/usr/share/perl5/Math/Derivative.pm is in libmath-derivative-perl 0.01-6.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 | # functions for calculating derivatives of data
# $Id: Derivative.pm,v 1.1 1995/12/26 16:26:59 willijar Exp $
=head1 NAME
Math::Derivative - Numeric 1st and 2nd order differentiation
=head1 SYNOPSIS
use Math::Derivative qw(Derivative1 Derivative2);
@dydx=Derivative1(\@x,\@y);
@d2ydx2=Derivative2(\@x,\@y);
@d2ydx2=Derivative2(\@x,\@y,$yp0,$ypn);
=head1 DESCRIPTION
This Perl package exports functions for performing numerical first
(B<Derivative1>) and second B<Derivative2>) order differentiation on
vectors of data. They both take references to two arrays containing
the x and y ordinates of the data and return an array of the 1st or
2nd derivative at the given x ordinates. B<Derivative2> may optionally
be given values to use for the first dervivative at the start and end
points of the data - otherwiswe 'natural' values are used.
=head1 HISTORY
$Log: Derivative.pm,v $
Revision 1.1 1995/12/26 16:26:59 willijar
Initial revision
=head1 BUGS
Let me know.
=head1 AUTHOR
John A.R. Williams <J.A.R.Williams@aston.ac.uk>
=cut
require Exporter;
package Math::Derivative;
@ISA=qw(Exporter);
@EXPORT_OK=qw(Derivative1 Derivative2);
use strict;
sub Derivative1 {
my ($x,$y)=@_;
my @y2;
my $n=$#{$x};
$y2[0]=($y->[1]-$y->[0])/($x->[1]-$x->[0]);
$y2[$n]=($y->[$n]-$y->[$n-1])/($x->[$n]-$x->[$n-1]);
my $i;
for($i=1; $i<$n; $i++) {
$y2[$i]=($y->[$i+1]-$y->[$i-1])/($x->[$i+1]-$x->[$i-1]);
}
return @y2;
}
sub Derivative2 {
my ($x,$y,$yp1,$ypn)=@_;
my $n=$#{$x};
my ($i,@y2,@u);
if (!defined $yp1) {
$y2[0]=0; $u[0]=0;
}
else {
$y2[0]=-0.5;
$u[0]=(3/($x->[1]-$x->[0]))*(($y->[1]-$y->[0])/($x->[1]-$x->[0])-$yp1);
}
for($i=1; $i<$n; $i++) {
my $sig=($x->[$i]-$x->[$i-1])/($x->[$i+1]-$x->[$i-1]);
my $p=$sig*$y2[$i-1]+2.0;
$y2[$i]=($sig-1.0)/$p;
$u[$i]=(6.0*( ($y->[$i+1]-$y->[$i])/($x->[$i+1]-$x->[$i])-
($y->[$i]-$y->[$i-1])/($x->[$i]-$x->[$i-1])
)/
($x->[$i+1]-$x->[$i-1])-$sig*$u[$i-1])/$p;
}
my ($qn,$un);
if (!defined $ypn) {
$qn=0;
$un=0;
}
else {
$qn=0.5;
$un=(3.0/($x->[$n]-$x->[$n-1]))*
($ypn-($y->[$n]-$y->[$n-1])/($x->[$n]-$x->[$n-1]));
}
$y2[$n]=($un-$qn*$u[$n-1])/($qn*$y2[$n-1]+1.0);
for($i=$n-1; $i>=0; --$i) {
$y2[$i]=$y2[$i]*$y2[$i+1]+$u[$i];
}
return @y2;
}
1;
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