ltpda: m-toolbox/classes/+utils/@math/vcfit.m annotate

annotate m-toolbox/classes/+utils/@math/vcfit.m @ 51:9d5c88356247 database-connection-manager

Make unit tests database connection parameters configurable

author	Daniele Nicolodi <nicolodi@science.unitn.it>
date	Wed, 07 Dec 2011 17:24:37 +0100
parents	f0afece42f48
children

rev	line source
0 f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1 % VCFIT Fits continuous models to frequency responses
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3 % DESCRIPTION:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	4 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	5 % Fits a continuous model to a frequency response using relaxed
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	6 % s-domain vector fitting algorithm [1, 2]. The function is able to fit more
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	7 % than one frequency response per time. In case that more than one
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	8 % frequency response is passed as input, they are fitted with a set of
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	9 % common poles. Model functions are expanded in partial fractions:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	10 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	11 % r1 rN
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	12 % f(s) = ------- + ... + ------- + d
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	13 % s - p1 s - pN
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	14 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	15 % CALL:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	16 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	17 % [res,poles,dterm,mresp,rdl] = vcfit(y,f,poles,weight,fitin)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	18 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	19 % INPUTS:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	20 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	21 % - y: Is a vector wuth the frequency response data.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	22 % - f: Is the frequency vector in Hz.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	23 % - poles: are a set of starting poles.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	24 % - weight: are a set of weights used in the fitting procedure.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	25 % - fitin: is a struct containing fitting options and parameters. fitin
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	26 % fields are:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	27 % - fitin.stable = 0; fit without forcing poles to be stable.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	28 % - fitin.stable = 1; force poles to be stable flipping unstable
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	29 % poles in the left side of the complex plane. s -> s - 2*conj(s).
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	30 % - fitin.dterm = 0; fit with d = 0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	31 % - fitin.dterm = 1; fit with d different from 0.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	32 % - fitin.polt = 0; fit without plotting results.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	33 % - fitin.plot = 1; plot fit results in loglog scale.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	34 % - fitin.plot = 2; plot fit results in semilogx scale.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	35 % - fitin.plot = 3; plot fit results in semilogy scale.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	36 % - fitin.plot = 4; plot fit results in linear xy scale.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	37 % - fitin.ploth = #; a plot handle to define the figure target for
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	38 % plotting. Default: [1]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	39 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	40 % OUTPUT:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	41 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	42 % - res: vector or residues.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	43 % - poles: vector of poles.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	44 % - dterm: direct term d.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	45 % - mresp: frequency response of the fitted model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	46 % - rdl: residuals y - mresp
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	47 % - mse: normalized mean squared error
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	48 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	49 % EXAMPLES:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	50 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	51 % - Fit on a single transfer function:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	52 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	53 % INPUT
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	54 % y is a (Nx1) or (1xN) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	55 % f is a (Nx1) or (1xN) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	56 % poles is a (Npx1) or (1xNp) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	57 % weight is a (Nx1) or (1xN) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	58 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	59 % OUTPUT
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	60 % res is a (Npx1) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	61 % poles is a (Npx1) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	62 % dterm is a constant
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	63 % mresp is a (Nx1) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	64 % rdl is a (Nx1) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	65 % mse is a constant
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	66 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	67 % - Fit Nt transfer function at the same time:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	68 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	69 % INPUT
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	70 % y is a (NxNt) or (NtxN) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	71 % f is a (Nx1) or (1xN) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	72 % poles is a (Npx1) or (1xNp) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	73 % weight is a (NxNt) or (NtxN) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	74 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	75 % OUTPUT
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	76 % res is a (NpxNt) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	77 % poles is a (Npx1) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	78 % dterm is a (1xNt) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	79 % mresp is a (NxNt) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	80 % rdl is a (NxNt) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	81 % mse is a (1xNt) vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	82 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	83 % REFERENCES:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	84 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	85 % [1] B. Gustavsen and A. Semlyen, "Rational approximation of frequency
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	86 % domain responses by Vector Fitting", IEEE Trans. Power Delivery
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	87 % vol. 14, no. 3, pp. 1052-1061, July 1999.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	88 % [2] B. Gustavsen, "Improving the Pole Relocating Properties of Vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	89 % Fitting", IEEE Trans. Power Delivery vol. 21, no. 3, pp.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	90 % 1587-1592, July 2006.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	91 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	92 % NOTE:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	93 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	94 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	95 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	96 % HISTORY: 12-09-2008 L Ferraioli
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	97 % Creation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	98 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	99 % VERSION: '$Id: vcfit.m,v 1.11 2010/02/08 19:05:59 luigi Exp $';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	100 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	101 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	102 function [res,poles,dterm,mresp,rdl,mse] = vcfit(y,f,poles,weight,fitin)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	103
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	104 warning off all
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	105 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	106 % Collecting inputs
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	107
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	108 % Default input struct
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	109 defaultparams = struct('stable',0, 'dterm',0, 'plot',0, 'ploth', 1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	110
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	111 names = {'stable','dterm','plot','ploth'};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	112
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	113 % collecting input and default params
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	114 if ~isempty(fitin)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	115 for jj=1:length(names)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	116 if isfield(fitin, names(jj)) && ~isempty(fitin.(names{1,jj}))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	117 defaultparams.(names{1,jj}) = fitin.(names{1,jj});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	118 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	119 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	120 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	121
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	122 stab = defaultparams.stable; % Enforce pole stability is is 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	123 dt = defaultparams.dterm; % 1 to fit with direct term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	124 plotting = defaultparams.plot; % set to 1 if plotting is required
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	125 plth = defaultparams.ploth; % set the figure target
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	126
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	127 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	128 % Inputs in row vectors
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	129
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	130 [a,b] = size(y);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	131 if a > b % shifting to row
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	132 y = y.';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	133 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	134
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	135 [a,b] = size(f);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	136 if a > b % shifting to row
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	137 f = f.';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	138 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	139
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	140 [a,b] = size(poles);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	141 if a > b % shifting to row
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	142 poles = poles.';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	143 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	144
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	145 clear w
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	146 w = weight;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	147 [a,b] = size(w);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	148 if a > b % shifting to row
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	149 w = w.';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	150 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	151
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	152 N = length(poles); % Model order
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	153
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	154 if dt
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	155 dl = 1; % Fit with direct term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	156 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	157 dl = 0; % Fit without direct term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	158 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	159
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	160 % definition of s
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	161 s = 1i.2.pi.*f;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	162
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	163 Nz = length(s);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	164 [Nc,Ny] = size(y);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	165 if Ny ~= Nz
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	166 error(' Number of data points different from number of frequency points! ')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	167 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	168
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	169 %Tolerances used by relaxed version of vector fitting
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	170 TOLlow=1e-8;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	171 TOLhigh=1e8;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	172
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	173 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	174 % Marking complex and real poles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	175
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	176 % cindex = 1; pole is complex, next conjugate pole is marked with cindex
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	177 % = 2. cindex = 0; pole is real
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	178 cindex=zeros(1,N);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	179 for m=1:N
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	180 if imag(poles(m))~=0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	181 if m==1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	182 cindex(m)=1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	183 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	184 if cindex(m-1)==0 \|\| cindex(m-1)==2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	185 cindex(m)=1; cindex(m+1)=2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	186 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	187 cindex(m)=2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	188 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	189 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	190 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	191 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	192
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	193 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	194 % Augmented problem
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	195 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	196
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	197 % Matrix initialinzation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	198 BA = zeros(Nc*Nz+1,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	199 Ak=zeros(Nz,N+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	200 AA=zeros(NzNc+1,(N+dl)Nc+N+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	201 nf = zeros(1,Nc*(N+dl)+N+1); % Normalization factor
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	202
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	203 % Defining Ak
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	204 for jj = 1:N
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	205 if cindex(jj) == 1 % conjugate complex couple of poles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	206 Ak(:,jj) = 1./(s-poles(jj)) + 1./(s-conj(poles(jj)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	207 Ak(:,jj+1) = 1i./(s-poles(jj)) - 1i./(s-conj(poles(jj)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	208 elseif cindex(jj) == 0 % real pole
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	209 Ak(:,jj) = 1./(s-poles(jj));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	210 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	211 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	212
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	213 Ak(1:Nz,N+1) = 1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	214
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	215 % Scaling factor
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	216 sc = 0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	217 for mm = 1:Nc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	218 sc = sc + (norm(w(mm,:).*y(mm,:)))^2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	219 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	220 sc=sqrt(sc)/Nz;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	221
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	222 for nn = 1:Nc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	223
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	224 wg = w(nn,:).'; % Weights
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	225
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	226 ida=(nn-1)*Nz+1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	227 idb=nn*Nz;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	228 idc=(nn-1)*(N+dl)+1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	229
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	230 for mm =1:N+dl % Diagonal blocks
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	231 AA(ida:idb,idc-1+mm) = wg.*Ak(1:Nz,mm);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	232 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	233 for mm =1:N+1 % Last right blocks
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	234 AA(ida:idb,Nc(N+dl)+mm) = -wg.(Ak(1:Nz,mm).*y(nn,1:Nz).');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	235 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	236
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	237 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	238
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	239 % setting the last row of AA and BA for the relaxion condition
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	240 for qq = 1:N+1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	241 AA(NcNz+1,Nc(N+dl)+qq) = real(sc*sum(Ak(:,qq)));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	242 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	243
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	244 AA = [real(AA);imag(AA)];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	245
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	246 % Last element of the solution vector
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	247 BA(NcNz+1) = Nzsc;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	248
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	249 xBA = real(BA);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	250 xxBA = imag(BA);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	251
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	252 Nrow = Nz*Nc+1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	253
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	254 BA = zeros(2*Nrow,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	255
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	256 BA(1:Nrow,1) = xBA;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	257 BA(Nrow+1:2*Nrow,1) = xxBA;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	258
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	259 % Normalization factor
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	260 % nf = zeros(2*N+dl+1,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	261 for pp = 1:length(AA(1,:))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	262 nf(pp) = norm(AA(:,pp),2); % Euclidean norm
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	263 AA(:,pp) = AA(:,pp)./nf(pp); % Normalization
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	264 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	265
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	266 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	267 % Solving augmented problem
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	268
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	269 % XA = pinv(AA)*BA;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	270 % XA = inv((AA.')AA)(AA.')*BA;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	271
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	272 % XA = AA.'AA\AA.'BA;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	273
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	274 XA = AA\BA;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	275
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	276 XA = XA./nf.'; % renormalization
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	277
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	278 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	279 % Checking the tolerance
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	280
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	281 if abs(XA(end))<TOLlow \|\| abs(XA(end))>TOLhigh
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	282
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	283 if XA(end)==0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	284 Dnew=1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	285 elseif abs(XA(end))<TOLlow
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	286 Dnew=sign(XA(end))*TOLlow;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	287 elseif abs(XA(end))>TOLhigh
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	288 Dnew=sign(XA(end))*TOLhigh;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	289 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	290
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	291 for pp = 1:length(AA(1,:))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	292 AA(:,pp) = AA(:,pp).*nf(pp); %removing previous scaling
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	293 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	294
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	295 ind=length(AA(:,1))/2; %index to additional row related to relaxation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	296
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	297 AA(ind,:)=[]; % removing relaxation term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	298
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	299 BA=-Dnew*AA(:,end); %new right side
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	300
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	301 AA(:,end)=[];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	302
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	303 nf(end)=[];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	304
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	305 for pp = 1:length(AA(1,:))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	306 nf(pp) = norm(AA(:,pp),2); % Euclidean norm
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	307 AA(:,pp) = AA(:,pp)./nf(pp); % Normalization
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	308 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	309
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	310 % XA=(AA.'AA)\(AA.'BA); % using normal equation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	311
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	312 XA=AA\BA;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	313
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	314 XA = XA./nf.'; % renormalization
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	315
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	316 XA=[XA;Dnew];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	317
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	318 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	319
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	320 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	321 % Finding zeros of sigma
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	322
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	323 lsr = XA((N+dl)Nc+1:(N+dl)Nc+N,1); % collect the least square results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	324
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	325 D = XA(end); % direct term of sigma
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	326
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	327 CPOLES = diag(poles);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	328 B = ones(N,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	329 C = lsr.';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	330
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	331 for kk = 1:N
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	332 if cindex(kk) == 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	333 CPOLES(kk,kk)=real(poles(kk));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	334 CPOLES(kk,kk+1)=imag(poles(kk));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	335 CPOLES(kk+1,kk)=-1*imag(poles(kk));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	336 CPOLES(kk+1,kk+1)=real(poles(kk));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	337 B(kk,1) = 2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	338 B(kk+1,1) = 0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	339 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	340 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	341
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	342 H = CPOLES-B*C/D;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	343
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	344 szeros=eig(H);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	345
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	346 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	347 % Ruling out unstable poles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	348
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	349 % This option force the poles of f to stay inside the left side of the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	350 % complex plane
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	351
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	352 if stab
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	353 unst = real(szeros)>0;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	354 szeros(unst) = szeros(unst)-2*real(szeros(unst)); % Mirroring respect to the complex axes
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	355 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	356 szeros = sort(szeros);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	357 N = length(szeros);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	358
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	359 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	360 % Separating complex poles from real poles and ordering
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	361
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	362 rnpoles = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	363 inpoles = [];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	364 for tt = 1:N
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	365 if imag(szeros(tt)) == 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	366 % collecting real poles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	367 rnpoles = [rnpoles; szeros(tt)];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	368 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	369 % collecting complex poles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	370 inpoles = [inpoles; szeros(tt)];
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 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	373
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	374 % Sorting complex poles in order to have them in the expected order a+jb
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	375 % and a-jb a>0 b>0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	376 inpoles = sort(inpoles);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	377 npoles = [rnpoles;inpoles];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	378 npoles = npoles - 2.1i.imag(npoles);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	379
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	380 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	381 % Marking complex and real poles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	382
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	383 cindex=zeros(N,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	384 for m=1:N
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	385 if imag(npoles(m))~=0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	386 if m==1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	387 cindex(m)=1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	388 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	389 if cindex(m-1)==0 \|\| cindex(m-1)==2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	390 cindex(m)=1; cindex(m+1)=2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	391 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	392 cindex(m)=2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	393 end
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 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	396 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	397
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	398 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	399 % Direct problem
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	400 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	401
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	402 % Matrix initialinzation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	403 nB(1:Nz,1:Nc) = real(w.*y).';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	404 nB(Nz+1:2Nz,1:Nc) = imag(w.y).';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	405
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	406 B = zeros(2*Nz,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	407 nAD = zeros(Nz,N+dl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	408 AD = zeros(2*Nz,N+dl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	409 Ak = zeros(Nz,N+dl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	410
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	411 % Defining Ak
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	412 for jj = 1:N
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	413 if cindex(jj) == 1 % conjugate complex couple of poles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	414 Ak(:,jj) = 1./(s-npoles(jj)) + 1./(s-npoles(jj+1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	415 Ak(:,jj+1) = 1i./(s-npoles(jj)) - 1i./(s-npoles(jj+1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	416 elseif cindex(jj) == 0 % real pole
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	417 Ak(:,jj) = 1./(s-npoles(jj));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	418 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	419 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	420
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	421 if dt
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	422 Ak(1:Nz,N+dl) = ones(Nz,1); % considering the direct term
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	423 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	424
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	425 XX = zeros(Nc,N+dl);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	426 for nn = 1:Nc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	427
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	428 % Defining AD
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	429 for m=1:N+dl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	430 nAD(1:Nz,m) = w(nn,:).'.*Ak(1:Nz,m);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	431 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	432
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	433 B(1:2Nz,1) = nB(1:2Nz,nn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	434
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	435 AD(1:Nz,:) = real(nAD);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	436 AD(Nz+1:2*Nz,:) = imag(nAD);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	437
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	438 % Normalization factor
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	439 nf = zeros(N+dl,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	440 for pp = 1:N+dl
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	441 nf(pp,1) = norm(AD(:,pp),2); % Euclidean norm
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	442 AD(:,pp) = AD(:,pp)./nf(pp,1); % Normalization
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
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	445 % Solving direct problem
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	446
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	447 % XD = inv((AD.')AD)(AD.')*B;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	448 % XD = AD.'AD\AD.'B;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	449 % XD = pinv(AD)*B;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	450 XD = AD\B;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	451
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	452 XD = XD./nf; % Renormalization
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	453
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	454 XX(nn,1:N) = XD(1:N).';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	455
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
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	458 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	459 % Final residues and poles of f
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	460
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	461 lsr = XX(:,1:N);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	462
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	463 res = zeros(N,Nc);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	464 % Real poles have real residues, complex poles have comples residues
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	465 for nn = 1:Nc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	466 for tt = 1:N
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	467 if cindex(tt) == 1 % conjugate complex couple of poles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	468 res(tt,nn) = lsr(nn,tt)+1i*lsr(nn,tt+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	469 res(tt+1,nn) = lsr(nn,tt)-1i*lsr(nn,tt+1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	470 elseif cindex(tt) == 0 % real pole
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	471 res(tt,nn) = lsr(nn,tt);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	472 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	473 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	474 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	475
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	476 poles = npoles;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	477
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	478 if dt
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	479 dterm = XX(:,N+dl).';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	480 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	481 dterm = zeros(1,Nc);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	482 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	483
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	484 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	485 % Calculating responses and residuals
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	486
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	487 mresp = zeros(Nz,Nc);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	488 rdl = zeros(Nz,Nc);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	489 mse = zeros(1,Nc);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	490
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	491 for nn = 1:Nc
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	492 % freq resp of the fit model
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	493 r = res(:,nn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	494 p = poles;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	495 d = dterm(:,nn);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	496
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	497 Nf = length(f);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	498 N = length(p);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	499
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	500 rsp = zeros(Nf,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	501 indx = (0:length(d)-1).';
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	502 for ii = 1:Nf
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	503 for jj = 1:N
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	504 rsptemp = r(jj)/(1i2pi*f(ii)-p(jj));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	505 rsp(ii) = rsp(ii) + rsptemp;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	506 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	507 % Direct terms response
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	508 rsp(ii) = rsp(ii) + sum((((1i2pif(ii))ones(length(d),1)).^indx).*d);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	509 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	510
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	511 % Model response
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	512 mresp(:,nn) = rsp;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	513
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	514 % Residual
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	515 rdl(:,nn) = y(nn,:).' - rsp;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	516
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	517 % RMS error
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	518 % mse(:,nn) = sqrt(sum((abs(rdl(:,nn)./(y(nn,:).')).^2))/(Nf-N));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	519 % Chi Square or mean squared error
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	520 % Note that this error is normalized to the input data in order to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	521 % comparable between different sets of data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	522 mse(:,nn) = sum((rdl(:,nn)./y(nn,:).').*conj((rdl(:,nn)./y(nn,:).')))/(Nf-N);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	523
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	524 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	525
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	526 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	527 % Plotting response
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	528
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	529 switch plotting
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	530
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	531 case 0
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	532 % No plot
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	533
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	534 case 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	535 % LogLog plot for absolute value
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	536 figure(plth)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	537 subplot(2,1,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	538 p1 = loglog(f,abs(y.'),'k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	539 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	540 p2 = loglog(f,abs(mresp),'r');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	541 p3 = loglog(f,abs(rdl),'b');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	542 xlabel('Frequency [Hz]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	543 ylabel('Amplitude')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	544 legend([p1(1) p2(1) p3(1)],'Original', 'VCFIT','Residual')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	545 hold off
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	546
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	547 subplot(2,1,2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	548 p4 = semilogx(f,(180/pi).*unwrap(angle(y.')),'k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	549 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	550 p5 = semilogx(f,(180/pi).*unwrap(angle(mresp)),'r');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	551 xlabel('Frequency [Hz]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	552 ylabel('Phase [Deg]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	553 legend([p4(1) p5(1)],'Original', 'VCFIT')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	554 hold off
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	555
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	556 case 2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	557 % Semilogx plot for absolute value
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	558 figure(plth)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	559 subplot(2,1,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	560 p1 = semilogx(f,abs(y.'),'k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	561 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	562 p2 = semilogx(f,abs(mresp),'r');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	563 p3 = semilogx(f,abs(rdl),'b');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	564 xlabel('Frequency [Hz]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	565 ylabel('Amplitude')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	566 legend([p1(1) p2(1) p3(1)],'Original', 'VCFIT','Residual')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	567 hold off
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	568
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	569 subplot(2,1,2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	570 p4 = semilogx(f,(180/pi).*unwrap(angle(y.')),'k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	571 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	572 p5 = semilogx(f,(180/pi).*unwrap(angle(mresp)),'r');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	573 xlabel('Frequency [Hz]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	574 ylabel('Phase [Deg]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	575 legend([p4(1) p5(1)],'Original', 'VCFIT')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	576 hold off
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	577
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	578 case 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	579 % Semilogy plot for absolute value
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	580 figure(plth)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	581 subplot(2,1,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	582 p1 = semilogy(f,abs(y.'),'k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	583 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	584 p2 = semilogy(f,abs(mresp),'r');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	585 p3 = semilogy(f,abs(rdl),'b');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	586 xlabel('Frequency [Hz]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	587 ylabel('Amplitude')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	588 legend([p1(1) p2(1) p3(1)],'Original', 'VCFIT','Residual')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	589 hold off
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	590
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	591 subplot(2,1,2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	592 p4 = semilogy(f,(180/pi).*unwrap(angle(y.')),'k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	593 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	594 p5 = semilogy(f,(180/pi).*unwrap(angle(mresp)),'r');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	595 xlabel('Frequency [Hz]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	596 ylabel('Phase [Deg]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	597 legend([p4(1) p5(1)],'Original', 'VCFIT')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	598 hold off
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	599
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	600 case 4
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	601 % Linear plot for absolute value
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	602 figure(plth)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	603 subplot(2,1,1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	604 p1 = plot(f,abs(y.'),'k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	605 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	606 p2 = plot(f,abs(mresp),'r');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	607 p3 = plot(f,abs(rdl),'b');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	608 xlabel('Frequency [Hz]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	609 ylabel('Amplitude')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	610 legend([p1(1) p2(1) p3(1)],'Original', 'VCFIT','Residual')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	611 hold off
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	612
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	613 subplot(2,1,2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	614 p4 = plot(f,(180/pi).*unwrap(angle(y.')),'k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	615 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	616 p5 = plot(f,(180/pi).*unwrap(angle(mresp)),'r');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	617 xlabel('Frequency [Hz]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	618 ylabel('Phase [Deg]')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	619 legend([p4(1) p5(1)],'Original', 'VCFIT')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	620 hold off
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	621
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	622 end

Mercurial > hg > ltpda

annotate m-toolbox/classes/+utils/@math/vcfit.m @ 51:9d5c88356247 database-connection-manager