Compare Correlation Matrices

"Remember, my friend, that knowledge is stronger than memory, and we should not trust the weaker." [Bram Stoker]
Some years ago I developed a Perl program for an Algorithmics client. Over time I enhanced this program and I made it read the RMLinks.cfg file so that new risk factors would automatically be included.
My implementation approach was:
1. Read first matrix
    Checks:
    Matrix quadratic?
    Risk factor order left->right (top row) == top->bottom (leftmost column)?
    Diagonals == 1 (warning)?
    No NC category (warning if there is)?
    Matrix symmetric: M(i,j) == M(j,i) for all i,j?
    [Not for DC files because not given there.]
2. Read second matrix
    Checks identical to above
3. Risk factors in both matrices identical?
    Warn about risk factors which are in first matrix but not in second and vice versa
    Highlight outliers per category
    Highlight outliers per ccy
Currently the program is supporting the following parameters:
b - breaches: do not report differences between the two input matrices but breaches beyond tolerances.
d - debug [level] gives debugging information at detail level level
    level 1: -
    level 2: -
    level 3: Print all elements of matrices 1 and 2
f - read deviation file [-f needs to be followed by a valid filename]
    Reads min and max values for all slices for differences which should
    be ignored during comparison. See option -w to get format example
h - help: list parameters and their explanation
i -  ignore risk factors in a given file [-i needs to be followed by a valid filename]
m - set max rank index [default is 6 (=return highest 3
    and lowest 3 of each slice); m needs to be even and >= 4 !
n - tolerate risk factor category NC
r - set Algo risk factor category file [default is ./RMLinks.cfg
s - summarize findings, no detailed warnings or error messages
t - read file with tolerated changes for each matrix element and apply tolerance check
v - print version
w - write deviation file with min and max values of all slices.
    This file is comma-separated to be easily readable via Excel.
    It can be amended and used with option -f later
    [-w needs to be followed by a valid filename, preferrably ending with .csv
x - read translation table [-x needs to be followed by a valid filename].
    Risk factor names of matrix 1 will be translated by second name in comma-separated row
A typical call of this program from a Shell script could look like:
Please read my Disclaimer.
$PERL_LIB/compareCM.pl \
-i $PERL_LIB/Ignored_RiskFactors.csv \
-m 6 \
-n \
-r $ALGO_TOP/RMLinks.cfg \
-w $PERL_LIB/VCV_Deviation_Matrix.csv \
$VCV_PREVIOUS \
$VCV_CURRENT
The source code of compareCM.pl:
#!/usr/bin/perl
#
# Implementation Approach:
#
# 1. Read first matrix
#    Checks:
#    Matrix quadratic?
#    Risk factor order left->right (top row) == top->bottom (leftmost column)?
#    Diagonals == 1 (warning)?
#    No NC category (warning if there is)?
#    Matrix symmetric: M(i,j) == M(j,i) for all i,j?
#    [Not for DC files because not given there.]
#
# 2. Read second matrix
#    Checks identical to above
#
# 3. Risk factors in both matrices identical?
#    Warn about risk factors which are in first matrix but not in second and vice versa
#    Highlight outliers per category
#    Highlight outliers per ccy
#
# Version Date       Author         Comment
# 1.18    26/12/2018 Bernd Plumhoff Anonymized version
my $version = "'1.18,26/12/2018";
​
use strict;
use warnings;
use List::Util qw[min max];
use feature "switch";
use Getopt::Std;
​
###########################################################
#                                                         #
#                   Process parameters                    #    
#                                                         # 
###########################################################       
​
our $opt_b;	# b - breaches: do not report differences between the two input matrices
			#     but breaches beyond tolerances
our $opt_d;	# d - debug ["level"] gives debugging information at detail level "level"
			#     level 1: -
			#     level 2: -
			#     level 3: Print all elements of matrices 1 and 2
our $opt_f;	# f - read deviation file [-f needs to be followed by a valid filename]
			#     Reads min and max values for all slices for differences which should
			#     be ignored during comparison. See option -w to get format example.
our $opt_h;	# h - help: list parameters and their explanation
our $opt_i;	# i - ignore risk factors in a given file [-i needs to be followed by
			#     a valid filename]
our $opt_m;	# m - set max rank index [default is 6 (=return highest 3
			#     and lowest 3 of each slice); m needs to be even and >= 4 !
our $opt_n;	# n - tolerate risk factor category NC
our $opt_r;	# r - set Algo risk factor category file [default is "./RMLinks.cfg"]
our $opt_s;	# s - summarize findings, no detailed warnings or error messages
our $opt_t;	# t - read tolerance file and apply tolerance check
our $opt_v;	# v - print version
our $opt_w;	# w - write deviation file with min and max values of all slices.
			#     This file is ","-separated to be easily readable via Excel.
			#     It can be amended and used with option -f later
			#     [-w needs to be followed by a valid filename,
			#     preferrably ending with ".csv"]
our $opt_x;	# x - read translation table [-x needs to be followed by a valid filename].
			#     Risk factor names of matrix 1 will be translated by second name in
			#     comma-separated row
​
getopts('bd:f:hi:m:nr:st:vw:x:');
​
if (defined $opt_h) {
	print "$0 parameters:\n" .
		"b - breaches: do not report differences between the two input matrices\n" .
		"    but breaches beyond tolerances\n" .
		"d - debug [\"level\"] gives debugging information at detail level \"level\"\n" .
		"    level 1: -\n" .
		"    level 2: -\n" .
		"    level 3: Print all elements of matrices 1 and 2\n" .
		"f - read deviation file [-f needs to be followed by a valid filename]\n" .
		"    Reads min and max values for all slices for differences which should\n" .
		"    be ignored during comparison. See option -w to get format example.\n" .
		"h - help: list parameters and their explanation\n" .
		"i - ignore risk factors in a given file [-i needs to be followed by\n" .
		"    a valid filename]\n" .
		"m - set max rank index [default is 6 (=return highest 3\n" .
		"    and lowest 3 of each slice); m needs to be even and >= 4 !\n" .
		"n - tolerate risk factor category NC\n" .
		"r - set Algo risk factor category file [default is \"./RMLinks.cfg\"]\n" .
		"s - summarize findings, no detailed warnings or error messages\n" .
		"t - read file with tolerated changes for each matrix element and apply\n" .
        "    tolerance check\n" .
		"v - print version\n" .
		"w - write deviation file with min and max values of all slices.\n" .
		"    This file is \",\"-separated to be easily readable via Excel.\n" .
		"    It can be amended and used with option -f later\n" .
		"    [-w needs to be followed by a valid filename,\n" .
		"    preferrably ending with \".csv\"]\n" .
		"x - read translation table [-x needs to be followed by a valid filename].\n" .
		"    Risk factor names of matrix 1 will be translated by second name in\n" .
		"    comma-separated row\n";
	exit(0);
}
​
if (defined $opt_v) {
	print "$0\tVersion: $version\n";
	exit(0);
}
​
$opt_m ||= 6;
if ($opt_m < 4 || $opt_m % 2 != 0) {
	die "$0: parameter -m needs to be followed by an even number >= 4!\n";
}
​
# Initialize risk factor categories from file
# Please note that you will find info to fill that file in $ALGO_TOP\cfg\
$opt_r ||= "./RMLinks.cfg";
​
our $doutfile;
if (defined $opt_w) {
	if (defined $opt_f) {
		die "$0: Do not use option -w together with option -f!\n";
	}
	open($doutfile, ">",  $opt_w) || die "$0: Can't open $opt_w: $!";
	$opt_b ||= "";
	print $doutfile "$0,$version,Min,Max,Total,Tolerance Breach Down,Tolerance Breach Up," .
		"$opt_b,Do not change cells on the left." .
		" They are used by an implicit format check.\n";
}
​
our $epsilon = 0.000001;	# Tolerance for floating number rounding errors. Please note that the 
				# value 1e-6 has been chosen carefully: it coincides with the precision
				# of printf's format %f (see sub printarr below, please).
​
###########################################################
#                                                         #
#                   Read deviation file                   #    
#                                                         # 
###########################################################       
​
our $dinfile;
our $line;
our @fields=();
our @devglobal=();		# Stores global deviations as read by -f option if any
our %devrfcat=();		# Stores deviations per category if any
our %devccy=();			# Stores deviations per ccy if they exist
our %devrfcpair=();		# Stores deviations per category pair if they exist
if (defined $opt_f) {
	open($dinfile, "<",  $opt_f) || die "$0: Can't open $opt_f: $!";
	@fields = split(",", <$dinfile>);
	if ($0 ne $fields[0] || $version ne $fields[1] . ";" . $fields[2]) {
		print STDERR "$0: Warning: $0,$version expected but $fields[0]," .
				"$fields[1],$fields[2] found.\n";
	}
	if (! $opt_b && $fields[5] || $opt_b && ! $fields[5]) {
		$opt_b ||= "";
		die "$0: Option -b setting ($opt_b) does not match deviation file setting ($fields[5])";
	}
	while($line = <$dinfile>) {
		@fields = split(";", substr($line,0,length($line)-2));
		given($fields[0]) {
			when ("GLOBAL") {
				$devglobal[0] = $fields[3];
				$devglobal[1] = $fields[4];
			}
			when ("CATEGORY") {
				$devrfcat{$fields[1]}[0] = $fields[3];
				$devrfcat{$fields[1]}[1] = $fields[4];
			}
			when ("CURRENCY") {
				$devccy{$fields[1]}[0] = $fields[3];
				$devccy{$fields[1]}[1] = $fields[4];
			}
			when ("CATEGORYPAIR") {
				$devrfcpair{$fields[1] . "," . $fields[2]}[0] = $fields[3];
				$devrfcpair{$fields[1] . "," . $fields[2]}[1] = $fields[4];
			}
			default {
				die "$0: I don't know what to do with deviation definition $fields[0]";
			}
		}
	}
	close $dinfile;
}
​
###########################################################
#                                                         #
#   Read file with riskfactors which should get ignored   #    
#                                                         # 
###########################################################       
​
our %rfignore=();	# Stores risk factors to be ignored
if (defined $opt_i) {
	open($dinfile, "<",  $opt_i) || die "$0: Can't open $opt_i: $!";
	while($line = <$dinfile>) {
		$line =~ s/[\r\n]+//g;
		$rfignore{$line} = 1;
	}
	close $dinfile;
}
​
###########################################################
#                                                         #
#    Read file with translation table for risk factors    #
#                                                         # 
###########################################################       
​
our %rftrans=();	# Stores risk factors to be translated
if (defined $opt_x) {
	open($dinfile, "<",  $opt_x) || die "$0: Can't open $opt_x: $!";
	while($line = <$dinfile>) {
		$line =~ s/[\r\n]+//g;
		@fields = split(",", $line);
		$rftrans{$fields[0]} = $fields[1];
	}
	close $dinfile;
}
​
###########################################################
#                                                         #
#                   Read tolerance matrix                 #    
#                                                         # 
###########################################################       
​
our $tinfile;
our @tnames=();		# risk factor names in tolerance matrix
our %hashtnames=();	# hash table of risk factor names and their position
our @tol=();		# array with tolerances (per risk factor)
our $i;			# row index for loops
our $j;			# column index in loops
if (defined $opt_t) {
	open($tinfile, "<",  $opt_t) || die "$0: Can't open $opt_t: $!";
	$line = <$tinfile>;
	$line =~ s/[\r\n]+//g;
	@tnames = split(",", $line);
	for ($i=1; $i<scalar(@tnames); $i++) {
		$hashtnames{$tnames[$i]} = $i;
	}
	while($line = <$tinfile>) {
		$line =~ s/[\r\n]+//g;
		@fields=split(",", $line);
​
		# Matrix quadratic?
		if (scalar(@tnames) != scalar(@fields)) {
			print STDERR "$ARGV[0]: matrix is not quadratic: # of columns (" . @tnames . 
					") != # of fields in row $. (" . @fields . ")!\n";
			exit(1);
		}
​
		# Risk factor order left->right (top row) == top->bottom (leftmost column)?
		if ($fields[0] ne @tnames[$. - 1]) {
			print STDERR "$ARGV[0], Row $.: risk factor \"$fields[0]\" does not match" .
				" corresponding column header \"@tnames[$. - 1]\".\n";
		}
​
		# No NC category (warning if there is)?
		! $opt_n && ! $opt_s && get_rf_category($fields[0]) eq "NC" && 
			print STDERR "$ARGV[0], Row $.: risk factor $fields[0] is linked to category NC.\n";
​
		# Please note that we only fill triangle above diagonal since we check for symmetry
		for ($i=$. - 2; $i<scalar(@tnames) - 1; $i++) {
			$tol[$. - 2][$i] = $fields[$i + 1];
			defined $opt_d && $opt_d > 2 && print "Tolerance[" . ($. - 2) . "][$i]=" . 
				$fields[$i + 1] . "\n"; 
		}
		for ($i=0; $i<$. - 1; $i++) {
			# Matrix symmetric: M(i,j) == M(j,i) for all i,j?
			if ($fields[$i + 1] != $tol[$i][$. - 2]) {
				print STDERR "$ARGV[0], Row $.: M[" . ($. - 2) . "][" . $i ."] != M[" . $i . 
						"][" . ($. - 2) . "]: " . $fields[$i + 1] . "!=" .
						$tol[$i][$. - 2] . ".\n";
			}
		}
	}
​
	# Matrix quadratic?
	if (scalar(@tnames) != $.) {
		print STDERR "$ARGV[0]: matrix is not quadratic: # of columns (" .
			scalar(@tnames) . ") != # of rows ($.)!\n";
		exit(1);
	}
​
	close $tinfile;
	
}
our %rfcatpat=();	# links search pattern to risk factor category
our %rfcat=();		# speeds up get_rf_category
our $rfcatcount=0;	# counts risk factor categories in order to build @rfcatrank
​
our @m1=(); 		# First matrix
our @m2=(); 		# Second matrix
our $m2val;		# Temporary value of second matrix
our @m3=(); 		# Diff matrix: Second minus First
our @names1=();		# risk factor names in matrix 1
our @names2=();		# risk factor names in matrix 2
our %rfnames1=();	# to store row number of risk factor names in matrix 1
our %rfnames2=();	# to store row number of risk factor names in matrix 2
our $ccy;
our $t;			# tolerance
​
# Variables to process DC file
our @hnames=();		# helper array to split up risk factor names in DC file
our $rf1;
our $rf2;
our $old_rf;		# for row change comparisons of the DC matrices
our $all_rfnames_read;	# Boolean
our $start_next_row;	# Boolean
our $is_upper_right_triangle;	# Boolean
# Variables to rank outliers detected
our @diagnotone1=();	# ranks diagonal values <> 1 of matrix 1
our $dno1idx = 0;	# number of elements in @diagnotone1
our @diagnotone2=();	# ranks diagonal values <> 1 of matrix 2
our $dno2idx = 0;	# number of elements in @diagnotone2
our @totaldiff=();	# ranks all differences of matrix 2 minus matrix 1
our $tdidx = 0;		# number of elements in @totaldiff
our %rfcatrank=();
our %rfcatidx=();	# number of elements in @{$rfcatrank{$rfcatidx{rfname}}}
our %rfcccyrank=();
our %rfcccyidx=();	# number of elements in @{$rfccyrank{$rfcccyidx{rfname}}}
our %rfcpairrank=();
our %rfcpairidx=();	# number of elements in @{$rfcpairrank{$rfcpairidx{rfname}}}
​
init_rf_category($opt_r);
​
###########################################################
#                                                         #
#                   1. Read first matrix                  #    
#                                                         # 
###########################################################       
​
open (FILE, "<", $ARGV[0]) || die "$0: Cannot open $ARGV[0]: $!";
$line = <FILE>;
$line =~ s/[\r\n]+//g;
if (substr($line,0,1) eq ",") {
​
	# We read a CSV file
​
	@names1 = split(",", $line);
	for ($i=1; $i<@names1; $i++) {
		$rftrans{$names1[$i]} ||= $names1[$i]; 
		$rfnames1{$rftrans{$names1[$i]}} = $i;
	}
​
	while($line = <FILE>) {
		$line =~ s/[\r\n]+//g;
		@fields=split(",", $line);
​
		# Matrix quadratic?
		if (scalar(@names1) != scalar(@fields)) {
			print STDERR "$ARGV[0]: matrix is not quadratic: # of columns (" . @names1 . 
					") != # of fields in row $. (" . @fields . ")!\n";
			exit(1);
		}
​
		# Risk factor order left->right (top row) == top->bottom (leftmost column)?
		if ($fields[0] ne @names1[$. - 1]) {
			print STDERR "$ARGV[0], Row $.: risk factor \"$fields[0]\" does not match" .
				" corresponding column header \"@names1[$. - 1]\".\n";
		}
​
		# No NC category (warning if there is)?
		! $opt_n && ! $opt_s && get_rf_category($fields[0]) eq "NC" && 
			print STDERR "$ARGV[0], Row $.: risk factor $fields[0] is linked to category NC.\n";
​
		# Diagonals == 1 (warning)?
		if (abs($fields[$. - 1] - 1) > $epsilon) {
			($dno1idx, @diagnotone1) = rankinsert($fields[$. - 1],
							"$ARGV[0], Row $.: $fields[0]",
						   	2, -2, 0, $dno1idx, @diagnotone1)
						   	unless $rfignore{$fields[0]};
			! $opt_s && print STDERR "$ARGV[0], Row $.: Diagonal element is not equal to 1: M[" . 
						($. - 1) . "," . ($. - 1) . "] == " . $fields[$. - 1] . ".\n";
		}
​
		# Please note that we only fill triangle above diagonal since we check for symmetry
		for ($i=$. - 2; $i<scalar(@names1) - 1; $i++) {
			$m1[$. - 2][$i] = $fields[$i + 1];
			defined $opt_d && $opt_d > 2 && print "Matrix1[" . ($. - 2) . "][$i]=" . 
				$fields[$i + 1] . "\n"; 
		}
		for ($i=0; $i<$. - 1; $i++) {
			# Matrix symmetric: M(i,j) == M(j,i) for all i,j?
			if ($fields[$i + 1] != $m1[$i][$. - 2]) {
				print STDERR "$ARGV[0], Row $.: M[" . ($. - 2) . "][" . $i ."] != M[" . $i . 
						"][" . ($. - 2) . "]: " . $fields[$i + 1] . "!=" .
						$m1[$i][$. - 2] . ".\n";
			}
		}
	}
​
	# Matrix quadratic?
	if (scalar(@names1) != $.) {
		print STDERR "$ARGV[0]: matrix is not quadratic: # of columns (" .
			scalar(@names1) . ") != # of rows ($.)!\n";
		exit(1);
	}
​
} elsif (substr($line,0,1) eq "\*") {
​
	# We read a DC file
​
	$all_rfnames_read = 0;	# We have not identified all risk factor names yet
	$i = 1;
	$is_upper_right_triangle = 0;
	$old_rf = "";
​
	while($line = <FILE>) {
		$line = substr($line,0,length($line)-2);
		next if (($line  =~ /^\*/));
		next if (($line  =~ /^$/));
​
		@fields = split(",", $line);
		@hnames = split(/\./, $fields[0]);
		if ($is_upper_right_triangle) {
			$rf1 = $hnames[0] . "." . $hnames[1];
			$rf2 = $hnames[2] . "." . $hnames[3];
		} else {
			$rf2 = $hnames[0] . "." . $hnames[1];
			$rf1 = $hnames[2] . "." . $hnames[3];
		}
		
		if ($. == 4) {
			if ($rf1 eq $old_rf) {
				# DC file is of upper right triangle form
				$is_upper_right_triangle = 1;
				$rf2 = $rf1;
				$rf1 = $hnames[0] . "." . $hnames[1];
			}
		}
​
		if ($rf2 ne $old_rf) {
			$start_next_row = 1;
		} else {
			$start_next_row = 0;
		}
		$old_rf = $rf2;
​
		if ($start_next_row) {
			if ($. > 3) {
				$all_rfnames_read = 1;
			}
			if ($rf1 ne $rf2) {
				print STDERR "$ARGV[0], Row $.: matrix is not quadratic: After change of 2." .
						" risk factor name the next diagonal element has" .
						" to have (name 1 == name 2)!\n";
				exit(1);
			}
			# Diagonals == 1 (warning)?
			if (abs($fields[1] - 1) > $epsilon) {
				($dno1idx, @diagnotone1) = rankinsert($fields[1],
								"$ARGV[0], Row $.: $rf1",
							   	2, -2, 0, $dno1idx, @diagnotone1)
							   	unless $rfignore{$rf1};
				! $opt_s && print STDERR "$ARGV[0], Row $.: Diagonal element is not equal to 1: M[" . 
						($rfnames1{$rftrans{$rf1}}) . "," . ($rfnames1{$rftrans{$rf2}}) .
						"] == " . $fields[1] . ".\n";
			}
		}			
​
		if (! $all_rfnames_read) {
			$rftrans{$rf1} ||= $rf1;
			$names1[$i] = $rftrans{$rf1};
			if (! defined $rfnames1{$rftrans{$rf1}}) {
				$rfnames1{$rftrans{$rf1}} = $i++;
			}
		} else {
			# Risk factor order left->right (top row) == top->bottom (leftmost column)?
			! defined $rftrans{$rf1} &&
				print STDERR "$ARGV[0], Row $.: risk factor \"$rf1\" does not exist.\n";
			! defined $rftrans{$rf2} &&
				print STDERR "$ARGV[0], Row $.: risk factor \"$rf2\" does not exist.\n";
		}
​
		# No NC category (warning if there is)?
		! $opt_n && ! $opt_s && get_rf_category($rf1) eq "NC" &&
			print STDERR "$ARGV[0], Row $.: risk factor $rf1 is linked to category NC.\n";
		! $opt_n && ! $opt_s && get_rf_category($rf2) eq "NC" &&
			print STDERR "$ARGV[0], Row $.: risk factor $rf2 is linked to category NC.\n";
​
		# Please note that we only fill triangle above diagonal
		$m1[$rfnames1{$rftrans{$rf2}} - 1][$rfnames1{$rftrans{$rf1}} - 1] = $fields[1];
		defined $opt_d && $opt_d > 2 && print "Matrix1[" . $rfnames1{$rftrans{$rf2}} . 
							"][$rfnames1{$rftrans{$rf1}}]=" . $fields[1] . "\n"; 
	}
​
	# Matrix quadratic?
	if (scalar(@names1) != sqrt(2*$. - 3.75) + 0.5) {
		print STDERR "$ARGV[0]: matrix is not quadratic: # of columns (" . scalar(@names1) . 
				") != # of rows (" . (sqrt(2*$. - 3.75) + 0.5) . ")!\n";
		# exit(1);
	}
​
}
​
close(FILE);
​
! $opt_s && $dno1idx && printarr("Diagonal in matrix 1 not 1:", $dno1idx, @diagnotone1);
​
###########################################################
#                                                         #
#                   2. Read second matrix                 #    
#                                                         # 
###########################################################       
our $m1name = $ARGV[0];
shift;
$all_rfnames_read = 0;
open (FILE, "<", $ARGV[0]) || die "Cannot open $ARGV[0]: $!";
​
$line = <FILE>;
$line =~ s/[\r\n]+//g;
if (substr($line,0,1) eq ",") {
​
	# We read a CSV file
​
	@names2 = split(",", $line);
	for ($i=1; $i<@names2; $i++) {
		$rfnames2{$names2[$i]} = $i;
	}
​
	while($line = <FILE>) {
		$line =~ s/[\r\n]+//g;
		@fields=split(",", $line);
​
		# Matrix quadratic?
		if (scalar(@names2) != scalar(@fields)) {
			print STDERR "$ARGV[0]: matrix is not quadratic: # of columns (" . @names2 . 
					") != # of fields in row $. (" . @fields . ")!\n";
			exit(1);
		}
​
		# Risk factor order left->right (top row) == top->bottom (leftmost column)?
		if ($fields[0] ne @names2[$. - 1]) {
			print STDERR "$ARGV[0], Row $.: risk factor \"$fields[0]\" does not match" .
				" corresponding column header \"@names2[$. - 1]\".\n";
		}
​
		# Warn about risk factors which are in first matrix but not in second
		#if (! (defined $rfnames1{$rftrans{$fields[0]}})) {
		#	print STDERR "$ARGV[0], Row $.: risk factor \"$fields[0]\" does not exist in " .
		#		 "$m1name" . "\n";
		#}
​
		# No NC category (warning if there is)?
		! $opt_n && ! $opt_s && get_rf_category($fields[0]) eq "NC" && 
			print STDERR "$ARGV[0], Row $.: risk factor $fields[0] is linked to category NC.\n";
​
		# Diagonals == 1 (warning)?
		if (abs($fields[$. - 1] - 1) > $epsilon) {
			($dno2idx, @diagnotone2) = rankinsert($fields[$. - 1],
							"$ARGV[0], Row $.: $fields[0]",
						   	2, -2, 0, $dno2idx, @diagnotone2)
						   	unless $rfignore{$fields[0]};
			! $opt_s && print STDERR "$ARGV[0], Row $.: Diagonal element is not equal to 1: M[" .
						 ($. - 1) . "," . ($. - 1) . "] == " . $fields[$. - 1] . ".\n";
		}
​
		# Please note that we only fill triangle above diagonal since we check for symmetry
		for ($i=$. - 2; $i<scalar(@names2) - 1; $i++) {
			$m2[$. - 2][$i] = $fields[$i + 1];
			defined $opt_d && $opt_d > 2 && print "Matrix2[" . ($. - 2) . "][$i]=" .
				 $fields[$i + 1] . "\n"; 
		}
		for ($i=0; $i<$. - 1; $i++) {
			# Matrix symmetric: M(i,j) == M(j,i) for all i,j?
			if ($fields[$i + 1] != $m2[$i][$. - 2]) {
				print STDERR "$ARGV[0], Row $.: M[" . ($. - 2) . "][" . $i ."] != M[" . $i . 
						"][" . ($. - 2) . "]: " . $fields[$i + 1] . "!=" .
						$m2[$i][$. - 2] . ".\n";
			}
		}
	}
​
	# Matrix quadratic?
	if (scalar(@names2) != $.) {
		print STDERR "$ARGV[0]: matrix is not quadratic: # of columns (" . scalar(@names2) .
			 ") != # of rows ($.)!\n";
		exit(1);
	}
​
} elsif (substr($line,0,1) eq "\*") {
​
	# We read a DC file
​
	$all_rfnames_read = 0;	# We have not identified all risk factor names yet
	$i = 1;
	$is_upper_right_triangle = 0;
	$old_rf = "";
​
	while($line = <FILE>) {
		$line = substr($line,0,length($line)-2);
		next if (($line  =~ /^\*/));
		next if (($line  =~ /^$/));
​
		@fields = split(",", $line);
		@hnames = split(/\./, $fields[0]);
		if ($is_upper_right_triangle) {
			$rf1 = $hnames[0] . "." . $hnames[1];
			$rf2 = $hnames[2] . "." . $hnames[3];
		} else {
			$rf2 = $hnames[0] . "." . $hnames[1];
			$rf1 = $hnames[2] . "." . $hnames[3];
		}
		
		if ($. == 4) {
			if ($rf1 eq $old_rf) {
				# DC file is of upper right triangle form
				$is_upper_right_triangle = 1;
				$rf2 = $rf1;
				$rf1 = $hnames[0] . "." . $hnames[1];
			}
		}
​
		if ($rf2 ne $old_rf) {
			$start_next_row = 1;
		} else {
			$start_next_row = 0;
		}
		$old_rf = $rf2;
​
		if ($start_next_row) {
			if ($. > 3) {
				$all_rfnames_read = 1;
			}
			if ($rf1 ne $rf2) {
				print STDERR "$ARGV[0], Row $.: matrix is not quadratic: After change of 2." .
					" risk factor name the next diagonal element has to be" .
					" given (name 1 == name 2)!\n";
				exit(1);
			}
			# Diagonals == 1 (warning)?
			if (abs($fields[1] - 1) > $epsilon) {
				($dno2idx, @diagnotone2) = rankinsert($fields[1],
								"$ARGV[0], Row $.: $rf1",
							   	2, -2, 0, $dno2idx, @diagnotone2)
							   	unless $rfignore{$rf1};
				! $opt_s && print STDERR "$ARGV[0], Row $.: Diagonal element is" .
						" not equal to 1: M[" . 
						($rfnames2{$rf1}) . "," . ($rfnames2{$rf2}) . "] == " .
						$fields[1] . ".\n";
			}
		}			
​
		if (! $all_rfnames_read) {
			$names2[$i] = $rf1;
			if (defined $rfnames2{$rf1}) {
				print STDERR "$ARGV[0], Row $.: risk factor \"$rf1\" already exists.\n";
			} else {
				$rfnames2{$rf1} = $i++;
			}
		} else {
			# Risk factor order left->right (top row) == top->bottom (leftmost column)?
			if (! (defined $rfnames2{$rf1})) {
				print STDERR "$ARGV[0], Row $.: risk factor \"$rf1\" does not exist.\n";
			}
			if (! (defined $rfnames2{$rf2})) {
				print STDERR "$ARGV[0], Row $.: risk factor \"$rf2\" does not exist.\n";
			}
		}
​
		# No NC category (warning if there is)?
		! $opt_n && ! $opt_s && get_rf_category($rf1) eq "NC" &&
			print STDERR "$ARGV[0], Row $.: risk factor $rf1 is linked to category NC.\n";
		! $opt_n && ! $opt_s && get_rf_category($rf2) eq "NC" &&
			print STDERR "$ARGV[0], Row $.: risk factor $rf2 is linked to category NC.\n";
​
		# Please note that we only fill triangle above diagonal
		$m2[$rfnames2{$rf2} - 1][$rfnames2{$rf1} - 1] = $fields[1];
		defined $opt_d && $opt_d > 2 && print "Matrix2[" . $rfnames2{$rf2} . 
							"][$rfnames2{$rf1}]=" . $fields[1] . "\n"; 
	}
​
	# Matrix quadratic?
	if (scalar(@names2) != sqrt(2*$. - 3.75) + 0.5) {
		print STDERR "$ARGV[0]: matrix is not quadratic: # of columns (" . scalar(@names2) .
				") != # of rows (" . (sqrt(2*$. - 3.75) + 0.5) . ")!\n";
		# exit(1);
	}
​
}
​
close(FILE);
​
! $opt_s && $dno2idx && printarr("Diagonal in matrix 2 not 1:", $dno2idx, @diagnotone2);
​
# Warn about risk factors which are in first matrix but not in second
foreach (keys %rfnames1) {
	if (! defined $rfnames2{$_}) {
		print STDERR "Risk factors in $m1name but not in $ARGV[0]\n";
		last;
	}
}
foreach (keys %rfnames1) {
	if (! defined $rfnames2{$_}) {
		if ($_ eq $rftrans{$_}) {
			print STDERR $rftrans{$_} . "\n";
		} else {
			print STDERR $rftrans{$_} . ",$_\n";
		}
	}
}
​
# Warn about risk factors which are in second matrix but not in first
foreach (keys %rfnames2) {
	if (! defined $rfnames1{$_}) {
		print STDERR "Risk factors in $ARGV[0] but not in $m1name\n";
		last;
	}
}
foreach (keys %rfnames2) {
	if (! defined $rfnames1{$_}) {
		print STDERR $_ . "\n";
	}
}
​
###########################################################
#                                                         #
#                     3. Compare Matrices                 #
#                                                         #
###########################################################
​
# Calculate differences
defined $opt_d && $opt_d > 2 && print "#Rows=" . scalar(@names1) . "\n";
for ($i=0; $i<scalar(@names1); $i++) {
	defined $opt_d && $opt_d > 2 && print "Row," . $i . ",Start\n";
	defined $opt_d && $opt_d > 2 && print "#Columns=" . scalar(@names1) . "\n";
	for ($j=$i; $j<scalar(@names1); $j++) {
		defined $opt_d && $opt_d > 2 && print "Row," . $i . ",Column," . $j . ",Start\n";
		if (defined $names1[$i + 1] && defined $names1[$j + 1] && 
			defined $rfnames2{$names1[$i + 1]} && defined $rfnames2{$names1[$j + 1]}) {
			$m2val = $m2[min($rfnames2{$names1[$i + 1]} - 1,
				      $rfnames2{$names1[$j + 1]} - 1)][max($rfnames2{$names1[$i + 1]} - 1, 
					$rfnames2{$names1[$j + 1]} - 1)];
			$m3[$i][$j] = $m2val - $m1[$i][$j];
			if (defined $hashtnames{$names1[$i + 1]} && defined $hashtnames{$names1[$j + 1]}) {
				$t = $tol[min($hashtnames{$names1[$i + 1]} - 1,
					$hashtnames{$names1[$j + 1]} - 1)][max($hashtnames{$names1[$i + 1]} - 1, 
					$hashtnames{$names1[$j + 1]} - 1)];
			} else {
				$t = 0;
			}
			defined $opt_d && $opt_d > 2 && print "Matrix3[" . $i . 
							"][$j]=" . $m3[$i][$j] . ",Tol=$t\n"; 
			($tdidx, @totaldiff) = rankinsert($m3[$i][$j],
				get_rf_category($names1[$i + 1]) . ",$names1[$i + 1]," .
				get_rf_category($names1[$j + 1]) . ",$names1[$j + 1]," .
				$m1[$i][$j] . "," . $m2val,
				$devglobal[0], $devglobal[1], $t,
				$tdidx, @totaldiff)
				unless $rfignore{$names1[$i + 1]} || $rfignore{$names1[$j + 1]};
			# If you like to understand the next statement please have a look at
			# http://perldoc.perl.org/perllol.html
			($rfcatidx{get_rf_category($names1[$i + 1])},
				@{$rfcatrank{get_rf_category($names1[$i + 1])}}) = rankinsert($m3[$i][$j], 
				get_rf_category($names1[$i + 1]) . ",$names1[$i + 1]," .
				get_rf_category($names1[$j + 1]) . ",$names1[$j + 1]," .
				$m1[$i][$j] . "," . $m2val,
				$devrfcat{get_rf_category($names1[$i + 1])}[0],
				$devrfcat{get_rf_category($names1[$i + 1])}[1], $t, 
				$rfcatidx{get_rf_category($names1[$i + 1])},
				@{$rfcatrank{get_rf_category($names1[$i + 1])}})
				unless $rfignore{$names1[$i + 1]} || $rfignore{$names1[$j + 1]};
			if (get_rf_category($names1[$i + 1]) ne get_rf_category($names1[$j + 1])) {
				($rfcatidx{get_rf_category($names1[$j + 1])},
					@{$rfcatrank{get_rf_category($names1[$j + 1])}}) = 
					rankinsert($m3[$i][$j], 
					get_rf_category($names1[$i + 1]) . ",$names1[$i + 1]," .
					get_rf_category($names1[$j + 1]) . ",$names1[$j + 1]," .
					$m1[$i][$j] . "," . $m2val,
					$devrfcat{get_rf_category($names1[$j + 1])}[0],
					$devrfcat{get_rf_category($names1[$j + 1])}[1], $t,
					$rfcatidx{get_rf_category($names1[$j + 1])},
					@{$rfcatrank{get_rf_category($names1[$j + 1])}})
					unless $rfignore{$names1[$i + 1]} || $rfignore{$names1[$j + 1]};
			}
			$rfcpairidx{get_rf_category($names1[$i + 1]) . "," . 
				get_rf_category($names1[$j + 1])} ||= 0;
			($rfcpairidx{get_rf_category($names1[$i + 1]) . "," . 
				get_rf_category($names1[$j + 1])}, 
				@{$rfcpairrank{get_rf_category($names1[$i + 1]) . "," .
				get_rf_category($names1[$j + 1])}}) = rankinsert($m3[$i][$j], 
				get_rf_category($names1[$i + 1]) . ",$names1[$i + 1]," .
				get_rf_category($names1[$j + 1]) . ",$names1[$j + 1]," .
				$m1[$i][$j] . "," . $m2val, 
				$devrfcpair{get_rf_category($names1[$i + 1]) . "," . 
				get_rf_category($names1[$j + 1])}[0], 
				$devrfcpair{get_rf_category($names1[$i + 1]) . "," . 
				get_rf_category($names1[$j + 1])}[1], $t,
				$rfcpairidx{get_rf_category($names1[$i + 1]) . "," . 
				get_rf_category($names1[$j + 1])},
				@{$rfcpairrank{get_rf_category($names1[$i + 1]) . "," .
				get_rf_category($names1[$j + 1])}})
				unless $rfignore{$names1[$i + 1]} || $rfignore{$names1[$j + 1]};
			$ccy = substr($names1[$i + 1], 0, 3);
			$rfcccyidx{$ccy} ||= 0;
			($rfcccyidx{$ccy}, @{$rfcccyrank{$ccy}}) = rankinsert($m3[$i][$j], 
				get_rf_category($names1[$i + 1]) . ",$names1[$i + 1]," .
				get_rf_category($names1[$j + 1]) . ",$names1[$j + 1]," .
				$m1[$i][$j] . "," . $m2val,
				$devccy{$ccy}[0], $devccy{$ccy}[1], $t,
				$rfcccyidx{$ccy}, @{$rfcccyrank{$ccy}})
				unless $rfignore{$names1[$i + 1]} || $rfignore{$names1[$j + 1]};
			if ($ccy ne substr($names1[$j + 1], 0, 3)) {
				$ccy = substr($names1[$j + 1], 0, 3);
				$rfcccyidx{$ccy} ||= 0;
				($rfcccyidx{$ccy}, @{$rfcccyrank{$ccy}}) = rankinsert($m3[$i][$j], 
					get_rf_category($names1[$i + 1]) . ",$names1[$i + 1]," .
					get_rf_category($names1[$j + 1]) . ",$names1[$j + 1]," .
					$m1[$i][$j] . "," . $m2val, 
					$devccy{$ccy}[0], $devccy{$ccy}[1], $t,
					$rfcccyidx{$ccy}, @{$rfcccyrank{$ccy}})
					unless $rfignore{$names1[$i + 1]} || $rfignore{$names1[$j + 1]};
			}
		}
		defined $opt_d && $opt_d > 2 && print "Row," . $i . ",Column," . $j . ",End\n";
	}
	defined $opt_d && $opt_d > 2 && print "Row," . $i . ",End\n";
}
​
###########################################################
#                                                         #
#               Now standard output to Stdout             #    
#                                                         # 
###########################################################       
​
print "$0,$version,";
print "Ignored risk factors in " . $opt_i if defined $opt_i;
print "\nSlice,[Category/Currency],[Category],\n";
print "Min/max difference";
print " beyond tolerance" unless ! $opt_b;
print ",Category 1,Risk Factor 1,Category 2,Risk Factor2,Old value,New value\n\n";
​
$tdidx && printarr("GLOBAL,,", $tdidx, @totaldiff);
our $rfk;
foreach my $rfk (sort keys %rfcatidx) {
	$rfcatidx{$rfk} && printarr("CATEGORY,$rfk,", $rfcatidx{$rfk}, @{$rfcatrank{$rfk}});
}
foreach $rfk (sort keys %rfcccyidx) {
	$rfcccyidx{$rfk} && printarr("CURRENCY,$rfk,", $rfcccyidx{$rfk}, @{$rfcccyrank{$rfk}});
}
foreach $rfk (sort keys %rfcpairidx) {
	$rfcpairidx{$rfk} && printarr("CATEGORYPAIR,$rfk", $rfcpairidx{$rfk}, @{$rfcpairrank{$rfk}});
}
​
$opt_w && close $doutfile;
​
exit(0);
​
sub printarr {
# Print array. With option -w write min & max into deviation file.
#
# Version Date       Author         Comment
# 1.4     26/12/2018 Bernd Plumhoff Anonymized version
	my ($title, $idx, @arr) = @_;
	my $i;
​
	print "$title\n";
	for ($i=0; $i<$idx; $i++) {
		printf STDOUT "%7.4f,%s,\n", $arr[$i][0], $arr[$i][1];
	}
	print "\n";
​
	if (defined $opt_w && $idx > 0) {
		# If we have min and/or max write them into deviation file.
		# Please note that in this version of Perl (5.12.4) the standard
		# precision of the %f format is 6 digits - which coincides with 
		# our definition of $epsilon above.
		$arr[$opt_m][0] ||= 0;
		$arr[$opt_m + 1][0] ||= 0;
		$arr[$opt_m + 2][0] ||= 0;
		printf $doutfile "%s,%.6f,%.6f,%u,%u,%u\n", $title, $arr[0][0],
			$arr[$idx - 1][0],$arr[$opt_m][0],$arr[$opt_m + 1][0],
			$arr[$opt_m + 2][0];
	}
}
​
sub init_rf_category {
# Initialize risk factor hashtable with recognition patterns
#
# Synopsis: init_rf_category(RF_Category_filename)
#
# Example:  init_rf_category("./RF_Categories.csv");
#
# Version Date       Author         Comment
# 1.3     26/12/2018 Bernd Plumhoff Anonymized version
	open (FILE, "<", $_[0]);
	while (my $rfline = <FILE>) {
		$rfline =~ s/[\r\n]+//g;
		if (substr($rfline,0,2) ne '//' and 4 < length($rfline)) {
			my @rffields = split(",", $rfline);
			my $matchpattern = $rffields[0];
			if (substr($matchpattern,0,1) eq '#') {
				$matchpattern = '^(.*)' . substr($matchpattern,1,length($matchpattern) - 1) . '\(T[0-9]+\)$';
			} else {
				$matchpattern = '^(.*)\.' . $matchpattern . '$';
			}
			$rfcatpat{$matchpattern} = $rffields[3];
		}
	}
	close (FILE);
}
​
sub get_rf_category {
# Return risk factor category (Super Category - SubCategory) for a recognized pattern
# or "NC-NC" if no pattern matched.
#
# Synopsis: get_rf_category(Risk_Factor)
#
# Example:  get_rf_category("USD.#SPREAD-CORP-BB(T1825)"); 
#           will result in "MR-CS-CORP".
#
# Version Date       Author         Comment
# 1.3     26/12/2018 Bernd Plumhoff Anonymized version
	defined $rfcat{$_[0]} && return $rfcat{$_[0]};
	my $searchpat = $_[0];
	my $success = "NC";
	$searchpat =~ s/\.\#/-/; # We have to substitute ".#" by "-" in order to match the patterns
	foreach my $pat (keys %rfcatpat) {
		# my $temp = $searchpat =~ /$pat/; 
		# print $searchpat . " =~ \"" . $pat . "\" -> " . $temp . "\n";
		# Please note that if this approach is too slow we can try to apply
		# the map, study and eval commands to speed this up later.
		# See http://perldoc.perl.org/functions/study.html, for example. [Bernd 25/01/2012]
		# General hints to speed perl up: http://www.ccl4.org/~nick/P/Fast_Enough/
		# [Bernd 08/03/2012]
		$success = $rfcatpat{$pat}, last if $searchpat =~ /$pat/;
	}
	if ($success eq "NC") {
		# This is a trick because the RAI regex are sometimes comparing 
		# against $ when there still is a bracket term.
		# For example: CZK.#SWAP(T30)
		# In this case we omit the bracket term and look up CZK.#SWAP.
		$searchpat = substr($searchpat, 0, index($searchpat, "("));
		foreach my $pat (keys %rfcatpat) {
			$success = $rfcatpat{$pat}, last if $searchpat =~ /$pat/;
		}
	}
	$rfcat{$_[0]} = $success;	# next call will be quicker
	$rfcatidx{$success} = 0;
	return $success;
}
​
sub rankinsert {
# Ranks and inserts value into array and stores text with it.
#
# Synopsis: rankinsert(value, text, deviation_lower_bound, deviation_upper_bound,
#		tolerance, arrayindex, array[][])
#
# Example:  rankinsert($fields[$. - 1], "$ARGV[0], Row $.: $fields[0]", 2, -2, 0, 
#                                       $dno1idx, @diagnotone1);
#
# Version Date       Author         Comment
# 1.1     26/12/2018 Bernd Plumhoff Anonymized version
​
my ($value, $text, $devlb, $devub, $tol, $idx, @arr) = @_;
my $i;
my $border = int($opt_m / 2) - 1;
if (defined $opt_b) {
	if ($value > $tol + $epsilon) {
		$value -= $tol;
		if (defined $devlb && defined $devub && 
			($value < $devlb - $epsilon || $value > $devub + $epsilon)) {
			return ($idx, @arr);
		}
		$arr[$opt_m + 2][0]++;	# Tolerance overshot
	} elsif ($value < -$tol - $epsilon) {
		$value += $tol;
		if (defined $devlb && defined $devub && 
			($value < $devlb - $epsilon || $value > $devub + $epsilon)) {
			return ($idx, @arr);
		}
		$arr[$opt_m + 1][0]++;	# Tolerance undershot
	} else {
		$arr[$opt_m][0]++;	# Total count for this slice
		return ($idx, @arr);
	}
} else {
	if ($value > $tol + $epsilon) {
		if (defined $devlb && defined $devub && 
			($value < $devlb - $epsilon || $value > $devub + $epsilon)) {
			return ($idx, @arr);
		}
		$arr[$opt_m + 2][0]++;	# Tolerance overshot
	} elsif ($value < -$tol - $epsilon) {
		if (defined $devlb && defined $devub && 
			($value < $devlb - $epsilon || $value > $devub + $epsilon)) {
			return ($idx, @arr);
		}
		$arr[$opt_m + 1][0]++;	# Tolerance undershot
	} else {
		$arr[$opt_m][0]++;	# Total count for this slice
		return ($idx, @arr);
	}
}
$arr[$opt_m][0]++;	# Total count for this slice
​
if ($idx >= $opt_m) {
	# @arr has been filled already. We potentially need to throw less extreme 
	# values out and we might need to move (apply a different rank to) others.
	$i = $border;
	if ($value < $arr[$i][0]) {
		# We found a small outlier
		do {
			if ($i < $border) {
				$arr[$i + 1][0] = $arr[$i][0];
				$arr[$i + 1][1] = $arr[$i][1];
			}
		} while (--$i >= 0 && $value < $arr[$i][0]);
		$arr[$i + 1][0] = $value;
		$arr[$i + 1][1] = $text;
		return ($idx, @arr);
	} else {
		$i++;
		if ($value > $arr[$i][0]) {
			# We found a big outlier
			while ($i + 1 < $opt_m && $value > $arr[$i + 1][0]) {
				$arr[$i][0] = $arr[$i + 1][0];
				$arr[$i][1] = $arr[$i + 1][1];
				$i++;
			}
			$arr[$i][0] = $value;
			$arr[$i][1] = $text;
		}
	}
} else {
	# @arr is not full yet. We are sure that the new value will be inserted 
	# but we might need to move (apply a different rank to) others.
	if ($idx == 0) {
		# Ok, it's the very first array member
		$arr[$idx][0] = $value;
		$arr[$idx++][1] = $text;
	} else {
		$i = $idx - 1;
		if ($value < $arr[$i][0]) {
			# We found a small outlier
			do {
				$arr[$i + 1][0] = $arr[$i][0];
				$arr[$i + 1][1] = $arr[$i][1];
			} while (--$i >= 0 && $value < $arr[$i][0]);
			$arr[$i + 1][0] = $value;
			$arr[$i + 1][1] = $text;
		} else {
			# A new max can simply be added at the end
			$i++;
			$arr[$i][0] = $value;
			$arr[$i][1] = $text;
		}
		$idx++;
	}
}
return ($idx, @arr);
}
​
Perl
Game of Nim
Last updated 8 months ago