line source
+ − % GAPFILLINGOPTIM fills possible gaps in data.
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − %
+ − % DESCRIPTION: GAPFILLINGOPTIM minimizes a chi square based on the signal's
+ − % expected PSD. It uses ao/optSubtraction for the small scale
+ − % algorithm, optSubstitution for the large scale algorithm.
+ − %
+ − % CALL: [aoGapsFilled, plOut, aoP, aoPini, aoWindow, aoWindowShift] = ao.gapfilling(plist)
+ − %
+ − % INPUTS: ao_data - data segment with the signal to reconstitue
+ − % pl - parameter list
+ − %
+ − % OUTPUTS: aoGapsFilled - data segment containing ao_data, with filled data gaps
+ − % plOut - output plist containing the output of
+ − % gapFillingOptim
+ − % aoP, aoPini - final and initial frequency PSD used to weight
+ − % the optimal problem
+ − % aoWindow - window used for estmating spectrum
+ − % aoWindowShift - shifted window used for optimizing spectrum
+ − %
+ − % <a href="matlab:utils.helper.displayMethodInfo('ao', 'gapfillingoptim')">Parameters Description</a>
+ − %
+ − % VERSION: $Id: gapfillingoptim.m,v 1.27 2011/06/11 14:11:27 adrien Exp $
+ − %
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ −
+ − function varargout = gapfillingoptim(varargin)
+ − % y ycalib fs isgap iscalib freq_weight ncalib ndata nfft ngaps
+ − %%% Check if this is a call for parameters
+ − if utils.helper.isinfocall(varargin{:})
+ − varargout{1} = getInfo(varargin{3});
+ − return
+ − end
+ −
+ − %% Collect input variable names
+ − in_names = cell(size(varargin));
+ − for ii = 1:nargin,in_names{ii} = inputname(ii);end
+ −
+ − % Collect all AOs
+ − [aos, ao_invars] = utils.helper.collect_objects(varargin(:), 'ao', in_names);
+ − pli = utils.helper.collect_objects(varargin(:), 'plist', in_names);
+ −
+ − % Get default parameters
+ − pl = combine(pli, getDefaultPlist);
+ −
+ − %% declaring global optData variable
+ − clear global optData
+ − global optData
+ −
+ − %% getting time-series to fill, and usefull data (frequencies, number of frequencies... )
+ − if numel(aos)==0
+ − error('Nothing to fill gaps!')
+ − elseif numel(aos)>1
+ − error('The filling algorithm only works for one single signal at a time')
+ − end
+ − optData.nData = numel(aos.y);
+ − optData.yNorm = norm(aos.y) / optData.nData;
+ − optData.y = aos.y / optData.yNorm;
+ − optData.Ts = 1/aos(1).fs;
+ − optData.nFreqs = floor(optData.nData/2)+1;
+ − optData.freqs = linspace(0, 1/(2*optData.Ts), optData.nFreqs);
+ − optData.keepFreqs = [true(1,sum(optData.nFreqs)) false(1,sum(optData.nFreqs)-1)];
+ −
+ − %% finding gaps
+ − aoGaps = pl.find('isgap');
+ − if isempty(aoGaps)
+ − error('no gap vector provided!')
+ − elseif isequal(aoGaps,'zeros')
+ − optData.isGap = (aos.y==0);
+ − elseif numel(isempty(aoGaps))>1
+ − error('please provide only one gap vector!')
+ − elseif isa(aoGaps.y, 'double')
+ − optData.isGap = (aoGaps.y==0);
+ − elseif isa(aoGaps.y, 'logical')
+ − optData.isGap = aoGaps.y;
+ − else
+ − error('wrong type for parameter "isGap"')
+ − end
+ − optData.gapsPos = find(optData.isGap);
+ − optData.nGaps = numel(optData.gapsPos);
+ − clear aoGaps
+ −
+ − %% checking number of gaps is not zero
+ − if numel(optData.gapsPos)==0
+ − error('No gap to fill!')
+ − end
+ − if numel(optData.isGap) ~= optData.nData
+ − error('gap vector is not the same length as the gapped vector!')
+ − end
+ −
+ − %% produce LF window
+ − Win = find(pl, 'Win');
+ − if isa(Win, 'plist')
+ − Win = ao( combine(plist( 'length', optData.nData), Win) );
+ − optData.lfWin = Win.y;
+ − elseif isa(Win, 'ao')
+ − if ~isa(Win.data, 'tsdata')
+ − error('An ao window should be a time series')
+ − end
+ − optData.lfWin = Win.y;
+ − if ~length(optData.lfWin)==optData.nData
+ − error('signals and windows don''t have the same length')
+ − end
+ − else
+ − error('input option Win is not acceptable (not a plist nor an ao)!')
+ − end
+ −
+ − %% produce HF window
+ − [shiftVals, shiftCounts, winHF, winsHfShift] = makeHFWindows(optData.nData, optData.gapsPos);
+ − optData.nShifts = numel(shiftVals);
+ − optData.shiftVals = shiftVals;
+ − optData.shiftCounts = shiftCounts;
+ − optData.hfWin = winHF;
+ − optData.win = optData.lfWin .* optData.hfWin;
+ − optData.winsHfShift = winsHfShift;
+ − optData.winsShift = winsHfShift;
+ − for iiShift = 1:(2*optData.nShifts)
+ − optData.winsShift(:, iiShift) = optData.winsHfShift(:, iiShift) .* optData.lfWin;
+ − end
+ − clear shiftVals shiftCounts winHF winsHfShift
+ −
+ − %% get initial M coefficient matrix
+ − M = pl.find('coefs');
+ − if isempty(M)
+ − M = zeros(1,optData.nGaps);
+ − end
+ −
+ − %% detrending (with a windowing agains HF noise)
+ − trends = [ones(optData.nData,1) linspace(-1,1,optData.nData).' ]; % two orthogonal vectors to subtract
+ − trendsWindowed = trends .* [optData.win optData.win]; % windowing is applied to estimate trends
+ − yWindowed = optData.y .* optData.win; % windowing is applied to de-trened data to be consistent
+ − optData.trend = pinv(trendsWindowed) * yWindowed; % solution of the least-square problem
+ − trendCorrection = trends * optData.trend; % trend is removed from the data while filling gaps. It is re-added later on.
+ − optData.y = optData.y - trendCorrection; % detrended vector
+ − optData.y(optData.gapsPos) = zeros(size(optData.gapsPos)); % setting to zero the gap-data
+ −
+ − %% get sPSD averaging linear-scaling averaging-width coefficient
+ − optData.linCoef = pl.find('linCoef');
+ − optData.logCoef = pl.find('logCoef');
+ −
+ − %% get MAX/EXP iterations termination conditions
+ − iterMax = pl.find('iterMax');
+ − optData.criterion = pl.find('fitCriterion');
+ − normCriterion = pl.find('normCriterion');
+ − normCoefs = pl.find('normCoefs');
+ −
+ − %% set optim CVG options
+ − options.MaxFunEvals = pl.find('maxCall');
+ − options.Display = pl.find('display');
+ − options.TolFun = min( pl.find('normCriterion'), 1e-12 );
+ − options.TolX = min( pl.find('normCoefs'), 1e-14 );
+ − options.MaxIter = pl.find('maxCall');
+ − doHessian = pl.find('Hessian');
+ − if ~isempty(doHessian)
+ − error('Hessian option is now deactivated as it is too demanding computationaly')
+ − end
+ −
+ − %% computing various useful quantities used for the criterion computation
+ − weightingMethod =pl.find('weightingMethod');
+ − switch weightingMethod
+ − case 'pzmodel'
+ − weightModel = pl.find('pzmodelWeight');
+ − if numel(weightModel) ~= 1
+ − error('there should be only one pzmodel')
+ − end
+ − weight = weightModel.resp(optData.freqs);
+ − weight = abs(weight).^2;
+ − Ploc = weight.y;
+ − [freqsAvg, pAvg, nFreqsAvg, nDofs, sumMat] = ltpda_spsd(optData.freqs, Ploc, optData.linCoef, optData.logCoef); %#ok<ASGLU>
+ − case 'ao'
+ − weight =pl.find('aoWeight');
+ − if numel(weight)~=1
+ − error('there should be as many pzmodels as weighted entries')
+ − end
+ − if ~isa(weight.data, 'tsdata')
+ − error('if the weight is an ao, it should be a FSdata')
+ − elseif length(weight.y)==optData.nFreqs
+ − error(['length of FS weight is not length of the FFT vector : ' num2str(length(weight.y)) 'instead of ' num2str(optData.nFreqs)])
+ − else
+ − Ploc = weight.y;
+ − [freqsAvg, pAvg, nFreqsAvg, nDofs, sumMat] = ltpda_spsd(optData.freqs, Ploc, optData.linCoef, optData.logCoef); %#ok<ASGLU>
+ − end
+ − case 'residual'
+ − [pAvg, freqsAvg, powSigma, sumMat, nFreqsAvg ] = computeWeight( optData.y, M, optData.gapsPos, optData.freqs);
+ − otherwise
+ − error('weighting method requested does not exist!')
+ − end
+ −
+ − %% Maximization Expectation iteration loop
+ − for i_iter = 1:iterMax
+ − utils.helper.msg(utils.const.msg.PROC3, ['starting iteration ', num2str(i_iter)]);
+ −
+ − %% setting weight in optData
+ − optData.sumMat = sumMat;
+ − optData.nFreqsAvg = nFreqsAvg;
+ − optData.powInv = pAvg.^-1;
+ − optData.logProbaDensityFactor = - nFreqsAvg * log(2) - gammaln(nFreqsAvg);
+ −
+ − %% initializing historical outputs
+ − if i_iter==1 % storing intial weight
+ − Pini = pAvg;
+ − MHist(1,:) = reshape(M, [1, numel(M)] );
+ − end
+ − fValIni = optimalCriterion(M);
+ −
+ − %% minimizing the criterion
+ − switch lower(optData.criterion)
+ − case 'ftest'
+ − M = solveProblemFTest( optData.gapsPos, optData.powInv, optData.nFreqsAvg); % very fast direct solver in this case
+ − fval = optimalCriterion(M);
+ − case 'ftest-nohfwin'
+ − M = solveProblemFTestNoHFWin( optData.gapsPos, optData.powInv, optData.nFreqsAvg); % very fast direct solver in this case
+ − fval = optimalCriterion(M);
+ − otherwise
+ − M = solveProblemFTest( optData.gapsPos, optData.powInv, optData.nFreqsAvg); % initialize with fast solver (with the wrong criterion, but it doesn't matter so much)
+ − [M, fval] = fminunc(@optimalCriterion,M,options); % further non-linear minimzation steps with correct criterion
+ − end
+ −
+ − %% updating weight
+ − [pAvg, freqsAvg] = computeWeight(optData.y, M, optData.gapsPos, optData.freqs);
+ −
+ − %% store history
+ − fValHist(i_iter) = fval/fValIni; %#ok<AGROW>
+ − MHist(i_iter+1,:) = reshape(M, [1, numel(M)] ); %#ok<AGROW>
+ −
+ − %% deciding whether to pursue or not ME (=bootstrap) iterations
+ − if strcmpi( weightingMethod, 'pzmodel')
+ − display('One iteration for Pzmodel weighting only')
+ − break
+ − elseif strcmpi( weightingMethod, 'ao')
+ − display('One iteration for ao weighting only')
+ − break
+ − elseif norm(fValHist(i_iter)-1) < normCriterion
+ − display(['Iterations stopped at iteration ' num2str(i_iter) ' because criterion did not make enough progress (see parameter "normCriterion")'])
+ − break
+ − elseif i_iter == iterMax
+ − display(['Iterations stopped at maximum number of iterations ' num2str(i_iter) ' (see parameter "iterMax")'])
+ − break
+ − elseif norm(MHist(i_iter+1,:)-MHist(i_iter,:))<normCoefs
+ − display(['Iterations stopped at iteration ' num2str(i_iter) ' because parameters did not make enough progress (see parameter "normCoefs")'])
+ − break
+ − end
+ − end % ending loop over MAX/EXP iterations
+ −
+ − %% creating output plist
+ − plOut = plist;
+ − p = param({ 'criterion' , 'last value of the criterion in the last optimization'}, fval );
+ − plOut.append(p);
+ − p = param({ 'M' , 'Best fitting value'}, (M + trendCorrection(optData.gapsPos).') * optData.yNorm );
+ − plOut.append(p);
+ −
+ − %% creating output aos for weights
+ − aoP = ao( fsdata(freqsAvg, pAvg * (optData.yNorm^2 * optData.Ts / optData.nData) ) );
+ − aoP.setName('final weight');
+ − aoP.setXunits('Hz');
+ − aoP.setYunits(aos.yunits^2 * unit('Hz^-1'));
+ − aoP.setDescription(['final weight for gap-filling after ' num2str(i_iter) ' iterations (identical to )']);
+ − aoP.setT0(aos.t0);
+ −
+ − aoPini = ao( fsdata(freqsAvg, Pini * (optData.yNorm^2 * optData.Ts / optData.nData) ) );
+ − aoPini.setName('initial weight');
+ − aoPini.setXunits('Hz');
+ − aoPini.setYunits(aos.yunits^2 * unit('Hz^-1'));
+ − aoPini.setDescription(['initial weight for gap-filling']);
+ − aoPini.setT0(aos.t0);
+ −
+ − %% creating filled output
+ − aoGapsFilled = ao( plist('yvals', ( trendCorrection + substitution( optData.y, M, optData.gapsPos)) * optData.yNorm, 'fs', 1/optData.Ts, 'type', 'tsdata' ));
+ − aoGapsFilled.setName('filled time-series');
+ − aoGapsFilled.setXunits('s');
+ − aoGapsFilled.setYunits(aos.yunits);
+ − aoGapsFilled.setDescription(['Filled time-series using the criteiron: ' optData.criterion ]);
+ − aoGapsFilled.setT0(aos.t0);
+ − aoGapsFilled.addHistory( getInfo('None'), pl , ao_invars, aos.hist );
+ −
+ − %% creating output windows
+ − aoWindow = ao( plist('yvals', optData.win, 'fs', 1/optData.Ts, 'type', 'tsdata' ));
+ − aoWindow.setName('initial window used to evaluate the spectrum');
+ − aoWindow.setXunits('s');
+ − aoWindow.setT0(aos.t0);
+ − aoWindow.addHistory( getInfo('None'), pl , ao_invars, aos.hist );
+ −
+ − if strcmpi(optData.criterion,'FTest-NoHfWin')
+ − aoWindowShift = ao( plist('yvals', optData.lfWin, 'fs', 1/optData.Ts, 'type', 'tsdata' ));
+ − else
+ − aoWindowShift = ao( plist('yvals', optData.winsShift(:, 1) , 'fs', 1/optData.Ts, 'type', 'tsdata' ));
+ − end
+ − aoWindowShift.setName('window used to optimize the spectrum');
+ − aoWindowShift.setXunits('s');
+ − aoWindowShift.setDescription(['one of the ' num2str(optData.nShifts) ' windows involved in the criterion']);
+ − aoWindowShift.setT0(aos.t0);
+ − aoWindowShift.addHistory( getInfo('None'), pl , ao_invars, aos.hist );
+ −
+ − %% assigning output
+ − varargout = {aoGapsFilled, plOut, aoP, aoPini, aoWindow, aoWindowShift};
+ −
+ − %% clearing optData from global workspace
+ − clear global optData
+ −
+ − end
+ −
+ − %% usefull function to compute the weights from the residual
+ − function [powAvgs, freqsAvg, powStd, sumMat, nFreqsAvg] = computeWeight(Y, M, gapsPos, freqs)
+ − global optData
+ − yFilled = substitution( Y, M, gapsPos);
+ − if strcmpi(optData.criterion,'FTest-NoHfWin')
+ − win = optData.lfWin;
+ − else
+ − win = optData.win;
+ − end
+ − errDft = fft( yFilled .* win, optData.nData);
+ − errDft = errDft(optData.keepFreqs); % removing aliased frequencies
+ − pow = imag(errDft).^2 + real(errDft).^2; % power
+ −
+ − [freqsAvg, powAvgs, nFreqsAvg, nDofs, sumMat] = ltpda_spsd(freqs, pow, optData.linCoef, optData.logCoef);
+ − powStd = powAvgs./sqrt(nDofs);
+ − end
+ −
+ − %% optimal criterion
+ − function j = optimalCriterion(M)
+ − global optData
+ − j = 0;
+ − yFilled = substitution(optData.y, M, optData.gapsPos);
+ − if strcmpi(optData.criterion, 'FTest-NoHfWin')
+ − errDft = fft( yFilled .* optData.lfWin, optData.nData); % FFT algirthm gets DFT, only a LF window is used here
+ − errDft = errDft(optData.keepFreqs); % keeping positive frequencies
+ − pow = imag(errDft).^2 + real(errDft).^2; % PSD of signal
+ − powSum = optData.sumMat * pow; % binning frequencies as in sPSD
+ − j = sum( powSum .* optData.powInv ); % summing FTest
+ − elseif strcmpi(optData.criterion, 'FTest')
+ − for iiWin=1:numel(optData.nShifts)
+ − for iiDirection = [0 1] % positive/negative window shift
+ − errDft = fft( yFilled .* optData.winsShift(:, 2*iiWin-1+iiDirection), optData.nData); % FFT algirthm gets DFT
+ − errDft = errDft(optData.keepFreqs); % keeping positive frequencies
+ − pow = imag(errDft).^2 + real(errDft).^2; % PSD of signal
+ − powSum = optData.sumMat * pow; % binning frequencies as in sPSD
+ − j = j + sum( powSum .* optData.powInv ) * optData.shiftCounts(iiWin);
+ − end
+ − end
+ − elseif strcmpi(optData.criterion, 'Chi2')
+ − for iiWin=1:numel(optData.nShifts)
+ − for iiDirection = [0 1] % positive/negative window shift
+ − errDft = fft( yFilled .* optData.winsShift(:, 2*iiWin-1+iiDirection), optData.nData); % FFT algirthm gets DFT
+ − errDft = errDft(optData.keepFreqs); % keeping positive frequencies
+ − pow = imag(errDft).^2 + real(errDft).^2; % PSD of signal
+ − powSum = optData.sumMat * pow; % binning frequencies as in sPSD
+ − normlzChi2Sum = (2*powSum) .* optData.powInv; % divide the sum by the expected average of each terms, so the chi2 is normalized
+ − logProbaDensities = optData.logProbaDensityFactor + (optData.nFreqsAvg-1).*log(normlzChi2Sum) - normlzChi2Sum/2 ; % here computing log of probability
+ − j = j - sum(logProbaDensities); % better than taking product of probabilities
+ − end
+ − end
+ − else
+ − error(['criterion badly specified' optData.criterion])
+ − end
+ − end
+ −
+ − %% function subtituting gaps in time-series
+ − function Y = substitution( Y, M, gapsPos)
+ − Y(gapsPos) = M;
+ − end
+ −
+ − %% Direct solver for "FTest" quadratic criterion
+ − function [M, hessian] = solveProblemFTest( gapsPos, powAvgInv, nFreqsAvg)
+ − global optData
+ − computeDuration = 1.3e-8 * 2 * optData.nShifts * numel(gapsPos)^2 * sum(nFreqsAvg);
+ − display(['expected time for linear solver: ' num2str(computeDuration) 's'])
+ − gapsPhase = exp( -1i*2*pi * (gapsPos-1)/numel(optData.y) ); % FFT value of a gap sample at base frequency
+ − nGaps = numel(gapsPos); % number of gaps
+ − nAvgs = numel(nFreqsAvg); % number of frequency bins
+ − B = zeros(nGaps,1);
+ − A = zeros(nGaps,nGaps);
+ − %% frequency weighted criterion
+ − for iiWin=1:numel(optData.nShifts) % loop on different shifts for HF window
+ − for iiDirection = [0 1] % positive/negative window shift
+ − W = optData.winsShift(:, 2*iiWin-1+iiDirection);
+ − errDft = fft( optData.y .* W, optData.nData); % FFT algirthm gets DFT
+ − errDft = errDft(optData.keepFreqs); % keeping positive frequencies
+ − gapsAmplitude = W(gapsPos); % amplitude of gaps once windowed
+ − gapsPhaseAtFreq = gapsPhase.^0; % FTF at fundamental : it is only the mean value
+ − iiFreq = 0; % frequency (before averaging with binning)
+ − for iiFreqAvg = 1:nAvgs % loop on frequency bins
+ − BLocal = zeros(nGaps,1);
+ − ALocal = zeros(nGaps,nGaps);
+ − for iiFreqInAvg = 1:nFreqsAvg(iiFreqAvg) % loop on frequencies inside frequency bin
+ − iiFreq = iiFreq + 1; % current frequency index (starting with 1!)
+ − gapDFT = reshape( gapsAmplitude .* gapsPhaseAtFreq , [nGaps,1]); % DFT of each windowed gap data at the frequency number iiFreq-1
+ − % gapDFT = reshape( gapsAmplitude .* gapsPhase.^(iiFreq-1) , [nGaps,1]); % DFT of each windowed gap data at the frequency number iiFreq-1
+ − gapsPhaseAtFreq = gapsPhaseAtFreq .* gapsPhase; % updating phase for future DFT samples at next frequency
+ − BLocal = BLocal + 2 * real( gapDFT * conj(errDft(iiFreq)) );
+ − ALocal = ALocal + 2 * real( gapDFT * gapDFT' );
+ − end
+ − B = B + BLocal * powAvgInv(iiFreqAvg);
+ − A = A + ALocal * powAvgInv(iiFreqAvg);
+ − end
+ − end
+ − end
+ − M = (-pinv(A)*B) .'; % solving least-square problem A*M+B=0
+ − hessian = A; % this is also the hessian of my criterion
+ − end
+ −
+ − %% Direct solver for "FTest" quadratic criterion with no windowing on each gap
+ − function [M, hessian] = solveProblemFTestNoHFWin( gapsPos, powAvgInv, nFreqsAvg)
+ − global optData
+ − computeDuration = 1.3e-8 * numel(gapsPos)^2 * sum(nFreqsAvg);
+ − display(['expected time for linear solver: ' num2str(computeDuration) 's'])
+ − gapsPhase = exp( -1i*2*pi * (gapsPos-1)/numel(optData.y) ); % FFT value of a gap sample at base frequency
+ − nGaps = numel(gapsPos); % number of gaps
+ − nAvgs = numel(nFreqsAvg); % number of frequency bins
+ − B = zeros(nGaps,1);
+ − A = zeros(nGaps,nGaps);
+ − %% frequency weighted criterion
+ − if strcmpi(optData.criterion, 'FTest-NoHfWin') % retrieving corresponding window
+ − W = optData.lfWin;
+ − else
+ − W = optData.winsShift(:, 2*iiWin-1+iiDirection);
+ − end
+ − errDft = fft( optData.y .* W, optData.nData); % FFT algirthm gets DFT
+ − errDft = errDft(optData.keepFreqs); % keeping positive frequencies
+ − gapsAmplitude = W(gapsPos); % amplitude of gaps once windowed
+ − gapsPhaseAtFreq = gapsPhase.^0; % FTF at fundamental : it is only the mean value
+ − iiFreq = 0; % frequency (before averaging with binning)
+ − for iiFreqAvg = 1:nAvgs % loop on frequency bins
+ − BLocal = zeros(nGaps,1);
+ − ALocal = zeros(nGaps,nGaps);
+ − for iiFreqInAvg = 1:nFreqsAvg(iiFreqAvg) % loop on frequencies inside frequency bin
+ − iiFreq = iiFreq + 1; % current frequency index (starting with 1!)
+ − gapDFT = reshape( gapsAmplitude .* gapsPhaseAtFreq , [nGaps,1]); % DFT of each windowed gap data at the frequency number iiFreq-1
+ − % gapDFT = reshape( gapsAmplitude .* gapsPhase.^(iiFreq-1) , [nGaps,1]); % DFT of each windowed gap data at the frequency number iiFreq-1
+ − gapsPhaseAtFreq = gapsPhaseAtFreq .* gapsPhase; % updating phase for future DFT samples at next frequency
+ − BLocal = BLocal + 2 * real( gapDFT * conj(errDft(iiFreq)) );
+ − ALocal = ALocal + 2 * real( gapDFT * gapDFT' );
+ − end
+ − B = B + BLocal * powAvgInv(iiFreqAvg);
+ − A = A + ALocal * powAvgInv(iiFreqAvg);
+ − end
+ − M = (-pinv(A)*B) .'; % solving least-square problem A*M+B=0
+ − hessian = A; % this is also the hessian of my criterion
+ − end
+ −
+ − %% function computing the high-frequency window and all its shifted components
+ − function [shiftVals, shiftCounts, winHF, winsHfShift] = makeHFWindows(ndata, gapsPos)
+ − gapsPos = [1; gapsPos; ndata];
+ − diffGapsPos = diff(gapsPos); % distance between consecutive gaps
+ − %% detecting segments and corresponding lengths
+ − beginSegments = gapsPos([diffGapsPos>1; false])+1;
+ − endSegments = gapsPos([false; diffGapsPos>1])-1;
+ − segmentsLength = endSegments-beginSegments+1;
+ − %% statitstics on segment (half) length
+ − timeShifts = floor(segmentsLength/2); % windows will be shifted by +/- half a segment
+ − [shiftCounts, shiftVals] = hist(timeShifts, 1:ndata);
+ − shiftVals = shiftVals(shiftCounts>0);
+ − shiftCounts = shiftCounts(shiftCounts>0);
+ − %% making main window
+ − winHF = zeros(ndata,1);
+ − for iiSegment=1:numel(segmentsLength) % a window for each segment
+ − phaseLocal = linspace(0, 2*pi, segmentsLength(iiSegment)+2).'; % building phase vector
+ − winLocal = 0.5 * (1 - cos(phaseLocal)); % making window
+ − winHF(beginSegments(iiSegment):endSegments(iiSegment)) = winLocal( 2:end-1 ); % assigning window to corresponding segment
+ − end
+ − %% making all time-shifted windows
+ − winsHfShift = zeros( ndata, 2*numel(shiftVals) );
+ − for iiShift=1:numel(shiftVals)
+ − winsHfShift(:, 2*iiShift-1) = circshift(winHF, shiftVals(iiShift)).';
+ − winsHfShift(:, 2*iiShift) = circshift(winHF, -shiftVals(iiShift)).';
+ − end
+ − end
+ −
+ − %--------------------------------------------------------------------------
+ − % Get Info Object
+ − %--------------------------------------------------------------------------
+ − function ii = getInfo(varargin)
+ − if nargin == 1 && strcmpi(varargin{1}, 'None')
+ − sets = {};
+ − pls = [];
+ − else
+ − sets = {'Default'};
+ − pls = getDefaultPlist;
+ − end
+ − % Build info object
+ − ii = minfo(mfilename, 'ao', 'ltpda', utils.const.categories.sigproc, '$Id: gapfillingoptim.m,v 1.27 2011/06/11 14:11:27 adrien Exp $', sets, pls);
+ − end
+ −
+ − %--------------------------------------------------------------------------
+ − % Get Default Plist
+ − %--------------------------------------------------------------------------
+ − function plout = getDefaultPlist()
+ − persistent pl;
+ − if exist('pl', 'var')==0 || isempty(pl)
+ − pl = buildplist();
+ − end
+ − plout = pl;
+ − end
+ −
+ − function pl = buildplist()
+ −
+ − pl = plist();
+ −
+ − % isgap
+ − p = param({'isgap', ['Logical ao giving position of gaps. If not<br>'...
+ − 'specified, gaps are positionned where there are zeros.']}, {1, {'zeros', ao}, paramValue.SINGLE});
+ − pl.append(p);
+ −
+ − % large scale or small scale algorithm?
+ − p = param({'scale', 'large scale or small scale algorithm'}, {1, {'large scale', 'small scale'}, paramValue.SINGLE});
+ − pl.append(p);
+ −
+ − % initial coefficients for subtraction initialization
+ − p = param({ 'coefs' , 'initial subtracted coefficients, must be a nY*nU double array. If not provided zeros are assumed'}, [] );
+ − pl.append(p);
+ −
+ − % weighting scheme
+ − p = param({ 'weightingMethod' , 'choose to define a frequency weighting scheme'}, {1, {'residual', 'ao', 'pzmodel'}, paramValue.SINGLE} );
+ − pl.append(p);
+ −
+ − p = param({ 'aoWeight' , 'ao to define a frequency weighting scheme (if chosen in ''weightingMethod'')'}, ao.initObjectWithSize(0,0) );
+ − pl.append(p);
+ −
+ − p = param({ 'pzmodelWeight' , 'pzmodel to define a frequency weighting scheme (if chosen in ''weightingMethod'')'}, pzmodel.initObjectWithSize(0,0) );
+ − pl.append(p);
+ −
+ − p = param({ 'lincoef' , 'linear coefficient for scaling frequencies in chi2'}, 20 );
+ − pl.append(p);
+ −
+ − p = param({ 'logcoef' , 'logarithmic coefficient for scaling frequencies in chi2'}, 0.0 );
+ − pl.append(p);
+ −
+ − p = param({'fitCriterion' , 'criterion to fit the amplitude spectra (increasing quality, increasing time)'}, {2, {'FTest-NoHfWin' 'FTest' 'chi2'}, paramValue.SINGLE});
+ − pl.append(p);
+ −
+ − % iterations convergence stop criterion
+ − p = param({ 'iterMax' , 'max number of Mex/Exp iterations (only makes sense for "FTest-NoHfWin" fitting criteiron)'}, 1 );
+ − pl.append(p);
+ −
+ − p = param({ 'normCoefs' , 'tolerance on inf norm of coefficient update '}, 1e-12 );
+ − pl.append(p);
+ −
+ − p = param({ 'normCriterion' , 'tolerance on norm of criterion variation'}, 1e-5 );
+ − pl.append(p);
+ −
+ − % windowing options
+ − p = param({ 'win' , 'window to operate FFT, may be a plist/ao'}, plist('win', 'levelledHanning', 'PSLL', 200, 'levelOrder', 2 ) );
+ − pl.append(p);
+ −
+ − % display
+ − p = param({ 'display' , 'choose how much to display of the optimizer output'}, {1, {'off', 'iter', 'final'}, paramValue.SINGLE} );
+ − pl.append(p);
+ −
+ − % optimizer options
+ − p = param({ 'maxcall' , 'maximum number of calls to the criterion function'}, 50000 );
+ − pl.append(p);
+ −
+ − end