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#!/usr/local/bin/perl
##############################################################################
# Time-stamp: <Sat Oct 28 1995 23:15:13 Stardate: [-31]6509.63 hwloidl>
#
# Usage: do ....
#
# Statistics package that is used in gran-extr, RTS2gran and friends.
# Most of the routines assume a list of integers as input.
# This package contains:
# - corr
# - mean_std_dev
# - cov
# - list_sum
# - list_max
# - list_min
#
##############################################################################
# ----------------------------------------------------------------------------
# Compute correlation of 2 vectors, having their sums precomputed.
# Usage: do corr(($n, $sum_1, @rest);
#
# Input: $n ... number of all elements in @list_1 as well as in @list_2
# (i.e. $n = $#list_1+1 = $#list_2+1).
# $sum_1 ... sum of all elements in @list_1
# @list_1 ... list of integers; first vector
# $sum_2 ... sum of all elements in @list_2
# @list_2 ... list of integers; first vector
# Output: correlation of @list_1 and @list_2
# ----------------------------------------------------------------------------
sub corr {
local ($n, $sum_1, @rest) = @_;
local (@list_1) = splice(@rest,0,$n);
local ($sum_2, @list_2) = @rest;
local ($mean_1,$mean_2,$std_dev_1,$std_dev_2);
if ( $opt_D ) {
print "\ncorr: n=$n sum_1=$sum_1 sum_2=$sum_2\n";
print " list_sum of list_1=" . &list_sum(@list_1) .
" list_sum of list_2=" . &list_sum(@list_2) . "\n";
print " len of list_1=$#list_1 len of list_2=$#list_2\n";
}
($mean_1, $std_dev_1) = &mean_std_dev($sum_1,@list_1);
($mean_2, $std_dev_2) = &mean_std_dev($sum_2,@list_2);
if ( $opt_D ) {
print "corr: $mean_1, $std_dev_1; $mean_2, $std_dev_2\n";
}
return ( ($std_dev_1 * $std_dev_2) == 0 ?
0 :
&cov($n, $mean_1, @list_1, $mean_2, @list_2) /
( $std_dev_1 * $std_dev_2 ) );
}
# ----------------------------------------------------------------------------
sub mean_std_dev {
local ($sum,@list) = @_;
local ($n, $s, $s_);
#print "\nmean_std_dev: sum is $sum ; list has length $#list";
$n = $#list+1;
$mean_value = $sum/$n;
$s_ = 0;
foreach $x (@list) {
$s_ += $x;
$s += ($mean_value - $x) ** 2;
}
if ( $sum != $s_ ) {
print "stat.pl: ERROR in mean_std_dev: provided sum is wrong " .
"(provided: $sum; computed: $s_ " .
";list_sum: " . &list_sum(@list) . "\n";
exit (2);
}
return ( ($mean_value, sqrt($s / ($n - 1)) ) );
}
# ----------------------------------------------------------------------------
sub _mean_std_dev {
return ( &mean_std_dev(&list_sum(@_), @_) );
}
# ----------------------------------------------------------------------------
# Compute covariance of 2 vectors, having their sums precomputed.
# Input: $n ... number of all elements in @list_1 as well as in @list_2
# (i.e. $n = $#list_1+1 = $#list_2+1).
# $mean_1 ... mean value of all elements in @list_1
# @list_1 ... list of integers; first vector
# $mean_2 ... mean value of all elements in @list_2
# @list_2 ... list of integers; first vector
# Output: covariance of @list_1 and @list_2
# ----------------------------------------------------------------------------
sub cov {
local ($n, $mean_1, @rest) = @_;
local (@list_1) = splice(@rest,0,$n);
local ($mean_2, @list_2) = @rest;
local ($i,$s,$s_1,$s_2);
for ($i=0; $i<$n; $i++) {
$s_1 += $list_1[$i];
$s_2 += $list_2[$i];
$s += ($mean_1 - $list_1[$i]) * ($mean_2 - $list_2[$i]);
}
if ( $mean_1 != ($s_1/$n) ) {
print "stat.pl: ERROR in cov: provided mean value is wrong " .
"(provided: $mean_1; computed: " . ($s_1/$n) . ")\n";
exit (2);
}
if ( $mean_2 != ($s_2/$n) ) {
print "stat.pl: ERROR in cov: provided mean value is wrong " .
"(provided: $mean_2; computed: " . ($s_2/$n) . ")\n";
exit (2);
}
return ( $s / ($n - 1) ) ;
}
# ---------------------------------------------------------------------------
sub list_sum {
local (@list) = @_;
local ($sum) = (0);
foreach $x (@list) {
$sum += $x;
}
return ($sum);
}
# ----------------------------------------------------------------------------
sub list_max {
local (@list) = @_;
local ($max) = shift;
foreach $x (@list) {
$max = $x if $x > $max;
}
return ($max);
}
# ----------------------------------------------------------------------------
sub list_min {
local (@list) = @_;
local ($min) = shift;
foreach $x (@list) {
$min = $x if $x < $min;
}
return ($min);
}
# ----------------------------------------------------------------------------
1;
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