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=head1 NAME |
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PDL::Fit::Linfit - routines for fitting data with linear combinations of functions. |
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=head1 DESCRIPTION |
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This module contains routines to perform general curve-fits to a set (linear combination) |
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of specified functions. |
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Given a set of Data: |
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(y0, y1, y2, y3, y4, y5, ...ynoPoints-1) |
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The fit routine tries to model y as: |
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y' = beta0*x0 + beta1*x1 + ... beta_noCoefs*x_noCoefs |
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Where x0, x1, ... x_noCoefs, is a set of functions (curves) that |
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the are combined linearly using the beta coefs to yield an approximation |
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of the input data. |
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The Sum-Sq error is reduced to a minimum in this curve fit. |
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B |
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=over 1 |
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=item $data |
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This is your data you are trying to fit. Size=n |
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=item $functions |
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2D array. size (n, noCoefs). Row 0 is the evaluation |
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of function x0 at all the points in y. Row 1 is the evaluation of |
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of function x1 at all the points in y, ... etc. |
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Example of $functions array Structure: |
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$data is a set of 10 points that we are trying to model using |
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the linear combination of 3 functions. |
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$functions = ( [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], # Constant Term |
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[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ], # Linear Slope Term |
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[ 0, 2, 4, 9, 16, 25, 36, 49, 64, 81] # quadradic term |
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) |
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=back |
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=head1 SYNOPSIS |
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$yfit = linfit1d $data, $funcs |
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=head1 FUNCTIONS |
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=head2 linfit1d |
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=for ref |
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1D Fit linear combination of supplied functions to data using min chi^2 (least squares). |
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=for usage |
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Usage: ($yfit, [$coeffs]) = linfit1d [$xdata], $data, $fitFuncs, [Options...] |
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=for sig |
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Signature: (xdata(n); ydata(n); $fitFuncs(n,order); [o]yfit(n); [o]coeffs(order)) |
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Uses a standard matrix inversion method to do a least |
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squares/min chi^2 fit to data. |
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Returns the fitted data and optionally the coefficients. |
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One can thread over extra dimensions to do multiple fits (except |
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the order can not be threaded over - i.e. it must be one fixed |
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set of fit functions C. |
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The data is normalised internally to avoid overflows (using the |
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mean of the abs value) which are common in large polynomial |
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series but the returned fit, coeffs are in |
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unnormalised units. |
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=for example |
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# Generate data from a set of functions |
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$xvalues = sequence(100); |
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$data = 3*$xvalues + 2*cos($xvalues) + 3*sin($xvalues*2); |
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# Make the fit Functions |
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$fitFuncs = cat $xvalues, cos($xvalues), sin($xvalues*2); |
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# Now fit the data, Coefs should be the coefs in the linear combination |
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# above: 3,2,3 |
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($yfit, $coeffs) = linfit1d $data,$fitFuncs; |
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=for options |
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Options: |
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Weights Weights to use in fit, e.g. 1/$sigma**2 (default=1) |
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=cut |
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package PDL::Fit::Linfit; |
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@EXPORT_OK = qw( linfit1d ); |
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%EXPORT_TAGS = (Func=>[@EXPORT_OK]); |
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use PDL::Core; |
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use PDL::Basic; |
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use PDL::Exporter; |
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@ISA = qw( PDL::Exporter ); |
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use PDL::Options ':Func'; |
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use PDL::Slatec; # For matinv() |
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sub PDL::linfit1d { |
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my $opthash = ref($_[-1]) eq "HASH" ? pop(@_) : {} ; |
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my %opt = parse( { Weights=>ones(1) }, $opthash ) ; |
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barf "Usage: linfit1d incorrect args\n" if $#_<1 or $#_ > 3; |
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my ($x, $y, $fitfuncs) = @_; |
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if ($#_ == 1) { |
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($y, $fitfuncs) = @_; |
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$x = $y->xvals; |
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} |
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my $wt = $opt{Weights}; |
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# Internally normalise data |
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my $ymean = (abs($y)->sum)/($y->nelem); |
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$ymean = 1 if $ymean == 0; |
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my $y2 = $y / $ymean; |
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# Do the fit |
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my $M = $fitfuncs->xchg(0,1); |
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my $C = $M->xchg(0,1) x ($M * $wt->dummy(0)) ; |
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my $Y = $M->xchg(0,1) x ($y2->dummy(0) * $wt->dummy(0)); |
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# Fitted coefficients vector |
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$c = matinv($C) x $Y; |
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# Fitted data |
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$yfit = ($M x $c)->clump(2); # Remove first dim=1 |
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$yfit *= $ymean; # Un-normalise |
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if (wantarray) { |
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my $coeff = $c->clump(2); |
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$coeff *= $ymean; # Un-normalise |
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return ($yfit, $coeff); |
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} |
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else{ |
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return $yfit; |
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} |
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} |
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*linfit1d = \&PDL::linfit1d; |
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1; |