pdl::fit::gaussian(3) [suse man page]
Gaussian(3) User Contributed Perl Documentation Gaussian(3) NAME
PDL::Fit::Gaussian - routines for fitting gaussians DESCRIPTION
This module contains some custom gaussian fitting routines. These were developed in collaboration with Alison Offer, they do a reasonably robust job and are quite useful. Gaussian fitting is something I do a lot of, so I figured it was worth putting in my special code. Note this code is also used in the Karma package. Note it is not clear to me that this code is fully debugged. The reason I say that is because I tried using the internal linear eqn solving C routines called elsewhere and they were giving erroneous results. So steal from this code with caution! However it does give good fits to reasonable looking gaussians and tests show correct parameters. KGB 29/Oct/2002 SYNOPSIS
use PDL; use PDL::Fit::Gaussian; ($cen, $pk, $fwhm, $back, $err, $fit) = fitgauss1d($x, $data); ($pk, $fwhm, $back, $err, $fit) = fitgauss1dr($r, $data); FUNCTIONS
fitgauss1d Fit 1D Gassian to data piddle ($cen, $pk, $fwhm, $back, $err, $fit) = fitgauss1d($x, $data); ($cen, $pk, $fwhm, $back, $err, $fit) = fitgauss1d($x, $data); xval(n); data(n); [o]xcentre();[o]peak_ht(); [o]fwhm(); [o]background();int [o]err(); [o]datafit(n); [t]sig(n); [t]xtmp(n); [t]ytmp(n); [t]yytmp(n); [t]rtmp(n); Fits a 1D Gaussian robustly free parameters are the centre, peak height, FWHM. The background is NOT fit, because I find this is generally unreliable, rather a median is determined in the 'outer' 10% of pixels (i.e. those at the start/end of the data piddle). The initial estimate of the FWHM is the length of the piddle/3, so it might fail if the piddle is too long. (This is non-robust anyway). Most data does just fine and this is a good default gaussian fitter. SEE ALSO: fitgauss1dr() for fitting radial gaussians fitgauss1dr Fit 1D Gassian to radial data piddle ($pk, $fwhm2, $back, $err, $fit) = fitgauss1dr($r, $data); ($pk, $fwhm2, $back, $err, $fit) = fitgauss1dr($r, $data); xval(n); data(n); [o]peak_ht(); [o]fwhm(); [o]background();int [o]err(); [o]datafit(n); [t]sig(n); [t]xtmp(n); [t]ytmp(n); [t]yytmp(n); [t]rtmp(n); Fits a 1D radial Gaussian robustly free parameters are the peak height, FWHM. Centre is assumed to be X=0 (i.e. start of piddle). The background is NOT fit, because I find this is generally unreliable, rather a median is determined in the 'outer' 10% of pixels (i.e. those at the end of the data piddle). The initial estimate of the FWHM is the length of the piddle/3, so it might fail if the piddle is too long. (This is non-robust anyway). Most data does just fine and this is a good default gaussian fitter. SEE ALSO: fitgauss1d() to fit centre as well. BUGS
May not converge for weird data, still pretty good! AUTHOR
This file copyright (C) 1999, Karl Glazebrook (kgb@aaoepp.aao.gov.au), Gaussian fitting code by Alison Offer (aro@aaocbn.aao.gov.au). All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file. perl v5.12.1 2010-07-05 Gaussian(3)
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Basic(3) User Contributed Perl Documentation Basic(3) NAME
PDL::Basic -- Basic utility functions for PDL DESCRIPTION
This module contains basic utility functions for creating and manipulating piddles. Most of these functions are simplified interfaces to the more flexible functions in the modules PDL::Primitive and PDL::Slices. SYNOPSIS
use PDL::Basic; FUNCTIONS
xvals Fills a piddle with X index values $x = xvals($somearray); $x = xvals([OPTIONAL TYPE],$nx,$ny,$nz...); etc. see zeroes. perldl> print xvals zeroes(5,10) [ [0 1 2 3 4] [0 1 2 3 4] [0 1 2 3 4] [0 1 2 3 4] [0 1 2 3 4] [0 1 2 3 4] [0 1 2 3 4] [0 1 2 3 4] [0 1 2 3 4] [0 1 2 3 4] ] yvals Fills a piddle with Y index values $x = yvals($somearray); yvals(inplace($somearray)); $x = yvals([OPTIONAL TYPE],$nx,$ny,$nz...); etc. see zeroes. perldl> print yvals zeroes(5,10) [ [0 0 0 0 0] [1 1 1 1 1] [2 2 2 2 2] [3 3 3 3 3] [4 4 4 4 4] [5 5 5 5 5] [6 6 6 6 6] [7 7 7 7 7] [8 8 8 8 8] [9 9 9 9 9] ] zvals Fills a piddle with Z index values $x = zvals($somearray); zvals(inplace($somearray)); $x = zvals([OPTIONAL TYPE],$nx,$ny,$nz...); etc. see zeroes. perldl> print zvals zeroes(3,4,2) [ [ [0 0 0] [0 0 0] [0 0 0] [0 0 0] ] [ [1 1 1] [1 1 1] [1 1 1] [1 1 1] ] ] xlinvals X axis values between endpoints (see xvals). $a = zeroes(100,100); $x = $a->xlinvals(0.5,1.5); $y = $a->ylinvals(-2,-1); # calculate Z for X between 0.5 and 1.5 and # Y between -2 and -1. $z = f($x,$y); "xlinvals", "ylinvals" and "zlinvals" return a piddle with the same shape as their first argument and linearly scaled values between the two other arguments along the given axis. ylinvals Y axis values between endpoints (see yvals). See xlinvals for more information. zlinvals Z axis values between endpoints (see zvals). See xlinvals for more information. hist Create histogram of a piddle $hist = hist($data,[$min,$max,$step]); ($xvals,$hist) = hist($data,[$min,$max,$step]); If requested, $xvals gives the computed bin centres A nice idiom (with PDL::Graphics::PGPLOT) is bin hist $data; # Plot histogram perldl> p $y [13 10 13 10 9 13 9 12 11 10 10 13 7 6 8 10 11 7 12 9 11 11 12 6 12 7] perldl> $h = hist $y,0,20,1; # hist with step 1, min 0 and 20 bins perldl> p $h [0 0 0 0 0 0 2 3 1 3 5 4 4 4 0 0 0 0 0 0] whist Create a weighted histogram of a piddle $hist = whist($data, $wt, [$min,$max,$step]); ($xvals,$hist) = whist($data, $wt, [$min,$max,$step]); If requested, $xvals gives the computed bin centres. $data and $wt should have the same dimensionality and extents. A nice idiom (with PDL::Graphics::PGPLOT) is bin whist $data, $wt; # Plot histogram perldl> p $y [13 10 13 10 9 13 9 12 11 10 10 13 7 6 8 10 11 7 12 9 11 11 12 6 12 7] perldl> $wt = grandom($y->nelem) perldl> $h = whist $y, $wt, 0, 20, 1 # hist with step 1, min 0 and 20 bins perldl> p $h [0 0 0 0 0 0 -0.49552342 1.7987439 0.39450696 4.0073722 -2.6255299 -2.5084501 2.6458365 4.1671676 0 0 0 0 0 0] sequence Create array filled with a sequence of values $a = sequence($b); $a = sequence [OPTIONAL TYPE], @dims; etc. see zeroes. perldl> p sequence(10) [0 1 2 3 4 5 6 7 8 9] perldl> p sequence(3,4) [ [ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11] ] rvals Fills a piddle with radial distance values from some centre. $r = rvals $piddle,{OPTIONS}; $r = rvals [OPTIONAL TYPE],$nx,$ny,...{OPTIONS}; Options: Centre => [$x,$y,$z...] # Specify centre Center => [$x,$y.$z...] # synonym. Squared => 1 # return distance squared (i.e., don't take the square root) perldl> print rvals long,7,7,{Centre=>[2,2]} [ [2 2 2 2 2 3 4] [2 1 1 1 2 3 4] [2 1 0 1 2 3 4] [2 1 1 1 2 3 4] [2 2 2 2 2 3 4] [3 3 3 3 3 4 5] [4 4 4 4 4 5 5] ] For a more general metric, one can define, e.g., sub distance { my ($a,$centre,$f) = @_; my ($r) = $a->allaxisvals-$centre; $f->($r); } sub l1 { sumover(abs($_[0])); } sub euclid { use PDL::Math 'pow'; pow(sumover(pow($_[0],2)),0.5); } sub linfty { maximum(abs($_[0])); } so now distance($a, $centre, &euclid); will emulate rvals, while "&l1" and "&linfty" will generate other well-known norms. axisvals Fills a piddle with index values on Nth dimension $z = axisvals ($piddle, $nth); This is the routine, for which xvals, yvals etc are mere shorthands. "axisvals" can be used to fill along any dimension. Note the 'from specification' style (see zeroes) is not available here, for obvious reasons. allaxisvals Generates a piddle with index values $z = allaxisvals ($piddle); "allaxisvals" produces an array with axis values along each dimension, adding an extra dimension at the start. "allaxisvals($piddle)->slice("($nth)")" will produce the same result as "axisvals($piddle,$nth)" (although with extra work and not inplace). It's useful when all the values will be required, as in the example given of a generalized rvals. transpose transpose rows and columns. $b = transpose($a); $b = ~$a; Also bound to the "~" unary operator in PDL::Matrix. perldl> $a = sequence(3,2) perldl> p $a [ [0 1 2] [3 4 5] ] perldl> p transpose( $a ) [ [0 3] [1 4] [2 5] ] perl v5.8.0 2001-10-24 Basic(3)