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	634 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	635
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	636 % if ~iscell(ADDP)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	637 % ADDP = {ADDP};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	638 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	639
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	640 % Get input options
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	641 switch Algorithm
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	642 case 'fminsearch'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	643 opts = optimset(@fminsearch);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	644 if isstruct(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	645 opts = optimset(opts, userOpts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	646 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	647 for j=1:2:numel(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	648 opts = optimset(opts, userOpts{j}, userOpts{j+1});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	649 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	650 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	651 case 'fminunc'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	652 opts = optimset(@fminunc);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	653 if isstruct(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	654 opts = optimset(opts, userOpts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	655 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	656 for j=1:2:numel(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	657 opts = optimset(opts, userOpts{j}, userOpts{j+1});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	658 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	659 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	660 case 'fmincon'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	661 opts = optimset(@fmincon);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	662 if isstruct(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	663 opts = optimset(opts, userOpts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	664 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	665 for j=1:2:numel(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	666 opts = optimset(opts, userOpts{j}, userOpts{j+1});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	667 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	668 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	669 case 'patternsearch'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	670 opts = psoptimset(@patternsearch);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	671 if isstruct(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	672 opts = psoptimset(opts, userOpts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	673 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	674 for j=1:2:numel(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	675 opts = psoptimset(opts, userOpts{j}, userOpts{j+1});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	676 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	677 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	678 case 'ga'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	679 opts = gaoptimset(@ga);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	680 if isstruct(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	681 opts = gaoptimset(opts, userOpts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	682 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	683 for j=1:2:numel(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	684 opts = gaoptimset(opts, userOpts{j}, userOpts{j+1});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	685 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	686 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	687 case 'simulannealbnd'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	688 opts = saoptimset(@simulannealbnd);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	689 if isstruct(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	690 opts = saoptimset(opts, userOpts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	691 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	692 for j=1:2:numel(userOpts)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	693 opts = saoptimset(opts, userOpts{j}, userOpts{j+1});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	694 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	695 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	696 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	697
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	698
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	699 % compute the right weights
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	700 [weights,unweighted] = find_weights(as,weights);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	701
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	702
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	703 % define number of free parameters
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	704 if ~MCsearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	705 Nfreeparams = length(P0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	706 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	707 Nfreeparams = length(lb);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	708 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	709
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	710 if Nch==1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	711 Pidx{1}=1:Nfreeparams;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	712 % modelFuncs{1}=modelFunc;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	713 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	714
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	715 % Check for user-supplied analytical gradient as cell-array of function
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	716 % handles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	717 if ~isempty(SymGrad)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	718 dFcns = cell(Nmdls,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	719 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	720 for ii=1:numel(SymGrad{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	721 dFcns{kk}{ii} = SymGrad{kk}{ii};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	722 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	723 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	724 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	725
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	726 % Check for user-supplied analytical hessian as cell-array of function
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	727 % handles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	728 if ~isempty(SymGrad) && ~isempty(SymHess)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	729 hFcns = cell(Nmdls,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	730 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	731 for jj=1:numel(dFcns{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	732 for ii=1:jj
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	733 hFcns{kk}{ii,jj} = SymHess{kk}{ii,jj};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	734 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	735 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	736 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	737 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	738
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	739 % If requested, compute the analytical gradient
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	740 if SymDiff \|\| linUnc && isempty(SymGrad)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	741 utils.helper.msg(msg.IMPORTANT, 'evaluating symbolic derivatives');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	742 if ~isa(targetFcn,'smodel')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	743 error('### smodel functions must be used in order to do symbolic differentiation')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	744 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	745 % compute symbolic 1st-order differentiation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	746 dFcnsSmodel = cell(Nmdls,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	747 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	748 p = targetFcn(kk).params;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	749 for ii=1:numel(p)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	750 dFcnsSmodel{kk}(ii) = diff(targetFcn(kk),p{ii});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	751 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	752 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	753 % extract anonymous function
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	754 dFcns = cell(Nmdls,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	755 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	756 for ii=1:numel(dFcnsSmodel{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	757 dFcns{kk}{ii} = dFcnsSmodel{kk}(ii).fitfunc;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	758 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	759 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	760 if DiffOrder==2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	761 % compute symbolic 2nd-order differentiation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	762 hFcnsSmodel = cell(Nmdls,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	763 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	764 p = targetFcn(kk).params;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	765 for jj=1:numel(p)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	766 for ii=1:jj
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	767 hFcnsSmodel{kk}(ii,jj) = diff(dFcnsSmodel{kk}(ii),p{jj});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	768 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	769 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	770 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	771 % extract anonymous function
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	772 hFcns = cell(Nmdls,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	773 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	774 for jj=1:numel(dFcnsSmodel{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	775 for ii=1:jj
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	776 hFcns{kk}{ii,jj} = hFcnsSmodel{kk}(ii,jj).fitfunc;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	777 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	778 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	779 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	780 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	781 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	782
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	783 % Set optimset in order to take care of eventual symbolic differentiation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	784 if ~isempty(dFcns) && any(strcmp(Algorithm,{'fminunc','fmincon'}))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	785 opts = optimset(opts, 'GradObj', 'on');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	786 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	787 if ~isempty(hFcns) && any(strcmp(Algorithm,{'fminunc','fmincon'}))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	788 opts = optimset(opts, 'Hessian', 'on');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	789 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	790
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	791 % Start the best-fit search
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	792
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	793 if MCsearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	794
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	795 utils.helper.msg(msg.IMPORTANT, 'performing a Monte Carlo search');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	796
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	797 % find best-fit by a Monte Carlo search
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	798 [P,chi2,exitflag,output,h,MChistory] = ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	799 find_bestfit_montecarlo(lb, ub, Npoints, Noptims, opts, Algorithm, FastHess);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	800
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	801 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	802
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	803 utils.helper.msg(msg.IMPORTANT, 'looking for a best-fit from the initial guess');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	804
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	805 % find best-fit starting from an initial guess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	806 [P,chi2,exitflag,output,h,chainHistory] = ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	807 find_bestfit_guess(P0, opts, Algorithm, FastHess);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	808
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	809 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	810
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	811
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	812 % degrees of freedom in the problem
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	813 % dof = Nch * (Ndata - Nfreeparams);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	814 dof = Nch * Ndata - Nfreeparams;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	815
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	816 % redefine MChistory's column to put the reduced chi2s
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	817 if MCsearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	818 MChistory(:,1) = MChistory(:,1)./dof;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	819 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	820
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	821 % redefine history to put the reduced chi2s
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	822 if ~MCsearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	823 chainHistory.fval = chainHistory.fval./dof;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	824 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	825
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	826 % Confidence intervals contruction
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	827
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	828 if FitUnc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	829
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	830 utils.helper.msg(msg.IMPORTANT, 'estimating confidence intervals');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	831
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	832 % find best-fit errors
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	833 [se,Sigma,Corr,I,H,errH,J,errJ] = ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	834 find_errors(modelFuncs, P, chi2, dof, UncMtd, FastHess, h, weights, unweighted, linUnc, dFcns);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	835
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	836
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	837 % report issue on covariance matrix in case of
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	838 % degeneracy/quasi-singularity/ill-conditioning, etc.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	839 posDef = all(diag(Sigma)>=0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	840 if ~posDef
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	841 % analysis of information matrix in order to cancel out un-important
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	842 % parameters
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	843 Inorm=I./norm(I);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	844 pnorms = zeros(1,size(Inorm,2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	845 for ii=1:size(I,2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	846 pnorms(ii) = norm(Inorm(:,ii));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	847 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	848 [pnorms_sort,IX] = sort(pnorms,'descend');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	849 if Nmdls>1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	850 pnames_sort = params(IX);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	851 elseif isa(targetFcn,'smodel') && Nmdls==1%&& ~isempty(targetFcn.params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	852 params = targetFcn.params;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	853 pnames_sort = params(IX);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	854 elseif isa(targetFcn,'function_handle') %&& ~isempty(targetFcn.params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	855 pnames_sort = pnames(IX);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	856 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	857 utils.helper.msg(msg.IMPORTANT, ['Information matrix is quasi-singular due to degeneracy or ill-conditioning: \n'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	858 'consider eliminating the parameters with low information.']); % ...'In the following, parameters are reported in descending order of information']);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	859 for ii=1:numel(pnorms_sort);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	860 if exist('pnames_sort','var')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	861 utils.helper.msg(msg.IMPORTANT, 'param %s: %g ', pnames_sort{ii}, pnorms_sort(ii));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	862 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	863 utils.helper.msg(msg.IMPORTANT, 'param %d: %g ', IX(ii), pnorms_sort(ii));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	864 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	865 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	866
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	867 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	868
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	869 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	870
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	871 utils.helper.msg(msg.IMPORTANT, 'final best-fit found at reduced chi2, dof: %g %d ', chi2/dof, dof);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	872
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	873 if FitUnc && ~isempty(se)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	874 for kk=1:numel(P)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	875 utils.helper.msg(msg.IMPORTANT, 'best-fit param %d: %g +- %2.1g ', kk, P(kk), se(kk));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	876 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	877 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	878 for kk=1:numel(P)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	879 utils.helper.msg(msg.IMPORTANT, 'best-fit param %d: %g ', kk, P(kk));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	880 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	881 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	882
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	883
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	884 % check the existence of all variables
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	885 if ~exist('se','var'); se = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	886 if ~exist('Sigma','var'); Sigma = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	887 if ~exist('Corr','var'); Corr = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	888 if ~exist('I','var'); I = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	889 if ~exist('H','var'); H = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	890 if ~exist('errH','var'); errH = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	891 if ~exist('J','var'); J = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	892 if ~exist('errJ','var'); errJ = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	893 if ~exist('Sigma','var'); Sigma = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	894 if ~exist('MChistory','var'); MChistory = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	895 % if ~exist('SVDhistory','var'); SVDhistory = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	896 if ~exist('output','var'); output = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	897
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	898
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	899 % Make output pest
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	900 out = pest;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	901 if Nch>1 %exist('params')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	902 out.setNames(params);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	903 elseif Nch==1 && isa(targetFcn, 'smodel')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	904 out.setNames(targetFcn.params);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	905 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	906 out.setY(P');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	907 out.setDy(se');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	908 out.setCov(Sigma);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	909 out.setCorr(Corr);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	910 out.setChi2(chi2/dof);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	911 out.setDof(dof);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	912 if ~MCsearch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	913 out.setChain([chainHistory.fval,chainHistory.x]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	914 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	915
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	916 % add the output best-fit models
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	917 outFcn = targetFcn;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	918 if isa(targetFcn, 'smodel') && Nmdls>1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	919 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	920 p = P(Pidx{kk});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	921 outFcn(kk).setValues(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	922 % outFcn(kk).setXvals(Xdata(:,1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	923 outFcn(kk).setXunits(Xunits);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	924 outFcn(kk).setYunits(Yunits(kk));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	925 outFcn(kk).setName(['Best-fit model ' num2str(kk)]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	926 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	927 out.setModels(outFcn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	928 elseif isa(targetFcn, 'smodel') && Nmdls==1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	929 outFcn.setValues(P');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	930 % outFcn.setXvals(Xdata(:,1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	931 outFcn.setXunits(Xunits);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	932 outFcn.setYunits(Yunits);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	933 outFcn.setName('Best-fit model');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	934 out.setModels(outFcn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	935 elseif ischar(targetFcn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	936 % convert regular expression into smodel
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	937 targetFcn = regexprep(targetFcn, 'Xdata', 'x');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	938 for ii=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	939 targetFcn = regexprep(targetFcn, ['P$' num2str(ii) '$'], ['P' num2str(ii)]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	940 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	941 outFcn = smodel((targetFcn));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	942 pnames = cell(1,Nfreeparams);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	943 for ii=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	944 pnames{ii} = ['P' num2str(ii)];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	945 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	946 outFcn.setParams(pnames, P');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	947 outFcn.setXvar('x');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	948 % outFcn.setXvals(Xdata);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	949 outFcn.setXunits(Xunits);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	950 outFcn.setYunits(Yunits);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	951 outFcn.setName('Best-fit model');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	952 out.setModels(outFcn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	953 out.setNames(pnames);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	954 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	955
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	956
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	957 % Set Name, History and Procinfo
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	958 if ~cellMdl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	959 mdlname = char(targetFcn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	960 if numel(mdlname)>20
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	961 mdlname = mdlname(1:20);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	962 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	963 out.name = sprintf('xfit(%s)', mdlname);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	964 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	965 mdlname = func2str(targetFcn{1});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	966 for kk=2:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	967 mdlname = strcat(mdlname,[',' func2str(targetFcn{kk})]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	968 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	969 out.name = sprintf('xfit(%s)', mdlname);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	970 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	971 out.addHistory(getInfo('None'), pl, ao_invars(:), [as(:).hist]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	972 out.procinfo = plist('algorithm', Algorithm, 'exitflag', exitflag, 'output', output, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	973 'InfoMatrix', I,...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	974 'MChistory', MChistory);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	975 % 'SVDhistory', SVDhistory, 'res', res, 'hess', H, 'errhess', errH, 'jac', J, 'errjac', errJ);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	976
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	977 % Set outputs
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	978 if nargout > 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	979 varargout{1} = out;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	980 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	981
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	982 clear global Pidx Ydata weights modelFuncs dFcns hFcns lb ub scale Nch Ndata estimator
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	983
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	984 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	985
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	986 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	987 % Included Functions
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	988 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	989
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	990 function [chi2,g,H] = fit_chi2(x)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	991
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	992 global Pidx Ydata weights modelFuncs dFcns hFcns lb ub scale estimator
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	993
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	994 Nfreeparams = numel(x);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	995 Nmdls = numel(modelFuncs);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	996 Ndata = numel(Ydata(:,1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	997
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	998 mdldata = zeros(Ndata,Nmdls);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	999 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1000 p = x(Pidx{kk}).*scale(Pidx{kk});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1001 mdldata(:,kk) = modelFuncs{kk}(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1002 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1003 res = (mdldata-Ydata).*weights;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1004 if all(x.scale>=lb & x.scale<=ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1005 % chi2 = res'*res;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1006 % chi2 = sum(diag(chi2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1007 if strcmp(estimator,'chi2')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1008 chi2 = sum(sum(res.^2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1009 elseif strcmp(estimator,'abs')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1010 chi2 = sum(sum(abs(res)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1011 elseif strcmp(estimator,'log')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1012 chi2 = sum(sum(log(1+res.^2/2)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1013 elseif strcmp(estimator,'median')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1014 dof = Ndata*Nmdls - Nfreeparams;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1015 res = reshape(res,numel(res),1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1016 chi2 = median(abs(res))*dof;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1017 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1018 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1019 chi2 = 10e50;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1020 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1021
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1022 if nargout > 1 % gradient required
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1023 % if all(x.scale>=lb & x.scale<=ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1024 grad = cell(Nmdls,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1025 g = zeros(Nmdls,Nfreeparams);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1026 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1027 p = x(Pidx{kk}).*scale(Pidx{kk});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1028 Np = numel(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1029 grad{kk} = zeros(Ndata,Np);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1030 for ii=1:Np
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1031 grad{kk}(:,ii) = dFcns{kk}{ii}(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1032 g(kk,Pidx{kk}(ii)) = 2.res(:,kk)'grad{kk}(:,ii);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1033 % dF=dFcns{kk}{ii}(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1034 % g(kk,Pidx{kk}(ii)) = 2.sum(res(:,kk)'dF);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1035 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1036 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1037 if Nmdls>1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1038 g = sum(g);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1039 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1040 % elseif any(x.*scale<lb)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1041 % g = repmat(-10e50,[1 Nfreeparams]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1042 % elseif any(x.*scale>ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1043 % g = repmat(10e50,[1 Nfreeparams]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1044 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1045 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1046
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1047 if nargout > 2 % hessian required
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1048 % hess = cell(Nmdls,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1049 H = zeros(Nmdls,Nfreeparams,Nfreeparams);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1050 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1051 p = x(Pidx{kk}).*scale(Pidx{kk});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1052 Np = numel(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1053 % hess{kk} = zeros(Ndata,Np);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1054 for jj=1:Np
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1055 for ii=1:jj
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1056 hF = hFcns{kk}{ii,jj}(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1057 H1 = sum(res(:,kk)'*hF);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1058 H2 = sum(weights(:,kk).grad{kk}(:,ii).grad{kk}(:,jj));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1059 H(kk,Pidx{kk}(ii),Pidx{kk}(jj)) = 2*(H1+H2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1060 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1061 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1062 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1063 H = squeeze(sum(H,1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1064 % if Nmdls>1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1065 % H = sum(H);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1066 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1067 H = H+triu(H,1)';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1068 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1069
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1070 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1071
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1072 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1073
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1074 % function chi2 = fit_chi2(P, ydata, weights, fcn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1075 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1076 % % evaluate model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1077 % mdldata = fcn(P);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1078 % % if ~isequal(size(mdldata), size(ydata))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1079 % % ydata = ydata.';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1080 % % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1081 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1082 % chi2 = sum((abs((mdldata-ydata)).^2).*weights);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1083 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1084 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1085
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1086 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1087
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1088 % function chi2 = fit_chi2_bounds(P, ydata, weights, fcn, LB, UB)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1089 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1090 % % evaluate model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1091 % mdldata = fcn(P);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1092 % % if ~isequal(size(mdldata), size(ydata))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1093 % % ydata = ydata.';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1094 % % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1095 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1096 % if all(P>=LB & P<=UB)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1097 % chi2 = sum((abs((mdldata-ydata)).^2).*weights);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1098 % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1099 % chi2 = 10e50;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1100 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1101 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1102 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1103
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1104 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1105
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1106 % function g = scaling(f, x, scale)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1107 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1108 % g = f(x.*scale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1109 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1110 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1111
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1112 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1113
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1114 function scale = find_scale(P0, LB, UB)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1115
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1116 if ~isempty(P0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1117 Nfreeparams = numel(P0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1118 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1119 Nfreeparams = numel(LB);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1120 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1121
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1122 % define parameter scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1123 % scale = ones(1,Nfreeparams);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1124
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1125 % if ~isempty(LB) & ~isempty(UB)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1126 % for ii=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1127 % if ~(LB(ii)==0 & UB(ii)==0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1128 % if LB(ii)==0 \| UB(ii)==0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1129 % scale(ii) = max(abs(LB(ii)),abs(UB(ii)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1130 % elseif abs(LB(ii))==abs(UB(ii))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1131 % scale(ii) = abs(UB);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1132 % elseif LB(ii)~=UB(ii)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1133 % scale(ii) = sqrt(abs(LB(ii)) * abs(UB(ii))); % (abs(lb(ii)) + abs(ub(ii)))/2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1134 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1135 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1136 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1137 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1138 if ~isempty(LB) && ~isempty(UB)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1139 scale = sqrt(abs(LB) .* abs(UB));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1140 for ii=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1141 if scale(ii)==0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1142 scale(ii) = max(abs(LB(ii)),abs(UB(ii)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1143 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1144 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1145 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1146 scale = abs(P0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1147 for ii=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1148 if scale(ii)==0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1149 scale(ii) = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1150 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1151 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1152 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1153
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1154 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1155
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1156 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1157
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1158 function [weightsOut,unweighted] = find_weights(as,weightsIn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1159
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1160 Ydata = as.y;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1161 dYdata = as.dy;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1162
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1163 noWeights = isempty(weightsIn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1164 noDY = isempty(dYdata);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1165
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1166 unweighted = noWeights & noDY;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1167
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1168 % check data uncertainties
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1169 if any(dYdata==0) && ~noDY
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1170 error('### some of the data uncertainties are zero: cannot fit')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1171 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1172
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1173 if length(dYdata)~=length(Ydata) && ~noDY
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1174 error('### length of Y fields and dY fields do not match')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1175 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1176
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1177 if noWeights
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1178 % The user did not input weights.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1179 % Looking for the dy field of the input data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1180 if noDY
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1181 % Really no input from user
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1182 weightsOut = ones(size(Ydata));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1183 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1184 % Uses uncertainties in Ydata to evaluate data weights
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1185 weightsOut = 1./dYdata.^2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1186 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1187 % elseif isnumeric(weightsIn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1188 % if size(weightsIn)~=size(Ydata)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1189 % weightsOut = weightsIn';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1190 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1191 elseif numel(weightsIn) == 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1192 if isnumeric(weightsIn)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1193 weightsOut = weightsIn .* ones(size(Ydata));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1194 elseif isa(weightsIn, 'ao')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1195 if weightsIn.yunits == as.yunits
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1196 weightsOut = weightsIn.y;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1197 elseif size(weightsIn.data.getY)~=size(Ydata)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1198 error('### size of data ao and weights ao do not match')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1199 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1200 error('### units for data and uncertainties do not match')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1201 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1202 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1203 error('### unknown format for weights parameter');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1204 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1205 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1206 weightsOut = weightsIn;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1207 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1208
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1209 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1210
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1211 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1212
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1213 function [params,mdl_params,paramidx] = cat_mdls(mdls)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1214
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1215 % This function concatenates the parameter names and values for
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1216 % all the input models to construct the new parameter list.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1217
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1218 Nmdls = numel(mdls);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1219
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1220 % create the full parameter name array
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1221 params_cat = horzcat(mdls(:).params);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1222 params_new = cell(1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1223 for ii=1:numel(params_cat)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1224 if ~strcmp(params_cat{ii},params_new)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1225 params_new = [params_new params_cat{ii}];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1226 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1227 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1228 params = params_new(2:numel(params_new));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1229
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1230 % create the parameter list for each model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1231 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1232 mdl_params{kk} = mdls(kk).params;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1233 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1234
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1235 % create a cell array of indeces which map the parameter vector of each
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1236 % model to the full one
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1237 paramidx = cell(1,Nmdls);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1238 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1239 for jdx=1:length(mdl_params{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1240 for idx=1:length(params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1241 if (strcmp(params{idx}, mdl_params{kk}(jdx)))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1242 paramidx{kk}(jdx) = idx;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1243 break;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1244 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1245 paramidx{kk}(jdx) = 0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1246 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1247 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1248 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1249 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1250
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1251 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1252
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1253 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1254
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1255 function [params,mdl_params,paramidx] = cat_mdls_cell(mdls, pnames)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1256
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1257 % This function concatenates the parameter names and values for
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1258 % all the input models to construct the new parameter list.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1259
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1260 Nmdls = numel(mdls);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1261
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1262 % create the full parameter name array
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1263 params_cat = horzcat(pnames{:});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1264 params_new = cell(1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1265 for ii=1:numel(params_cat)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1266 if ~strcmp(params_cat{ii},params_new)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1267 params_new = [params_new params_cat{ii}];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1268 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1269 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1270 params = params_new(2:numel(params_new));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1271
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1272 % create the parameter list for each model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1273 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1274 mdl_params{kk} = pnames{kk};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1275 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1276
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1277 % create a cell array of indeces which map the parameter vector of each
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1278 % model to the full one
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1279 paramidx = cell(1,Nmdls);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1280 for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1281 for jdx=1:length(mdl_params{kk})
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1282 for idx=1:length(params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1283 if (strcmp(params{idx}, mdl_params{kk}(jdx)))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1284 paramidx{kk}(jdx) = idx;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1285 break;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1286 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1287 paramidx{kk}(jdx) = 0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1288 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1289 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1290 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1291 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1292
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1293 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1294
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1295 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1296
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1297 % function chi2 = fit_chi2_multich(P, Pidx, ydata, weights, fcns)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1298 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1299 % Nmdls = numel(fcns);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1300 % Ndata = numel(ydata(:,1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1301 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1302 % mdldata = zeros(Ndata,Nmdls);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1303 % for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1304 % p = P(Pidx{kk});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1305 % mdldata(:,kk) = fcns{kk}(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1306 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1307 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1308 % res = (ydata-mdldata).*weights;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1309 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1310 % chi2 = res'*res;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1311 % chi2 = sum(diag(chi2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1312 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1313 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1314
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1315 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1316
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1317 % function chi2 = fit_chi2_multich_bounds(P, Pidx, ydata, weights, fcns, LB, UB)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1318 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1319 % if all(P>=LB & P<=UB)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1320 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1321 % Nmdls = numel(fcns);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1322 % Ndata = numel(ydata(:,1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1323 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1324 % mdldata = zeros(Ndata,Nmdls);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1325 % for kk=1:Nmdls
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1326 % p = P(Pidx{kk});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1327 % mdldata(:,kk) = fcns{kk}(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1328 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1329 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1330 % res = (ydata-mdldata).*weights;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1331 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1332 % chi2 = res'*res;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1333 % chi2 = sum(diag(chi2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1334 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1335 % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1336 % chi2 = 10e50;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1337 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1338 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1339 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1340
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1341 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1342
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1343 function chi2_guesses = montecarlo(func, LB, UB, Npoints)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1344
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1345 Nfreeparams = numel(LB);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1346
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1347 % construct the guess matrix: each rows contain the chi2 and the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1348 % parameter guess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1349 guesses = zeros(Npoints,Nfreeparams);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1350 for jj=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1351 guesses(:,jj) = LB(jj)+(UB(jj)-LB(jj))*rand(1,Npoints);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1352 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1353
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1354 % evaluate the chi2 at each guess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1355 chi2_guesses = zeros(1,Nfreeparams+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1356 for ii=1:Npoints
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1357 % check = ii-1/Npoints*100;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1358 % if rem(fix(check),10)==0 && check==fix(check)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1359 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1360 % disp(sprintf('%d%% done',check));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1361 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1362 chi2_guess = func(guesses(ii,:));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1363 chi2_guesses = cat(1,chi2_guesses,[chi2_guess,guesses(ii,:)]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1364 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1365 chi2_guesses(1,:) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1366
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1367 % sort the guesses for ascending chi2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1368 chi2_guesses = sortrows(chi2_guesses);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1369
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1370 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1371
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1372 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1373
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1374 function [x,fval,exitflag,output,h,MChistory] = ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1375 find_bestfit_montecarlo(LB, UB, Npoints, Noptims, opts, algorithm, FastHess)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1376
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1377 global scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1378
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1379 Nfreeparams = length(LB);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1380
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1381 % check Npoints
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1382 if isempty(Npoints)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1383 Npoints = 100000;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1384 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1385 % check Noptims
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1386 if isempty(Noptims)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1387 Noptims = 10;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1388 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1389
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1390 if Npoints<Noptims
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1391 error('### Npoints must be at least equal to Noptims')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1392 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1393
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1394 % define parameter scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1395 scale = find_scale([], LB, UB);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1396
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1397 % scale function to minimize
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1398 % func = @(x)scaling(func, x, scale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1399
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1400 % scale bounds
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1401 LB = LB./scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1402 UB = UB./scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1403
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1404 % do a Monte Carlo search
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1405 chi2_guesses = montecarlo(@fit_chi2, LB, UB, Npoints);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1406
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1407 % minimize over the first guesses
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1408 fitresults = zeros(Noptims,Nfreeparams+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1409 exitflags = {};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1410 outputs = {};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1411 hs = {};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1412 for ii=1:Noptims
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1413 P0 = chi2_guesses(ii,2:Nfreeparams+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1414 if strcmpi(algorithm,'fminunc')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1415 [x,fval,exitflag,output,dummy,h] = fminunc(@fit_chi2, P0, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1416 elseif strcmpi(algorithm,'fmincon')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1417 [x,fval,exitflag,output,dummy,dummy,h] = fmincon(@fit_chi2, P0, [], [], [], [], LB, UB, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1418 elseif strcmpi(algorithm,'patternsearch')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1419 [x,fval,exitflag,output] = patternsearch(@fit_chi2, P0, [], [], [], [], LB, UB, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1420 elseif strcmpi(algorithm,'ga')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1421 [x,fval,exitflag,output] = ga(@fit_chi2, numel(P0), [], [], [], [], LB, UB, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1422 elseif strcmpi(algorithm,'simulannealbnd')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1423 [x,fval,exitflag,output] = simulannealbnd(@fit_chi2, P0, LB, UB, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1424 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1425 [x,fval,exitflag,output] = fminsearch(@fit_chi2, P0, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1426 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1427 fitresults(ii,1) = fval;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1428 fitresults(ii,2:Nfreeparams+1) = x;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1429 exitflags{ii} = exitflag;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1430 outputs{ii} = output;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1431 if FastHess && ~exist('h','var')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1432 h = fastHessian(@fit_chi2,x,fval);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1433 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1434 if exist('h','var')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1435 hs{ii} = h;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1436 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1437 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1438
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1439 % sort the results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1440 [dummy, ix] = sort(fitresults(:,1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1441 fitresults = fitresults(ix,:);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1442
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1443 % % refine fit over the first bestfit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1444 % P0 = fitresults(1,2:Nfreeparams+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1445 % if strcmpi(algorithm,'fminunc')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1446 % [x,fval,exitflag,output] = fminunc(func, P0, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1447 % elseif strcmpi(algorithm,'fmincon')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1448 % [x,fval,exitflag,output] = fmincon(func, P0, [], [], [], [], LB, UB, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1449 % elseif strcmpi(algorithm,'patternsearch')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1450 % [x,fval,exitflag,output] = patternsearch(func, P0, [], [], [], [], LB, UB, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1451 % elseif strcmpi(algorithm,'ga')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1452 % [x,fval,exitflag,output] = ga(func, numel(P0), [], [], [], [], LB, UB, [], opts); % ga does not improve the bestfit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1453 % elseif strcmpi(algorithm,'simulannealbnd')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1454 % [x,fval,exitflag,output] = simulannealbnd(func, P0, LB, UB, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1455 % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1456 % [x,fval,exitflag,output] = fminsearch(func, P0, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1457 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1458
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1459 % set the best-fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1460 fval = fitresults(1,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1461 x = fitresults(1,2:Nfreeparams+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1462
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1463 % scale best-fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1464 x = x.*scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1465
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1466 % scale hessian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1467 if exist('hs','var')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1468 for kk=1:numel(hs)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1469 for ii=1:numel(x)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1470 for jj=1:numel(x)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1471 hs{kk}(ii,jj) = hs{kk}(ii,jj)/scale(ii)/scale(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1472 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1473 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1474 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1475 % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1476 % h = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1477 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1478
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1479 % scale fit results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1480 MChistory = fitresults;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1481 for ii=1:size(MChistory,1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1482 MChistory(ii,2:Nfreeparams+1) = MChistory(ii,2:Nfreeparams+1).*scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1483 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1484
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1485 % set the proper exitflag & output
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1486 exitflags = exitflags(ix);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1487 outputs = outputs(ix);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1488 if exist('hs','var') && ~(isempty(hs))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1489 hs = hs(ix);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1490 h = hs{1};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1491 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1492 h = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1493 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1494 exitflag = exitflags{1};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1495 output = outputs{1};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1496
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1497 clear global scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1498
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1499 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1500
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1501 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1502
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1503 function [x,fval,exitflag,output,h,outHistory] = ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1504 find_bestfit_guess(P0, opts, algorithm, FastHess)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1505
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1506 global lb ub scale chainHistory
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1507
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1508 if isempty(lb)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1509 lb = -Inf;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1510 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1511 if isempty(ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1512 ub = Inf;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1513 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1514
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1515 % define parameter scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1516 scale = find_scale(P0, [], []);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1517
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1518 % scale initial guess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1519 P0 = P0./scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1520
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1521 % initialize history
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1522 chainHistory.x = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1523 chainHistory.fval = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1524 opts=optimset(opts,'outputfcn',@outfun);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1525
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1526 % minimize over the initial guess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1527 if strcmpi(algorithm,'fminunc')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1528 [x,fval,exitflag,output,dummy,h] = fminunc(@fit_chi2, P0, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1529 elseif strcmpi(algorithm,'fmincon')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1530 [x,fval,exitflag,output,dummy,dummy,h] = fmincon(@fit_chi2, P0, [], [], [], [], lb, ub, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1531 elseif strcmpi(algorithm,'patternsearch')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1532 [x,fval,exitflag,output] = patternsearch(@fit_chi2, P0, [], [], [], [], lb, ub, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1533 elseif strcmpi(algorithm,'ga')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1534 [x,fval,exitflag,output] = ga(@fit_chi2, numel(P0), [], [], [], [], lb, ub, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1535 elseif strcmpi(algorithm,'simulannealbnd')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1536 [x,fval,exitflag,output] = simulannealbnd(@fit_chi2, P0, lb, ub, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1537 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1538 [x,fval,exitflag,output] = fminsearch(@fit_chi2, P0, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1539 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1540
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1541 if FastHess && ~exist('h','var')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1542 h = fastHessian(@fit_chi2,x,fval);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1543 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1544
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1545 % scale best-fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1546 x = x.*scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1547
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1548 % scale hessian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1549 if exist('h','var')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1550 for ii=1:numel(x)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1551 for jj=1:numel(x)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1552 h(ii,jj) = h(ii,jj)/scale(ii)/scale(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1553 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1554 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1555 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1556 h = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1557 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1558
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1559 outHistory = chainHistory;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1560 outHistory.x = chainHistory.x.*repmat(scale,size(chainHistory.x,1),1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1561
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1562 clear global lb ub scale chainHistory
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1563
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1564 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1565
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1566 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1567
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1568 function stop = outfun(x,optimvalues,state)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1569
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1570 global chainHistory
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1571
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1572 stop = false;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1573 if strcmp(state,'iter')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1574 chainHistory.fval = [chainHistory.fval; optimvalues.fval];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1575 chainHistory.x = [chainHistory.x; x];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1576 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1577
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1578 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1579
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1580 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1581
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1582 function hess = fastHessian(fun,x0,fx0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1583 % fastHessian calculates the numerical Hessian of fun evaluated at x
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1584 % using finite differences.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1585
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1586 nVars = numel(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1587
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1588 hess = zeros(nVars);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1589
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1590 % Define stepsize
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1591 stepSize = eps^(1/4)sign(x0).max(abs(x0),1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1592
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1593 % Min e Max change
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1594 DiffMinChange = 1e-008;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1595 DiffMaxChange = 0.1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1596
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1597 % Make sure step size lies within DiffMinChange and DiffMaxChange
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1598 stepSize = sign(stepSize+eps).*min(max(abs(stepSize),DiffMinChange),DiffMaxChange);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1599 % Calculate the upper triangle of the finite difference Hessian element
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1600 % by element, using only function values. The forward difference formula
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1601 % we use is
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1602 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1603 % Hessian(i,j) = 1/(h(i)h(j)) [f(x+h(i)ei+h(j)ej) - f(x+h(i)*ei)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1604 % - f(x+h(j)*ej) + f(x)] (2)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1605 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1606 % The 3rd term in (2) is common within each column of Hessian and thus
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1607 % can be reused. We first calculate that term for each column and store
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1608 % it in the row vector fplus_array.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1609 fplus_array = zeros(1,nVars);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1610 for j = 1:nVars
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1611 xplus = x0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1612 xplus(j) = x0(j) + stepSize(j);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1613 % evaluate
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1614 fplus = fun(xplus);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1615 fplus_array(j) = fplus;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1616 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1617
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1618 for i = 1:nVars
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1619 % For each row, calculate the 2nd term in (4). This term is common to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1620 % the whole row and thus it can be reused within the current row: we
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1621 % store it in fplus_i.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1622 xplus = x0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1623 xplus(i) = x0(i) + stepSize(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1624 % evaluate
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1625 fplus_i = fun(xplus);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1626
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1627 for j = i:nVars % start from i: only upper triangle
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1628 % Calculate the 1st term in (2); this term is unique for each element
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1629 % of Hessian and thus it cannot be reused.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1630 xplus = x0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1631 xplus(i) = x0(i) + stepSize(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1632 xplus(j) = xplus(j) + stepSize(j);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1633 % evaluate
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1634 fplus = fun(xplus);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1635
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1636 hess(i,j) = (fplus - fplus_i - fplus_array(j) + fx0)/(stepSize(i)*stepSize(j));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1637 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1638 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1639
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1640 % Fill in the lower triangle of the Hessian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1641 hess = hess + triu(hess,1)';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1642
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1643 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1644
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1645 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1646
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1647 % function [x,fval,exitflag,output,h,SVDhistory] = ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1648 % find_bestfit_guess_SVD(P0, lb, ub, opts, algorithm, FastHess, nSVD)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1649 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1650 % if isempty(lb)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1651 % lb = -Inf;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1652 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1653 % if isempty(ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1654 % ub = Inf;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1655 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1656 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1657 % % define parameter scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1658 % scale = find_scale(P0, [], []);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1659 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1660 % % % scale function to minimize
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1661 % % func = @(x)scaling(func, x, scale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1662 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1663 % % scale initial guess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1664 % P0 = P0./scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1665 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1666 % % scale bounds
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1667 % if ~isempty(lb)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1668 % lb = lb./scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1669 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1670 % if ~isempty(ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1671 % ub = ub./scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1672 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1673 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1674 % % set the guess for 0-iteration
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1675 % x = P0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1676 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1677 % Nfreeparams = numel(P0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1678 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1679 % fitresults = zeros(nSVD,Nfreeparams+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1680 % exitflags = {};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1681 % outputs = {};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1682 % hs = {};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1683 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1684 % % start SVD loop
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1685 % for ii=1:nSVD
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1686 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1687 % % minimize over the old parameter space
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1688 % if strcmpi(algorithm,'fminunc')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1689 % [x,fval,exitflag,output,grad,h] = fminunc(@fit_chi2, x, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1690 % elseif strcmpi(algorithm,'fmincon')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1691 % [x,fval,exitflag,output,lambda,grad,h] = fmincon(@fit_chi2, x, [], [], [], [], lb, ub, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1692 % elseif strcmpi(algorithm,'patternsearch')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1693 % [x,fval,exitflag,output] = patternsearch(@fit_chi2, P0, [], [], [], [], lb, ub, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1694 % elseif strcmpi(algorithm,'ga')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1695 % [x,fval,exitflag,output] = ga(@fit_chi2, numel(P0), [], [], [], [], lb, ub, [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1696 % elseif strcmpi(algorithm,'simulannealbnd')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1697 % [x,fval,exitflag,output] = simulannealbnd(@fit_chi2, P0, lb, ub, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1698 % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1699 % [x,fval,exitflag,output] = fminsearch(@fit_chi2, P0, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1700 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1701 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1702 % if FastHess && ~exist('h','var')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1703 % h = fastHessian(func,x,fval);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1704 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1705 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1706 % % compute Jacobian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1707 % J = zeros(Nch*Ndata,Np);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1708 % for kk=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1709 % for ll=1:Np
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1710 % J(((ii-1)Ndata+1):iiNdata,ll) = dFcns{kk}{ll}(x.*scale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1711 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1712 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1713 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1714 % % take SVD decomposition of hessian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1715 % [U,S,V] = svd(J);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1716 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1717 % % cancel out column with very low information
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1718 % thresh = 100*eps;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1719 % idx = (diag(S)./norm(diag(S)))<=thresh;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1720 % pos = find(idx~=0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1721 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1722 % % reduced matrix
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1723 % Sred = S;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1724 % Ured = U;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1725 % Vred = V;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1726 % Sred(:,pos) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1727 % Sred(pos,:) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1728 % Ured(:,pos) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1729 % Ured(pos,:) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1730 % Vred(:,pos) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1731 % Vred(pos,:) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1732 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1733 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1734 % % start from here inserting norm-rescaling... also in funcSVD!
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1735 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1736 % % guess in the new parameter space
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1737 % % pay attention because here x is row-vector and xSVD ic column-vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1738 % xSVD = U'*x';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1739 % xSVD(pos) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1740 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1741 % % % bounds in the new parameter space
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1742 % % if ~isempty(lb) && ~isempty(ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1743 % % lbSVD = U'*lb';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1744 % % ubSVD = U'*ub';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1745 % % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1746 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1747 % % do the change in the variables
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1748 % funcSVD = @(xSVD)func_SVD(func,xSVD,U,pos);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1749 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1750 % % minimize over the new parameter space
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1751 % if strcmpi(algorithm,'fminunc')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1752 % [xSVD,fvalSVD,exitflag,output,grad,hSVD] = fminunc(funcSVD, xSVD, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1753 % elseif strcmpi(algorithm,'fmincon')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1754 % [xSVD,fvalSVD,exitflag,output,lambda,grad,hSVD] = fmincon(funcSVD, xSVD, [], [], [], [], [], [], [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1755 % elseif strcmpi(algorithm,'patternsearch')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1756 % [xSVD,fvalSVD,exitflag,output] = patternsearch(funcSVD, xSVD, [], [], [], [], [], [], [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1757 % elseif strcmpi(algorithm,'ga')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1758 % [xSVD,fvalSVD,exitflag,output] = ga(funcSVD, numel(xSVD), [], [], [], [], [], [], [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1759 % elseif strcmpi(algorithm,'simulannealbnd')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1760 % [xSVD,fvalSVD,exitflag,output] = simulannealbnd(funcSVD, xSVD, [], [], opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1761 % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1762 % [xSVD,fvalSVD,exitflag,output] = fminsearch(funcSVD, xSVD, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1763 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1764 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1765 % if FastHess && ~exist('hSVD','var')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1766 % hSVD = fastHessian(funcSVD,xSVD,fvalSVD);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1767 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1768 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1769 % % if fvalSVD<fval
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1770 % % % take the new
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1771 % % x = (U'*xSVD)';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1772 % % fval = fvalSVD;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1773 % % % trasformare la nuova h nella vecchia
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1774 % % h = U'*hSVD;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1775 % % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1776 % % % take the old
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1777 % % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1778 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1779 % % return to the full parameter vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1780 % xSVDfull = zeros(numel(xSVD)+numel(pos),1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1781 % setVals = setdiff(1:numel(xSVDfull),pos);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1782 % xSVDfull(setVals) = xSVD;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1783 % % x = xb;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1784 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1785 % % back to the old parameter space
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1786 % x = (U*xSVDfull)';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1787 % fval = fvalSVD;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1788 % hRed = UredhSVDVred';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1789 % h = hRed;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1790 % for kk=1:numel(pos)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1791 % h(pos(kk),:) = zeros(1,size(h,2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1792 % h(:,pos(kk)) = zeros(size(h,1),1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1793 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1794 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1795 % fitresults(ii,1) = fval;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1796 % fitresults(ii,2:Nfreeparams+1) = x;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1797 % exitflags{ii} = exitflag;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1798 % outputs{ii} = output;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1799 % hs{ii} = h;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1800 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1801 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1802 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1803 % % sort the results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1804 % [chi2s, ix] = sort(fitresults(:,1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1805 % fitresults = fitresults(ix,:);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1806 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1807 % % set the best-fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1808 % fval = fitresults(1,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1809 % x = fitresults(1,2:Nfreeparams+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1810 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1811 % % scale best-fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1812 % x = x.*scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1813 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1814 % % scale hessian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1815 % for ii=1:numel(x)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1816 % for jj=1:numel(x)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1817 % h(ii,jj) = h(ii,jj)/scale(ii)/scale(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1818 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1819 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1820 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1821 % % scale fit results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1822 % SVDhistory = fitresults;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1823 % for ii=1:size(SVDhistory,1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1824 % SVDhistory(ii,2:Nfreeparams+1) = SVDhistory(ii,2:Nfreeparams+1).*scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1825 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1826 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1827 % % set the proper exitflag & output
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1828 % exitflags = exitflags(ix);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1829 % outputs = outputs(ix);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1830 % hs = hs(ix);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1831 % exitflag = exitflags{1};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1832 % output = outputs{1};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1833 % h = hs{1};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1834 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1835 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1836
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1837 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1838
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1839 % function z = func_SVD(func,y,U,pos)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1840 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1841 % yFull = zeros(numel(y)+numel(pos),1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1842 % setVals = setdiff(1:numel(yFull),pos);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1843 % yFull(setVals) = y;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1844 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1845 % x = (U*yFull)';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1846 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1847 % z = func(x);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1848 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1849 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1850
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1851 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1852
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1853 % function adaptive_scaling(P0, scaleIn, func, Niter, opts, algorithm)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1854 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1855 % Nfreeparams = numel(P0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1856 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1857 % for ii=1:Niter
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1858 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1859 % % new guess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1860 % P0_new = P0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1861 % % new scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1862 % scale = find_scale(P0, [], []);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1863 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1864 % % scale bounds
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1865 % LB = LB./scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1866 % UB = UB./scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1867 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1868 % % if ~multiCh
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1869 % % rescale model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1870 % modelFunc = @(x)scaling(modelFunc, x, scale_new./scale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1871 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1872 % % define function to minimize
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1873 % if isempty(lb) & isempty(ub)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1874 % func = @(x)fit_chi2(x, Ydata, weights, modelFunc);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1875 % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1876 % lb = lb.*scale./scale_new;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1877 % ub = ub.*scale./scale_new;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1878 % func = @(x)fit_chi2_bounds(x, Ydata, weights, modelFunc, lb, ub);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1879 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1880 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1881 % % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1882 % % % func = @(x)fit_chi2_multich(params, x, Ydata, mdl_params, modelFuncs);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1883 % % func = @(x)scaling(func, x, scale_new/scale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1884 % % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1885 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1886 % % Make new fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1887 % [x,fval_new,exitflag,output] = fminsearch(func, P0_new./scale_new, opts);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1888 % % stopping criterion
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1889 % if abs(fval_new-fval) <= 3*eps(fval_new-fval)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1890 % fval = fval_new;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1891 % scale = scale_new;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1892 % break
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1893 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1894 % fval = fval_new;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1895 % scale = scale_new;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1896 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1897 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1898 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1899 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1900
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1901 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1902
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1903 function [se,Sigma,Corr,I,H,errH,J,errJ] = find_errors(modelFcn, x, fval, dof, UncMtd, FastHess, h, weights, unweighted, linUnc, dFcns)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1904
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1905 global scale Nch Ndata lb ub
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1906
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1907 % set infinite bounds
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1908 lb = repmat(-Inf,size(x));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1909 ub = repmat(Inf,size(x));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1910
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1911 % check on UncMtd and FastHess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1912 if strcmpi(UncMtd,'jacobian')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1913 FastHess = 0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1914 elseif FastHess==1 && isempty(h)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1915 FastHess = 0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1916 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1917
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1918 Nfreeparams = numel(x);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1919
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1920 if ~FastHess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1921
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1922 % find new scale based on the best-fit found
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1923 scale = find_scale(x, [], []);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1924
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1925 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1926
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1927 scale = ones(1,Nfreeparams);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1928
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1929 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1930
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1931 % scale best-fit
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1932 x = x./scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1933
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1934
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1935 % standard deviation of the residuals
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1936 sdr = sqrt(fval/dof);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1937
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1938 % compute information matrix from linear approximation: error propagation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1939 % from symbolical gradient
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1940 if linUnc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1941 % compute Jacobian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1942 J = zeros(Nch*Ndata,Nfreeparams);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1943 for ii=1:Nch
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1944 for ll=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1945 J(((ii-1)Ndata+1):iiNdata,ll) = dFcns{ii}{ll}(x.*scale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1946 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1947 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1948 elseif ~strcmpi(UncMtd,'jacobian') \|\| numel(modelFcn)~=1 && ~linUnc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1949
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1950 % Hessian method.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1951 % Brief description.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1952 % Here I use the most general method: Hessian of chi2 function. For further readings see
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1953 % Numerical Recipes. Note that for inv, H should be non-singular.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1954 % Badly-scaled matrices may take to singularities: use Cholesky
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1955 % factorization instead.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1956 % In practice, a singular Hessian matrix may go out for the following main reasons:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1957 % 1 - you have reached a false minimum (H should be strictly
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1958 % positive-definite for a well-behaved minimum);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1959 % 2 - strong correlation between some parameters;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1960 % 3 - independency of the model on some parameters.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1961 % In the last two cases you should reduce the dimensionality of the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1962 % problem.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1963 % One last point discussed here in Trento is that the Hessian method reduces
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1964 % to the Jacobian, when considering linear models.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1965 % Feedbacks are welcome.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1966 % Trento, Giuseppe Congedo
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1967
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1968 if ~FastHess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1969 % scale function to find the hessian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1970 % func = @(x)scaling(func, x, scale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1971
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1972 [H,errH] = hessian(@fit_chi2,x);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1973
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1974 elseif ~isempty(h) && FastHess % here the hessian is not scaled
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1975 H = h;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1976 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1977
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1978 if unweighted
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1979 % information matrix based on sdr
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1980 I = H / sdr^2 / 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1981 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1982 % information matrix based on canonical form
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1983 I = H./2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1984 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1985
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1986 elseif ~linUnc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1987
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1988 % % scale function to find the jacobian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1989 % modelFcn = @(x)scaling(modelFcn, x, scale);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1990
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1991 % Jacobian method
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1992 [J,errJ] = jacobianest(modelFcn{1},x);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1993 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1994
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1995 if exist('J','var')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1996 if unweighted
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1997 % information matrix based on sdr
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1998 I = J'*J ./ sdr^2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1999 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2000 % redefine the jacobian to take care of the weights
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2001 if size(weights)~=size(J(:,1))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2002 weights = weights';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2003 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2004 for ii=1:size(J,2)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2005 J(:,ii) = sqrt(weights).*J(:,ii);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2006 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2007 % information matrix based on jacobian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2008 I = J'*J;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2009 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2010
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2011 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2012
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2013 % check positive-definiteness
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2014 % [R,p] = chol(I);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2015 % posDef = p==0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2016
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2017 % Covariance matrix from inverse
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2018 Sigma = inv(I);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2019
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2020 % % Covariance matrix from pseudo-inverse
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2021 % if issparse(I)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2022 % % [U,S,V] = svds(I,Nfreeparams);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2023 % % I = full(I);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2024 % I = full(I);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2025 % [U,S,V] = svd(I);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2026 % else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2027 % [U,S,V] = svd(I);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2028 % end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2029 % Sigma = V/S*U';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2030
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2031 % Does the covariance give proper positive-definite variances?
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2032 posDef = all(diag(Sigma)>=0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2033
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2034 if posDef
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2035
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2036 % Compute correlation matrix
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2037 Corr = zeros(size(Sigma));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2038 for ii=1:size(Sigma,1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2039 for jj=1:size(Sigma,2)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2040 Corr(ii,jj) = Sigma(ii,jj) / sqrt(Sigma(ii,ii)) / sqrt(Sigma(jj,jj));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2041 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2042 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2043
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2044 % Parameter standard errors
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2045 se = sqrt(diag(Sigma))';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2046
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2047 % rescale errors and covariance matrix
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2048 if ~FastHess && ~linUnc % otherwise H is already scaled in find_bestfit function
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2049 se = se.*scale;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2050 for ii=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2051 for jj=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2052 Sigma(ii,jj) = Sigma(ii,jj)scale(ii)scale(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2053 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2054 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2055 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2056 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2057
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2058 % rescale information matrix
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2059 if ~FastHess && ~linUnc % otherwise H is already scaled in find_bestfit function
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2060 for ii=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2061 for jj=1:Nfreeparams
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2062 I(ii,jj) = I(ii,jj)/scale(ii)/scale(jj);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2063 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2064 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2065 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2066
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2067 if ~exist('se','var'); se = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2068 if ~exist('Sigma','var'); Sigma = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2069 if ~exist('Corr','var'); Corr = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2070 if ~exist('I','var'); I = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2071 if ~exist('H','var'); H = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2072 if ~exist('errH','var'); errH = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2073 if ~exist('J','var'); J = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2074 if ~exist('errJ','var'); errJ = []; end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2075
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2076 clear global scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2077
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2078 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2079
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2080 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2081 % Get Info Object
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2082 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2083 function ii = getInfo(varargin)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2084 if nargin == 1 && strcmpi(varargin{1}, 'None')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2085 sets = {};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2086 pl = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2087 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2088 sets = {'Default'};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2089 pl = getDefaultPlist;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2090 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2091 % Build info object
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2092 ii = minfo(mfilename, 'ao', 'ltpda', utils.const.categories.sigproc, '$Id: xfit.m,v 1.83 2011/05/12 07:46:29 mauro Exp $', sets, pl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2093 ii.setModifier(false);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2094 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2095
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2096 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2097 % Get Default Plist
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2098 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2099 function plout = getDefaultPlist()
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2100 persistent pl;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2101 if exist('pl', 'var')==0 \|\| isempty(pl)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2102 pl = buildplist();
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2103 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2104 plout = pl;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2105 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2106
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2107 function pl = buildplist()
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2108
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2109 pl = plist();
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2110
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2111 % Function
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2112 p = param({'Function', 'The function (or symbolic model <tt>smodel</tt>) of Xdata that you want to fit. For example: ''P(1)*Xdata''.'}, paramValue.EMPTY_STRING);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2113 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2114
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2115 % Weights
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2116 p = param({'Weights', ['An array of weights, one value per X sample.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2117 'By default, <tt>xfit</tt> takes data uncertainties from the dy field of the input object.'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2118 'If provided, <tt>weights</tt> make <tt>xfit</tt> ignore these.'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2119 'Otherwise <tt>weights</tt> will be considered as ones.']}, paramValue.EMPTY_STRING);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2120 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2121
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2122 % P0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2123 p = param({'P0', ['An array of starting guesses for the parameters.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2124 'This is not necessary if you fit with <tt>smodel</tt>s; in that case the parameter'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2125 'values from the <tt>smodel</tt> are taken as the initial guess.']}, paramValue.EMPTY_DOUBLE);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2126 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2127
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2128 % % ADDP
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2129 % p = param({'ADDP', 'A cell-array of additional parameters to pass to the function. These will not be fit.'}, {1, {'{}'}, paramValue.OPTIONAL});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2130 % pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2131
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2132 % LB
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2133 p = param({'LB', ['Lower bounds for the parameters.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2134 'This improves the convergency. Mandatory for Monte Carlo.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2135 'For multichannel fitting it has to be a cell-array.']}, paramValue.EMPTY_DOUBLE);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2136 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2137
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2138 % UB
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2139 p = param({'UB', ['Upper bounds for the parameters.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2140 'This improves the convergency. Mandatory for Monte Carlo.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2141 'For multichannel fitting it has to be a cell-array.']}, paramValue.EMPTY_DOUBLE);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2142 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2143
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2144 % Algorithm
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2145 p = param({'ALGORITHM', ['A string defining the fitting algorithm.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2146 '<tt>fminunc</tt>, <tt>fmincon</tt> require ''Optimization Toolbox'' to be installed.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2147 '<tt>patternsearch</tt>, <tt>ga</tt>, <tt>simulannealbnd</tt> require ''Genetic Algorithm and Direct Search'' to be installed.<br>']}, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2148 {1, {'fminsearch', 'fminunc', 'fmincon', 'patternsearch', 'ga', 'simulannealbnd'}, paramValue.SINGLE});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2149 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2150
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2151 % OPTSET
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2152 p = param({'OPTSET', ['An optimisation structure to pass to the fitting algorithm.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2153 'See <tt>fminsearch</tt>, <tt>fminunc</tt>, <tt>fmincon</tt>, <tt>optimset</tt>, for details.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2154 'See <tt>patternsearch</tt>, <tt>psoptimset</tt>, for details.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2155 'See <tt>ga</tt>, <tt>gaoptimset</tt>, for details.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2156 'See <tt>simulannealbnd</tt>, <tt>saoptimset</tt>, for details.']}, paramValue.EMPTY_STRING);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2157 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2158
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2159 % FitUnc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2160 p = param({'FitUnc', 'Fit parameter uncertainties or not.'}, paramValue.YES_NO);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2161 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2162
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2163 % UncMtd
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2164 p = param({'UncMtd', ['Choose the uncertainties estimation method.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2165 'For multi-channel fitting <tt>hessian</tt> is mandatory.']}, {1, {'hessian', 'jacobian'}, paramValue.SINGLE});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2166 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2167
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2168 % FastHess
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2169 p = param({'FastHess', ['Choose whether or not the hessian should be estimated from a fast-forward finite differences algorithm; '...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2170 'use this method to achieve better performance in CPU-time, but accuracy is not ensured; '...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2171 'otherwise, the default (computer expensive, but more accurate) method will be used.']}, paramValue.NO_YES);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2172 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2173
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2174 % MonteCarlo
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2175 p = param({'MonteCarlo', ['Do a Monte Carlo search in the parameter space.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2176 'Useful when dealing with high multiplicity of local minima. May be computer-expensive.<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2177 'Note that, if used, P0 will be ignored. It also requires to define LB and UB.']}, paramValue.NO_YES);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2178 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2179
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2180 % Npoints
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2181 p = param({'Npoints', 'Set the number of points in the parameter space to be extracted.'}, 100000);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2182 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2183
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2184 % Noptims
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2185 p = param({'Noptims', 'Set the number of optimizations to be performed after the Monte Carlo.'}, 10);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2186 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2187
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2188 % estimator
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2189 p = param({'estimator', ['Choose the robust local M-estimate as the statistical estimator of the fit:<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2190 ' ''chi2'' (least square) for data with normal distribution;<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2191 ' ''abs'' (mean absolute deviation) for data with double exponential distribution;<br>'...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2192 ' ''log'' (log least square) for data with Lorentzian distribution.']}, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2193 {1, {'chi2', 'abs', 'log'}, paramValue.SINGLE});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2194 pl.append(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2195
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2196
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2197 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2198 % END
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2199
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2200 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2201
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2202 % Author: John D'Errico
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2203 % e-mail: woodchips@rochester.rr.com
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2204
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2205 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2206 % DERIVEST SUITE
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2207 %--------------------------------------------------------------------------
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2208
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2209 function [der,errest,finaldelta] = derivest(fun,x0,varargin)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2210 % DERIVEST: estimate the n'th derivative of fun at x0, provide an error estimate
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2211 % usage: [der,errest] = DERIVEST(fun,x0) % first derivative
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2212 % usage: [der,errest] = DERIVEST(fun,x0,prop1,val1,prop2,val2,...)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2213 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2214 % Derivest will perform numerical differentiation of an
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2215 % analytical function provided in fun. It will not
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2216 % differentiate a function provided as data. Use gradient
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2217 % for that purpose, or differentiate a spline model.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2218 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2219 % The methods used by DERIVEST are finite difference
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2220 % approximations of various orders, coupled with a generalized
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2221 % (multiple term) Romberg extrapolation. This also yields
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2222 % the error estimate provided. DERIVEST uses a semi-adaptive
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2223 % scheme to provide the best estimate that it can by its
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2224 % automatic choice of a differencing interval.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2225 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2226 % Finally, While I have not written this function for the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2227 % absolute maximum speed, speed was a major consideration
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2228 % in the algorithmic design. Maximum accuracy was my main goal.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2229 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2230 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2231 % Arguments (input)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2232 % fun - function to differentiate. May be an inline function,
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2233 % anonymous, or an m-file. fun will be sampled at a set
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2234 % of distinct points for each element of x0. If there are
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2235 % additional parameters to be passed into fun, then use of
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2236 % an anonymous function is recommended.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2237 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2238 % fun should be vectorized to allow evaluation at multiple
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2239 % locations at once. This will provide the best possible
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2240 % speed. IF fun is not so vectorized, then you MUST set
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2241 % 'vectorized' property to 'no', so that derivest will
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2242 % then call your function sequentially instead.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2243 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2244 % Fun is assumed to return a result of the same
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2245 % shape as its input x0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2246 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2247 % x0 - scalar, vector, or array of points at which to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2248 % differentiate fun.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2249 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2250 % Additional inputs must be in the form of property/value pairs.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2251 % Properties are character strings. They may be shortened
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2252 % to the extent that they are unambiguous. Properties are
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2253 % not case sensitive. Valid property names are:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2254 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2255 % 'DerivativeOrder', 'MethodOrder', 'Style', 'RombergTerms'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2256 % 'FixedStep', 'MaxStep'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2257 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2258 % All properties have default values, chosen as intelligently
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2259 % as I could manage. Values that are character strings may
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2260 % also be unambiguously shortened. The legal values for each
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2261 % property are:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2262 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2263 % 'DerivativeOrder' - specifies the derivative order estimated.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2264 % Must be a positive integer from the set [1,2,3,4].
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2265 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2266 % DEFAULT: 1 (first derivative of fun)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2267 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2268 % 'MethodOrder' - specifies the order of the basic method
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2269 % used for the estimation.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2270 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2271 % For 'central' methods, must be a positive integer
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2272 % from the set [2,4].
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2273 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2274 % For 'forward' or 'backward' difference methods,
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2275 % must be a positive integer from the set [1,2,3,4].
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2276 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2277 % DEFAULT: 4 (a second order method)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2278 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2279 % Note: higher order methods will generally be more
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2280 % accurate, but may also suffere more from numerical
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2281 % problems.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2282 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2283 % Note: First order methods would usually not be
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2284 % recommended.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2285 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2286 % 'Style' - specifies the style of the basic method
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2287 % used for the estimation. 'central', 'forward',
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2288 % or 'backwards' difference methods are used.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2289 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2290 % Must be one of 'Central', 'forward', 'backward'.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2291 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2292 % DEFAULT: 'Central'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2293 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2294 % Note: Central difference methods are usually the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2295 % most accurate, but sometiems one must not allow
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2296 % evaluation in one direction or the other.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2297 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2298 % 'RombergTerms' - Allows the user to specify the generalized
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2299 % Romberg extrapolation method used, or turn it off
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2300 % completely.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2301 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2302 % Must be a positive integer from the set [0,1,2,3].
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2303 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2304 % DEFAULT: 2 (Two Romberg terms)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2305 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2306 % Note: 0 disables the Romberg step completely.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2307 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2308 % 'FixedStep' - Allows the specification of a fixed step
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2309 % size, preventing the adaptive logic from working.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2310 % This will be considerably faster, but not necessarily
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2311 % as accurate as allowing the adaptive logic to run.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2312 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2313 % DEFAULT: []
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2314 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2315 % Note: If specified, 'FixedStep' will define the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2316 % maximum excursion from x0 that will be used.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2317 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2318 % 'Vectorized' - Derivest will normally assume that your
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2319 % function can be safely evaluated at multiple locations
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2320 % in a single call. This would minimize the overhead of
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2321 % a loop and additional function call overhead. Some
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2322 % functions are not easily vectorizable, but you may
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2323 % (if your matlab release is new enough) be able to use
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2324 % arrayfun to accomplish the vectorization.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2325 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2326 % When all else fails, set the 'vectorized' property
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2327 % to 'no'. This will cause derivest to loop over the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2328 % successive function calls.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2329 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2330 % DEFAULT: 'yes'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2331 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2332 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2333 % 'MaxStep' - Specifies the maximum excursion from x0 that
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2334 % will be allowed, as a multiple of x0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2335 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2336 % DEFAULT: 100
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2337 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2338 % 'StepRatio' - Derivest uses a proportionally cascaded
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2339 % series of function evaluations, moving away from your
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2340 % point of evaluation. The StepRatio is the ratio used
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2341 % between sequential steps.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2342 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2343 % DEFAULT: 2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2344 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2345 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2346 % See the document DERIVEST.pdf for more explanation of the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2347 % algorithms behind the parameters of DERIVEST. In most cases,
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2348 % I have chosen good values for these parameters, so the user
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2349 % should never need to specify anything other than possibly
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2350 % the DerivativeOrder. I've also tried to make my code robust
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2351 % enough that it will not need much. But complete flexibility
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2352 % is in there for your use.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2353 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2354 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2355 % Arguments: (output)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2356 % der - derivative estimate for each element of x0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2357 % der will have the same shape as x0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2358 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2359 % errest - 95% uncertainty estimate of the derivative, such that
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2360 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2361 % abs(der(j) - f'(x0(j))) < erest(j)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2362 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2363 % finaldelta - The final overall stepsize chosen by DERIVEST
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2364 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2365 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2366 % Example usage:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2367 % First derivative of exp(x), at x == 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2368 % [d,e]=derivest(@(x) exp(x),1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2369 % d =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2370 % 2.71828182845904
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2371 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2372 % e =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2373 % 1.02015503167879e-14
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2374 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2375 % True derivative
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2376 % exp(1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2377 % ans =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2378 % 2.71828182845905
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2379 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2380 % Example usage:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2381 % Third derivative of x.^3+x.^4, at x = [0,1]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2382 % derivest(@(x) x.^3 + x.^4,[0 1],'deriv',3)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2383 % ans =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2384 % 6 30
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2385 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2386 % True derivatives: [6,30]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2387 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2388 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2389 % See also: gradient
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2390 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2391 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2392 % Author: John D'Errico
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2393 % e-mail: woodchips@rochester.rr.com
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2394 % Release: 1.0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2395 % Release date: 12/27/2006
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2396
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2397 par.DerivativeOrder = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2398 par.MethodOrder = 4;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2399 par.Style = 'central';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2400 par.RombergTerms = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2401 par.FixedStep = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2402 par.MaxStep = 100;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2403 par.StepRatio = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2404 par.NominalStep = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2405 par.Vectorized = 'yes';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2406
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2407 na = length(varargin);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2408 if (rem(na,2)==1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2409 error 'Property/value pairs must come as PAIRS of arguments.'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2410 elseif na>0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2411 par = parse_pv_pairs(par,varargin);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2412 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2413 par = check_params(par);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2414
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2415 % Was fun a string, or an inline/anonymous function?
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2416 if (nargin<1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2417 help derivest
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2418 return
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2419 elseif isempty(fun)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2420 error 'fun was not supplied.'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2421 elseif ischar(fun)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2422 % a character function name
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2423 fun = str2func(fun);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2424 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2425
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2426 % no default for x0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2427 if (nargin<2) \|\| isempty(x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2428 error 'x0 was not supplied'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2429 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2430 par.NominalStep = max(x0,0.02);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2431
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2432 % was a single point supplied?
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2433 nx0 = size(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2434 n = prod(nx0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2435
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2436 % Set the steps to use.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2437 if isempty(par.FixedStep)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2438 % Basic sequence of steps, relative to a stepsize of 1.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2439 delta = par.MaxStep*par.StepRatio .^(0:-1:-25)';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2440 ndel = length(delta);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2441 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2442 % Fixed, user supplied absolute sequence of steps.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2443 ndel = 3 + ceil(par.DerivativeOrder/2) + ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2444 par.MethodOrder + par.RombergTerms;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2445 if par.Style(1) == 'c'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2446 ndel = ndel - 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2447 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2448 delta = par.FixedStep*par.StepRatio .^(-(0:(ndel-1)))';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2449 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2450
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2451 % generate finite differencing rule in advance.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2452 % The rule is for a nominal unit step size, and will
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2453 % be scaled later to reflect the local step size.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2454 fdarule = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2455 switch par.Style
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2456 case 'central'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2457 % for central rules, we will reduce the load by an
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2458 % even or odd transformation as appropriate.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2459 if par.MethodOrder==2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2460 switch par.DerivativeOrder
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2461 case 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2462 % the odd transformation did all the work
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2463 fdarule = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2464 case 2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2465 % the even transformation did all the work
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2466 fdarule = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2467 case 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2468 % the odd transformation did most of the work, but
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2469 % we need to kill off the linear term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2470 fdarule = [0 1]/fdamat(par.StepRatio,1,2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2471 case 4
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2472 % the even transformation did most of the work, but
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2473 % we need to kill off the quadratic term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2474 fdarule = [0 1]/fdamat(par.StepRatio,2,2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2475 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2476 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2477 % a 4th order method. We've already ruled out the 1st
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2478 % order methods since these are central rules.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2479 switch par.DerivativeOrder
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2480 case 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2481 % the odd transformation did most of the work, but
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2482 % we need to kill off the cubic term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2483 fdarule = [1 0]/fdamat(par.StepRatio,1,2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2484 case 2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2485 % the even transformation did most of the work, but
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2486 % we need to kill off the quartic term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2487 fdarule = [1 0]/fdamat(par.StepRatio,2,2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2488 case 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2489 % the odd transformation did much of the work, but
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2490 % we need to kill off the linear & quintic terms
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2491 fdarule = [0 1 0]/fdamat(par.StepRatio,1,3);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2492 case 4
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2493 % the even transformation did much of the work, but
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2494 % we need to kill off the quadratic and 6th order terms
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2495 fdarule = [0 1 0]/fdamat(par.StepRatio,2,3);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2496 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2497 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2498 case {'forward' 'backward'}
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2499 % These two cases are identical, except at the very end,
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2500 % where a sign will be introduced.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2501
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2502 % No odd/even trans, but we already dropped
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2503 % off the constant term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2504 if par.MethodOrder==1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2505 if par.DerivativeOrder==1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2506 % an easy one
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2507 fdarule = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2508 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2509 % 2:4
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2510 v = zeros(1,par.DerivativeOrder);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2511 v(par.DerivativeOrder) = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2512 fdarule = v/fdamat(par.StepRatio,0,par.DerivativeOrder);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2513 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2514 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2515 % par.MethodOrder methods drop off the lower order terms,
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2516 % plus terms directly above DerivativeOrder
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2517 v = zeros(1,par.DerivativeOrder + par.MethodOrder - 1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2518 v(par.DerivativeOrder) = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2519 fdarule = v/fdamat(par.StepRatio,0,par.DerivativeOrder+par.MethodOrder-1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2520 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2521
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2522 % correct sign for the 'backward' rule
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2523 if par.Style(1) == 'b'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2524 fdarule = -fdarule;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2525 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2526
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2527 end % switch on par.style (generating fdarule)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2528 nfda = length(fdarule);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2529
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2530 % will we need fun(x0)?
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2531 if (rem(par.DerivativeOrder,2) == 0) \|\| ~strncmpi(par.Style,'central',7)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2532 if strcmpi(par.Vectorized,'yes')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2533 f_x0 = fun(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2534 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2535 % not vectorized, so loop
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2536 f_x0 = zeros(size(x0));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2537 for j = 1:numel(x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2538 f_x0(j) = fun(x0(j));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2539 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2540 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2541 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2542 f_x0 = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2543 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2544
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2545 % Loop over the elements of x0, reducing it to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2546 % a scalar problem. Sorry, vectorization is not
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2547 % complete here, but this IS only a single loop.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2548 der = zeros(nx0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2549 errest = der;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2550 finaldelta = der;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2551 for i = 1:n
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2552 x0i = x0(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2553 h = par.NominalStep(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2554
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2555 % a central, forward or backwards differencing rule?
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2556 % f_del is the set of all the function evaluations we
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2557 % will generate. For a central rule, it will have the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2558 % even or odd transformation built in.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2559 if par.Style(1) == 'c'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2560 % A central rule, so we will need to evaluate
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2561 % symmetrically around x0i.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2562 if strcmpi(par.Vectorized,'yes')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2563 f_plusdel = fun(x0i+h*delta);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2564 f_minusdel = fun(x0i-h*delta);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2565 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2566 % not vectorized, so loop
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2567 f_minusdel = zeros(size(delta));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2568 f_plusdel = zeros(size(delta));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2569 for j = 1:numel(delta)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2570 f_plusdel(j) = fun(x0i+h*delta(j));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2571 f_minusdel(j) = fun(x0i-h*delta(j));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2572 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2573 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2574
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2575 if ismember(par.DerivativeOrder,[1 3])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2576 % odd transformation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2577 f_del = (f_plusdel - f_minusdel)/2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2578 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2579 f_del = (f_plusdel + f_minusdel)/2 - f_x0(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2580 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2581 elseif par.Style(1) == 'f'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2582 % forward rule
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2583 % drop off the constant only
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2584 if strcmpi(par.Vectorized,'yes')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2585 f_del = fun(x0i+h*delta) - f_x0(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2586 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2587 % not vectorized, so loop
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2588 f_del = zeros(size(delta));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2589 for j = 1:numel(delta)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2590 f_del(j) = fun(x0i+h*delta(j)) - f_x0(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2591 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2592 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2593 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2594 % backward rule
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2595 % drop off the constant only
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2596 if strcmpi(par.Vectorized,'yes')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2597 f_del = fun(x0i-h*delta) - f_x0(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2598 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2599 % not vectorized, so loop
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2600 f_del = zeros(size(delta));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2601 for j = 1:numel(delta)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2602 f_del(j) = fun(x0i-h*delta(j)) - f_x0(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2603 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2604 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2605 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2606
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2607 % check the size of f_del to ensure it was properly vectorized.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2608 f_del = f_del(:);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2609 if length(f_del)~=ndel
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2610 error 'fun did not return the correct size result (fun must be vectorized)'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2611 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2612
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2613 % Apply the finite difference rule at each delta, scaling
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2614 % as appropriate for delta and the requested DerivativeOrder.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2615 % First, decide how many of these estimates we will end up with.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2616 ne = ndel + 1 - nfda - par.RombergTerms;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2617
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2618 % Form the initial derivative estimates from the chosen
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2619 % finite difference method.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2620 der_init = vec2mat(f_del,ne,nfda)*fdarule.';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2621
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2622 % scale to reflect the local delta
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2623 der_init = der_init(:)./(h*delta(1:ne)).^par.DerivativeOrder;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2624
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2625 % Each approximation that results is an approximation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2626 % of order par.DerivativeOrder to the desired derivative.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2627 % Additional (higher order, even or odd) terms in the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2628 % Taylor series also remain. Use a generalized (multi-term)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2629 % Romberg extrapolation to improve these estimates.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2630 switch par.Style
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2631 case 'central'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2632 rombexpon = 2*(1:par.RombergTerms) + par.MethodOrder - 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2633 otherwise
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2634 rombexpon = (1:par.RombergTerms) + par.MethodOrder - 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2635 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2636 [der_romb,errors] = rombextrap(par.StepRatio,der_init,rombexpon);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2637
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2638 % Choose which result to return
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2639
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2640 % first, trim off the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2641 if isempty(par.FixedStep)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2642 % trim off the estimates at each end of the scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2643 nest = length(der_romb);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2644 switch par.DerivativeOrder
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2645 case {1 2}
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2646 trim = [1 2 nest-1 nest];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2647 case 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2648 trim = [1:4 nest+(-3:0)];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2649 case 4
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2650 trim = [1:6 nest+(-5:0)];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2651 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2652
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2653 [der_romb,tags] = sort(der_romb);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2654
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2655 der_romb(trim) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2656 tags(trim) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2657 errors = errors(tags);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2658 trimdelta = delta(tags);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2659
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2660 [errest(i),ind] = min(errors);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2661
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2662 finaldelta(i) = h*trimdelta(ind);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2663 der(i) = der_romb(ind);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2664 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2665 [errest(i),ind] = min(errors);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2666 finaldelta(i) = h*delta(ind);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2667 der(i) = der_romb(ind);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2668 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2669 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2670
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2671 end % mainline end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2672
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2673
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2674 function [jac,err] = jacobianest(fun,x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2675 % gradest: estimate of the Jacobian matrix of a vector valued function of n variables
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2676 % usage: [jac,err] = jacobianest(fun,x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2677 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2678 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2679 % arguments: (input)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2680 % fun - (vector valued) analytical function to differentiate.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2681 % fun must be a function of the vector or array x0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2682 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2683 % x0 - vector location at which to differentiate fun
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2684 % If x0 is an nxm array, then fun is assumed to be
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2685 % a function of n*m variables.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2686 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2687 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2688 % arguments: (output)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2689 % jac - array of first partial derivatives of fun.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2690 % Assuming that x0 is a vector of length p
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2691 % and fun returns a vector of length n, then
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2692 % jac will be an array of size (n,p)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2693 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2694 % err - vector of error estimates corresponding to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2695 % each partial derivative in jac.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2696 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2697 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2698 % Example: (nonlinear least squares)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2699 % xdata = (0:.1:1)';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2700 % ydata = 1+2exp(0.75xdata);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2701 % fun = @(c) ((c(1)+c(2)exp(c(3)xdata)) - ydata).^2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2702 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2703 % [jac,err] = jacobianest(fun,[1 1 1])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2704 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2705 % jac =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2706 % -2 -2 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2707 % -2.1012 -2.3222 -0.23222
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2708 % -2.2045 -2.6926 -0.53852
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2709 % -2.3096 -3.1176 -0.93528
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2710 % -2.4158 -3.6039 -1.4416
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2711 % -2.5225 -4.1589 -2.0795
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2712 % -2.629 -4.7904 -2.8742
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2713 % -2.7343 -5.5063 -3.8544
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2714 % -2.8374 -6.3147 -5.0518
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2715 % -2.9369 -7.2237 -6.5013
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2716 % -3.0314 -8.2403 -8.2403
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2717 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2718 % err =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2719 % 5.0134e-15 5.0134e-15 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2720 % 5.0134e-15 0 2.8211e-14
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2721 % 5.0134e-15 8.6834e-15 1.5804e-14
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2722 % 0 7.09e-15 3.8227e-13
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2723 % 5.0134e-15 5.0134e-15 7.5201e-15
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2724 % 5.0134e-15 1.0027e-14 2.9233e-14
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2725 % 5.0134e-15 0 6.0585e-13
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2726 % 5.0134e-15 1.0027e-14 7.2673e-13
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2727 % 5.0134e-15 1.0027e-14 3.0495e-13
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2728 % 5.0134e-15 1.0027e-14 3.1707e-14
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2729 % 5.0134e-15 2.0053e-14 1.4013e-12
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2730 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2731 % (At [1 2 0.75], jac should be numerically zero)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2732 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2733 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2734 % See also: derivest, gradient, gradest
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2735 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2736 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2737 % Author: John D'Errico
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2738 % e-mail: woodchips@rochester.rr.com
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2739 % Release: 1.0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2740 % Release date: 3/6/2007
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2741
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2742 % get the length of x0 for the size of jac
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2743 nx = numel(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2744
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2745 MaxStep = 100;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2746 StepRatio = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2747
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2748 % was a string supplied?
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2749 if ischar(fun)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2750 fun = str2func(fun);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2751 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2752
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2753 % get fun at the center point
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2754 f0 = fun(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2755 f0 = f0(:);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2756 n = length(f0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2757 if n==0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2758 % empty begets empty
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2759 jac = zeros(0,nx);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2760 err = jac;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2761 return
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2762 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2763
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2764 relativedelta = MaxStep*StepRatio .^(0:-1:-25);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2765 nsteps = length(relativedelta);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2766
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2767 % total number of derivatives we will need to take
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2768 jac = zeros(n,nx);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2769 err = jac;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2770 for i = 1:nx
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2771 x0_i = x0(i);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2772 if x0_i ~= 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2773 delta = x0_i*relativedelta;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2774 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2775 delta = relativedelta;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2776 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2777
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2778 % evaluate at each step, centered around x0_i
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2779 % difference to give a second order estimate
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2780 fdel = zeros(n,nsteps);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2781 for j = 1:nsteps
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2782 fdif = fun(swapelement(x0,i,x0_i + delta(j))) - ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2783 fun(swapelement(x0,i,x0_i - delta(j)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2784
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2785 fdel(:,j) = fdif(:);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2786 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2787
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2788 % these are pure second order estimates of the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2789 % first derivative, for each trial delta.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2790 derest = fdel.*repmat(0.5 ./ delta,n,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2791
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2792 % The error term on these estimates has a second order
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2793 % component, but also some 4th and 6th order terms in it.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2794 % Use Romberg exrapolation to improve the estimates to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2795 % 6th order, as well as to provide the error estimate.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2796
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2797 % loop here, as rombextrap coupled with the trimming
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2798 % will get complicated otherwise.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2799 for j = 1:n
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2800 [der_romb,errest] = rombextrap(StepRatio,derest(j,:),[2 4]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2801
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2802 % trim off 3 estimates at each end of the scale
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2803 nest = length(der_romb);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2804 trim = [1:3, nest+(-2:0)];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2805 [der_romb,tags] = sort(der_romb);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2806 der_romb(trim) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2807 tags(trim) = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2808
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2809 errest = errest(tags);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2810
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2811 % now pick the estimate with the lowest predicted error
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2812 [err(j,i),ind] = min(errest);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2813 jac(j,i) = der_romb(ind);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2814 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2815 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2816
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2817 end % mainline function end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2818
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2819
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2820 function [grad,err,finaldelta] = gradest(fun,x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2821 % gradest: estimate of the gradient vector of an analytical function of n variables
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2822 % usage: [grad,err,finaldelta] = gradest(fun,x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2823 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2824 % Uses derivest to provide both derivative estimates
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2825 % and error estimates. fun needs not be vectorized.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2826 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2827 % arguments: (input)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2828 % fun - analytical function to differentiate. fun must
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2829 % be a function of the vector or array x0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2830 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2831 % x0 - vector location at which to differentiate fun
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2832 % If x0 is an nxm array, then fun is assumed to be
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2833 % a function of n*m variables.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2834 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2835 % arguments: (output)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2836 % grad - vector of first partial derivatives of fun.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2837 % grad will be a row vector of length numel(x0).
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2838 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2839 % err - vector of error estimates corresponding to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2840 % each partial derivative in grad.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2841 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2842 % finaldelta - vector of final step sizes chosen for
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2843 % each partial derivative.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2844 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2845 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2846 % Example:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2847 % [grad,err] = gradest(@(x) sum(x.^2),[1 2 3])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2848 % grad =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2849 % 2 4 6
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2850 % err =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2851 % 5.8899e-15 1.178e-14 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2852 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2853 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2854 % Example:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2855 % At [x,y] = [1,1], compute the numerical gradient
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2856 % of the function sin(x-y) + y*exp(x)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2857 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2858 % z = @(xy) sin(diff(xy)) + xy(2)*exp(xy(1))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2859 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2860 % [grad,err ] = gradest(z,[1 1])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2861 % grad =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2862 % 1.7183 3.7183
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2863 % err =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2864 % 7.537e-14 1.1846e-13
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2865 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2866 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2867 % Example:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2868 % At the global minimizer (1,1) of the Rosenbrock function,
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2869 % compute the gradient. It should be essentially zero.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2870 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2871 % rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2872 % [g,err] = gradest(rosen,[1 1])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2873 % g =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2874 % 1.0843e-20 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2875 % err =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2876 % 1.9075e-18 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2877 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2878 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2879 % See also: derivest, gradient
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2880 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2881 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2882 % Author: John D'Errico
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2883 % e-mail: woodchips@rochester.rr.com
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2884 % Release: 1.0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2885 % Release date: 2/9/2007
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2886
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2887 % get the size of x0 so we can reshape
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2888 % later.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2889 sx = size(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2890
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2891 % total number of derivatives we will need to take
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2892 nx = numel(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2893
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2894 grad = zeros(1,nx);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2895 err = grad;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2896 finaldelta = grad;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2897 for ind = 1:nx
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2898 [grad(ind),err(ind),finaldelta(ind)] = derivest( ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2899 @(xi) fun(swapelement(x0,ind,xi)), ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2900 x0(ind),'deriv',1,'vectorized','no', ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2901 'methodorder',2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2902 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2903
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2904 end % mainline function end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2905
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2906
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2907 function [HD,err,finaldelta] = hessdiag(fun,x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2908 % HESSDIAG: diagonal elements of the Hessian matrix (vector of second partials)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2909 % usage: [HD,err,finaldelta] = hessdiag(fun,x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2910 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2911 % When all that you want are the diagonal elements of the hessian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2912 % matrix, it will be more efficient to call HESSDIAG than HESSIAN.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2913 % HESSDIAG uses DERIVEST to provide both second derivative estimates
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2914 % and error estimates. fun needs not be vectorized.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2915 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2916 % arguments: (input)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2917 % fun - SCALAR analytical function to differentiate.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2918 % fun must be a function of the vector or array x0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2919 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2920 % x0 - vector location at which to differentiate fun
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2921 % If x0 is an nxm array, then fun is assumed to be
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2922 % a function of n*m variables.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2923 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2924 % arguments: (output)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2925 % HD - vector of second partial derivatives of fun.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2926 % These are the diagonal elements of the Hessian
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2927 % matrix, evaluated at x0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2928 % HD will be a row vector of length numel(x0).
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2929 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2930 % err - vector of error estimates corresponding to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2931 % each second partial derivative in HD.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2932 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2933 % finaldelta - vector of final step sizes chosen for
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2934 % each second partial derivative.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2935 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2936 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2937 % Example usage:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2938 % [HD,err] = hessdiag(@(x) x(1) + x(2)^2 + x(3)^3,[1 2 3])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2939 % HD =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2940 % 0 2 18
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2941 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2942 % err =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2943 % 0 0 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2944 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2945 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2946 % See also: derivest, gradient, gradest
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2947 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2948 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2949 % Author: John D'Errico
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2950 % e-mail: woodchips@rochester.rr.com
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2951 % Release: 1.0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2952 % Release date: 2/9/2007
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2953
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2954 % get the size of x0 so we can reshape
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2955 % later.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2956 sx = size(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2957
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2958 % total number of derivatives we will need to take
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2959 nx = numel(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2960
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2961 HD = zeros(1,nx);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2962 err = HD;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2963 finaldelta = HD;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2964 for ind = 1:nx
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2965 [HD(ind),err(ind),finaldelta(ind)] = derivest( ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2966 @(xi) fun(swapelement(x0,ind,xi)), ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2967 x0(ind),'deriv',2,'vectorized','no');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2968 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2969
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2970 end % mainline function end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2971
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2972
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2973 function [hess,err] = hessian(fun,x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2974 % hessian: estimate elements of the Hessian matrix (array of 2nd partials)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2975 % usage: [hess,err] = hessian(fun,x0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2976 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2977 % Hessian is NOT a tool for frequent use on an expensive
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2978 % to evaluate objective function, especially in a large
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2979 % number of dimensions. Its computation will use roughly
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2980 % O(6*n^2) function evaluations for n parameters.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2981 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2982 % arguments: (input)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2983 % fun - SCALAR analytical function to differentiate.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2984 % fun must be a function of the vector or array x0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2985 % fun does not need to be vectorized.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2986 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2987 % x0 - vector location at which to compute the Hessian.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2988 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2989 % arguments: (output)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2990 % hess - nxn symmetric array of second partial derivatives
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2991 % of fun, evaluated at x0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2992 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2993 % err - nxn array of error estimates corresponding to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2994 % each second partial derivative in hess.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2995 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2996 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2997 % Example usage:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2998 % Rosenbrock function, minimized at [1,1]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2999 % rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3000 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3001 % [h,err] = hessian(rosen,[1 1])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3002 % h =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3003 % 842 -420
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3004 % -420 210
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3005 % err =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3006 % 1.0662e-12 4.0061e-10
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3007 % 4.0061e-10 2.6654e-13
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3008 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3009 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3010 % Example usage:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3011 % cos(x-y), at (0,0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3012 % Note: this hessian matrix will be positive semi-definite
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3013 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3014 % hessian(@(xy) cos(xy(1)-xy(2)),[0 0])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3015 % ans =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3016 % -1 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3017 % 1 -1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3018 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3019 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3020 % See also: derivest, gradient, gradest, hessdiag
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3021 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3022 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3023 % Author: John D'Errico
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3024 % e-mail: woodchips@rochester.rr.com
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3025 % Release: 1.0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3026 % Release date: 2/10/2007
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3027
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3028 % parameters that we might allow to change
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3029 params.StepRatio = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3030 params.RombergTerms = 3;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3031
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3032 % get the size of x0 so we can reshape
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3033 % later.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3034 sx = size(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3035
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3036 % was a string supplied?
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3037 if ischar(fun)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3038 fun = str2func(fun);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3039 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3040
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3041 % total number of derivatives we will need to take
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3042 nx = length(x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3043
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3044 % get the diagonal elements of the hessian (2nd partial
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3045 % derivatives wrt each variable.)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3046 [hess,err] = hessdiag(fun,x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3047
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3048 % form the eventual hessian matrix, stuffing only
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3049 % the diagonals for now.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3050 hess = diag(hess);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3051 err = diag(err);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3052 if nx<2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3053 % the hessian matrix is 1x1. all done
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3054 return
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3055 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3056
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3057 % get the gradient vector. This is done only to decide
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3058 % on intelligent step sizes for the mixed partials
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3059 [grad,graderr,stepsize] = gradest(fun,x0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3060
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3061 % Get params.RombergTerms+1 estimates of the upper
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3062 % triangle of the hessian matrix
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3063 dfac = params.StepRatio.^(-(0:params.RombergTerms)');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3064 for i = 2:nx
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3065 for j = 1:(i-1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3066 dij = zeros(params.RombergTerms+1,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3067 for k = 1:(params.RombergTerms+1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3068 dij(k) = fun(x0 + swap2(zeros(sx),i, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3069 dfac(k)stepsize(i),j,dfac(k)stepsize(j))) + ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3070 fun(x0 + swap2(zeros(sx),i, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3071 -dfac(k)stepsize(i),j,-dfac(k)stepsize(j))) - ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3072 fun(x0 + swap2(zeros(sx),i, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3073 dfac(k)stepsize(i),j,-dfac(k)stepsize(j))) - ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3074 fun(x0 + swap2(zeros(sx),i, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3075 -dfac(k)stepsize(i),j,dfac(k)stepsize(j)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3076
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3077 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3078 dij = dij/4/prod(stepsize([i,j]));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3079 dij = dij./(dfac.^2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3080
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3081 % Romberg extrapolation step
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3082 [hess(i,j),err(i,j)] = rombextrap(params.StepRatio,dij,[2 4]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3083 hess(j,i) = hess(i,j);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3084 err(j,i) = err(i,j);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3085 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3086 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3087
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3088
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3089 end % mainline function end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3090
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3091
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3092
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3093 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3094 % subfunction - romberg extrapolation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3095 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3096 function [der_romb,errest] = rombextrap(StepRatio,der_init,rombexpon)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3097 % do romberg extrapolation for each estimate
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3098 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3099 % StepRatio - Ratio decrease in step
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3100 % der_init - initial derivative estimates
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3101 % rombexpon - higher order terms to cancel using the romberg step
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3102 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3103 % der_romb - derivative estimates returned
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3104 % errest - error estimates
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3105 % amp - noise amplification factor due to the romberg step
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3106
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3107 srinv = 1/StepRatio;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3108
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3109 % do nothing if no romberg terms
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3110 nexpon = length(rombexpon);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3111 rmat = ones(nexpon+2,nexpon+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3112 switch nexpon
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3113 case 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3114 % rmat is simple: ones(2,1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3115 case 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3116 % only one romberg term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3117 rmat(2,2) = srinv^rombexpon;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3118 rmat(3,2) = srinv^(2*rombexpon);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3119 case 2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3120 % two romberg terms
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3121 rmat(2,2:3) = srinv.^rombexpon;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3122 rmat(3,2:3) = srinv.^(2*rombexpon);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3123 rmat(4,2:3) = srinv.^(3*rombexpon);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3124 case 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3125 % three romberg terms
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3126 rmat(2,2:4) = srinv.^rombexpon;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3127 rmat(3,2:4) = srinv.^(2*rombexpon);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3128 rmat(4,2:4) = srinv.^(3*rombexpon);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3129 rmat(5,2:4) = srinv.^(4*rombexpon);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3130 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3131
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3132 % qr factorization used for the extrapolation as well
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3133 % as the uncertainty estimates
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3134 [qromb,rromb] = qr(rmat,0);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3135
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3136 % the noise amplification is further amplified by the Romberg step.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3137 % amp = cond(rromb);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3138
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3139 % this does the extrapolation to a zero step size.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3140 ne = length(der_init);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3141 rhs = vec2mat(der_init,nexpon+2,max(1,ne - (nexpon+2)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3142 rombcoefs = rromb\(qromb.'*rhs);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3143 der_romb = rombcoefs(1,:).';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3144
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3145 % uncertainty estimate of derivative prediction
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3146 s = sqrt(sum((rhs - rmat*rombcoefs).^2,1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3147 rinv = rromb\eye(nexpon+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3148 cov1 = sum(rinv.^2,2); % 1 spare dof
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3149 errest = s.'12.7062047361747sqrt(cov1(1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3150
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3151 end % rombextrap
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3152
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3153
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3154 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3155 % subfunction - vec2mat
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3156 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3157 function mat = vec2mat(vec,n,m)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3158 % forms the matrix M, such that M(i,j) = vec(i+j-1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3159 [i,j] = ndgrid(1:n,0:m-1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3160 ind = i+j;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3161 mat = vec(ind);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3162 if n==1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3163 mat = mat.';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3164 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3165
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3166 end % vec2mat
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3167
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3168
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3169 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3170 % subfunction - fdamat
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3171 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3172 function mat = fdamat(sr,parity,nterms)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3173 % Compute matrix for fda derivation.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3174 % parity can be
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3175 % 0 (one sided, all terms included but zeroth order)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3176 % 1 (only odd terms included)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3177 % 2 (only even terms included)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3178 % nterms - number of terms
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3179
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3180 % sr is the ratio between successive steps
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3181 srinv = 1./sr;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3182
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3183 switch parity
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3184 case 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3185 % single sided rule
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3186 [i,j] = ndgrid(1:nterms);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3187 c = 1./factorial(1:nterms);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3188 mat = c(j).srinv.^((i-1).j);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3189 case 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3190 % odd order derivative
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3191 [i,j] = ndgrid(1:nterms);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3192 c = 1./factorial(1:2:(2*nterms));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3193 mat = c(j).srinv.^((i-1).(2*j-1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3194 case 2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3195 % even order derivative
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3196 [i,j] = ndgrid(1:nterms);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3197 c = 1./factorial(2:2:(2*nterms));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3198 mat = c(j).srinv.^((i-1).(2*j));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3199 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3200
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3201 end % fdamat
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3202
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3203
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3204 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3205 % subfunction - check_params
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3206 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3207 function par = check_params(par)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3208 % check the parameters for acceptability
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3209 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3210 % Defaults
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3211 % par.DerivativeOrder = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3212 % par.MethodOrder = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3213 % par.Style = 'central';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3214 % par.RombergTerms = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3215 % par.FixedStep = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3216
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3217 % DerivativeOrder == 1 by default
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3218 if isempty(par.DerivativeOrder)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3219 par.DerivativeOrder = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3220 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3221 if (length(par.DerivativeOrder)>1) \|\| ~ismember(par.DerivativeOrder,1:4)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3222 error 'DerivativeOrder must be scalar, one of [1 2 3 4].'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3223 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3224 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3225
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3226 % MethodOrder == 2 by default
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3227 if isempty(par.MethodOrder)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3228 par.MethodOrder = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3229 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3230 if (length(par.MethodOrder)>1) \|\| ~ismember(par.MethodOrder,[1 2 3 4])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3231 error 'MethodOrder must be scalar, one of [1 2 3 4].'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3232 elseif ismember(par.MethodOrder,[1 3]) && (par.Style(1)=='c')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3233 error 'MethodOrder==1 or 3 is not possible with central difference methods'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3234 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3235 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3236
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3237 % style is char
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3238 valid = {'central', 'forward', 'backward'};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3239 if isempty(par.Style)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3240 par.Style = 'central';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3241 elseif ~ischar(par.Style)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3242 error 'Invalid Style: Must be character'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3243 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3244 ind = find(strncmpi(par.Style,valid,length(par.Style)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3245 if (length(ind)==1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3246 par.Style = valid{ind};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3247 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3248 error(['Invalid Style: ',par.Style])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3249 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3250
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3251 % vectorized is char
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3252 valid = {'yes', 'no'};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3253 if isempty(par.Vectorized)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3254 par.Vectorized = 'yes';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3255 elseif ~ischar(par.Vectorized)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3256 error 'Invalid Vectorized: Must be character'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3257 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3258 ind = find(strncmpi(par.Vectorized,valid,length(par.Vectorized)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3259 if (length(ind)==1)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3260 par.Vectorized = valid{ind};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3261 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3262 error(['Invalid Vectorized: ',par.Vectorized])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3263 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3264
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3265 % RombergTerms == 2 by default
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3266 if isempty(par.RombergTerms)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3267 par.RombergTerms = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3268 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3269 if (length(par.RombergTerms)>1) \|\| ~ismember(par.RombergTerms,0:3)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3270 error 'RombergTerms must be scalar, one of [0 1 2 3].'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3271 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3272 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3273
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3274 % FixedStep == [] by default
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3275 if (length(par.FixedStep)>1) \|\| (~isempty(par.FixedStep) && (par.FixedStep<=0))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3276 error 'FixedStep must be empty or a scalar, >0.'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3277 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3278
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3279 % MaxStep == 10 by default
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3280 if isempty(par.MaxStep)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3281 par.MaxStep = 10;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3282 elseif (length(par.MaxStep)>1) \|\| (par.MaxStep<=0)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3283 error 'MaxStep must be empty or a scalar, >0.'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3284 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3285
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3286 end % check_params
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3287
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3288
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3289 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3290 % Included subfunction - parse_pv_pairs
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3291 % ============================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3292 function params=parse_pv_pairs(params,pv_pairs)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3293 % parse_pv_pairs: parses sets of property value pairs, allows defaults
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3294 % usage: params=parse_pv_pairs(default_params,pv_pairs)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3295 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3296 % arguments: (input)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3297 % default_params - structure, with one field for every potential
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3298 % property/value pair. Each field will contain the default
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3299 % value for that property. If no default is supplied for a
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3300 % given property, then that field must be empty.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3301 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3302 % pv_array - cell array of property/value pairs.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3303 % Case is ignored when comparing properties to the list
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3304 % of field names. Also, any unambiguous shortening of a
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3305 % field/property name is allowed.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3306 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3307 % arguments: (output)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3308 % params - parameter struct that reflects any updated property/value
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3309 % pairs in the pv_array.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3310 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3311 % Example usage:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3312 % First, set default values for the parameters. Assume we
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3313 % have four parameters that we wish to use optionally in
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3314 % the function examplefun.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3315 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3316 % - 'viscosity', which will have a default value of 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3317 % - 'volume', which will default to 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3318 % - 'pie' - which will have default value 3.141592653589793
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3319 % - 'description' - a text field, left empty by default
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3320 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3321 % The first argument to examplefun is one which will always be
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3322 % supplied.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3323 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3324 % function examplefun(dummyarg1,varargin)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3325 % params.Viscosity = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3326 % params.Volume = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3327 % params.Pie = 3.141592653589793
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3328 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3329 % params.Description = '';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3330 % params=parse_pv_pairs(params,varargin);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3331 % params
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3332 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3333 % Use examplefun, overriding the defaults for 'pie', 'viscosity'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3334 % and 'description'. The 'volume' parameter is left at its default.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3335 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3336 % examplefun(rand(10),'vis',10,'pie',3,'Description','Hello world')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3337 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3338 % params =
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3339 % Viscosity: 10
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3340 % Volume: 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3341 % Pie: 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3342 % Description: 'Hello world'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3343 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3344 % Note that capitalization was ignored, and the property 'viscosity'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3345 % was truncated as supplied. Also note that the order the pairs were
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3346 % supplied was arbitrary.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3347
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3348 npv = length(pv_pairs);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3349 n = npv/2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3350
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3351 if n~=floor(n)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3352 error 'Property/value pairs must come in PAIRS.'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3353 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3354 if n<=0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3355 % just return the defaults
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3356 return
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3357 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3358
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3359 if ~isstruct(params)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3360 error 'No structure for defaults was supplied'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3361 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3362
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3363 % there was at least one pv pair. process any supplied
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3364 propnames = fieldnames(params);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3365 lpropnames = lower(propnames);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3366 for i=1:n
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3367 p_i = lower(pv_pairs{2*i-1});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3368 v_i = pv_pairs{2*i};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3369
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3370 ind = strmatch(p_i,lpropnames,'exact');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3371 if isempty(ind)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3372 ind = find(strncmp(p_i,lpropnames,length(p_i)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3373 if isempty(ind)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3374 error(['No matching property found for: ',pv_pairs{2*i-1}])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3375 elseif length(ind)>1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3376 error(['Ambiguous property name: ',pv_pairs{2*i-1}])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3377 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3378 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3379 p_i = propnames{ind};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3380
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3381 % override the corresponding default in params
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3382 params = setfield(params,p_i,v_i); %#ok
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3383
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3384 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3385
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3386 end % parse_pv_pairs
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3387
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3388
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3389 % =======================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3390 % sub-functions
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3391 % =======================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3392 function vec = swapelement(vec,ind,val)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3393 % swaps val as element ind, into the vector vec
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3394 vec(ind) = val;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3395
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3396 end % sub-function end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3397
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3398
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3399 % =======================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3400 % sub-functions
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3401 % =======================================
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3402 function vec = swap2(vec,ind1,val1,ind2,val2)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3403 % swaps val as element ind, into the vector vec
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3404 vec(ind1) = val1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3405 vec(ind2) = val2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3406
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3407 end % sub-function end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3408
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3409 % End of DERIVEST SUITE
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3410

Mercurial > hg > ltpda

annotate m-toolbox/classes/@ao/xfit.m @ 45:a59cdb8aaf31 database-connection-manager