LTPDA Toolbox™

contents

Method ao/xfit

  XFIT fit a function of x to data.
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  DESCRIPTION: XFIT performs a non-linear fit of a function of x to data.
  smodels fitting is also supported.
  
  ALGORITHM: XFIT does a chi-squared minimization by means of different
  algorithms (see details in the default plist). Covariance matrix is also
  computed from the Fisher's Information Matrix. In case the Information
  Matrix is not positive-definite, uncertainties will not be stored in the
  output. 
 
  CALL:        b = xfit(a, pl)
 
  INPUTS:      a  - input AO to fit to
               pl - parameter list (see below)
 
  OUTPUTs:     b  - a pest object containing the best-fit parameters,
                    goodness-of-fit reduced chi-squared, fit degree-of-freedom
                    covariance matrix and uncertainties. Additional
                    quantities, like the Information Matrix, are contained 
                    within the procinfo. The best-fit model can be evaluated
                    from pest\eval.
 
  Parameters Description
 
  EXAMPLES:
 
  % 1) Fit to a frequency-series
 
    % Create a frequency-series
    datapl = plist('fsfcn', '0.01./(0.0001+f) + 5*abs(randn(size(f))) ', 'f1', 1e-5, 'f2', 5, 'nf', 1000, ...
       'xunits', 'Hz', 'yunits', 'N/Hz');
    data = ao(datapl);
    data.setName;
  
    % Do fit
    fitpl = plist('Function', 'P(1)./(P(2) + Xdata) + P(3)', ...
      'P0', [0.1 0.01 1]);
    params = xfit(data, fitpl)
  
    % Evaluate model
    BestModel = eval(params,plist('type','fsdata','xdata',data,'xfield','x'));
    BestModel.setName;
    
    % Display results
    iplot(data,BestModel)
 
  % 2) Fit to a noisy sine-wave
 
    % Create a noisy sine-wave
    fs    = 10;
    nsecs = 500;
    datapl = plist('waveform', 'Sine wave', 'f', 0.01, 'A', 0.6, 'fs', fs, 'nsecs', nsecs, ...
      'xunits', 's', 'yunits', 'm');
    sw = ao(datapl);
    noise = ao(plist('tsfcn', '0.01*randn(size(t))', 'fs', fs, 'nsecs', nsecs));
    data = sw+noise;
    data.setName;
  
    % Do fit
    fitpl = plist('Function', 'P(1).*sin(2*pi*P(2).*Xdata + P(3))', ...
      'P0', [1 0.01 0]);
    params = xfit(data, fitpl)
  
    % Evaluate model
    BestModel = eval(params,plist('type','tsdata','xdata',sw,'xfield','x'));
    BestModel.setName;
    
    % Display results
    iplot(data,BestModel)
 
  % 3) Fit an smodel of a straight line to some data
 
    % Create a noisy straight-line
    datapl = plist('xyfcn', '2.33 + 0.1*x + 0.01*randn(size(x))', 'x', 0:0.1:10, ...
      'xunits', 's', 'yunits', 'm');
    data = ao(datapl);
    data.setName;
  
    % Model to fit
    mdl = smodel('a + b*x');
    mdl.setXvar('x');
    mdl.setParams({'a', 'b'}, {1 2});
  
    % Fit model
    fitpl = plist('Function', mdl, 'P0', [1 1]);
    params = xfit(data, fitpl)
  
    % Evaluate model
    BestModel = eval(params,plist('xdata',data,'xfield','x'));
    BestModel.setName;
    
    % Display results
    iplot(data,BestModel)
 
  % 4) Fit a chirp-sine firstly starting from an initial guess (quite close
  % to the true values) (bad convergency) and secondly by a Monte Carlo
  % search (good convergency)
 
    % Create a noisy chirp-sine
    fs    = 10;
    nsecs = 1000;
    
    % Model to fit and generate signal
    mdl = smodel(plist('name', 'chirp', 'expression', 'A.*sin(2*pi*(f + f0.*t).*t + p)', ...
      'params', {'A','f','f0','p'}, 'xvar', 't', 'xunits', 's', 'yunits', 'm'));
  
    % signal
    s = mdl.setValues({10,1e-4,1e-5,0.3});
    s.setXvals(0:1/fs:nsecs-1/fs);
    signal = s.eval;
    signal.setName;
  
    % noise
    noise = ao(plist('tsfcn', '1*randn(size(t))', 'fs', fs, 'nsecs', nsecs));
  
    % data
    data = signal + noise;
    data.setName;
  
    % Fit model from the starting guess
    fitpl_ig = plist('Function', mdl, 'P0',[8,9e-5,9e-6,0]);
    params_ig = xfit(data, fitpl_ig);
  
    % Evaluate model
    BestModel_ig = eval(params_ig,plist('xdata',data,'xfield','x'));
    BestModel_ig.setName;
    
    % Display results
    iplot(data,BestModel_ig)
    
    % Fit model by a Monte Carlo search
    fitpl_mc = plist('Function', mdl, ...
      'MonteCarlo', true, 'Npoints', 1000, 'LB', [8,9e-5,9e-6,0], 'UB', [11,3e-4,2e-5,2*pi]);
    params_mc = xfit(data, fitpl_mc)
    
    % Evaluate model
    BestModel_mc = eval(params_mc,plist('xdata',data,'xfield','x'));
    BestModel_mc.setName;
    
    % Display results
    iplot(data,BestModel_mc)
 
  % 5) Multichannel fit of smodels
 
    % Ch.1 data
    datapl = plist('xyfcn', '0.1*x + 0.01*randn(size(x))', 'x', 0:0.1:10, 'name', 'channel 1', ...
      'xunits', 'K', 'yunits', 'Pa');
    a1 = ao(datapl);
    % Ch.2 data
    datapl = plist('xyfcn', '2.5*x + 0.1*sin(2*pi*x) + 0.01*randn(size(x))', 'x', 0:0.1:10, 'name', 'channel 2', ...
      'xunits', 'K', 'yunits', 'T');
    a2 = ao(datapl);
    
    % Model to fit
    mdl1 = smodel('a*x');
    mdl1.setXvar('x');
    mdl1.setParams({'a'}, {1});
    mdl1.setXunits('K');
    mdl1.setYunits('Pa');
    
    mdl2 = smodel('b*x + a*sin(2*pi*x)');
    mdl2.setXvar('x');
    mdl2.setParams({'a','b'}, {1,2});
    mdl2.setXunits('K');
    mdl2.setYunits('T');
    
    % Fit model
    params = xfit(a1,a2, plist('Function', [mdl1,mdl2]));
    
    % evaluate model
    b = eval(params, plist('index',1,'xdata',a1,'xfield','x'));
    b.setName('fit Ch.1');
    r = a1-b;
    r.setName('residuals');
    iplot(a1,b,r)
    
    b = eval(params, plist('index',2,'xdata',a2,'xfield','x'));
    b.setName('fit Ch.2');
    r = a2-b;
    r.setName('residuals');
    iplot(a2,b,r)
 
  Parameters Description
 
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Parameter Description

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Method: ao/xcorr

Method: ao/zDomainFit

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