use Math::Cephes::Matrix qw(mat);
$a = mat [[1, 2], [3, 4]];
$b = [1, 1];
print "@{$a->mul($b)}";
# print "3 7"    
    
##</code><code>##

use  Math::MatrixReal;
$a = Math::MatrixReal-&gt;new_from_rows( [[1, 2], [3, 4]] );
$b = Math::MatrixReal->new_from_cols( [ [1, 1] ] );
print $a*$b;
# print "[  3.000000000000E+000 ]
#        [  7.000000000000E+000 ]"    
    
##</code><code>##

use PDL;
$a = pdl [[1, 2],[3, 4]];
$b = pdl [[1], [1]];
print $a x $b;
# print "[
#         [3]
#         [7]
#        ]"    
    
##</code><code>##

>> a = [1, 2; 3, 4];
>> b = [1; 1];
>> a*b
ans =

        3
        7
    
##</code><code>##

> a = matrix(c(1,2,3,4), ncol=2, byrow=T)
> b = matrix(c(1,1), ncol=1)
> a%*%b
     [,1]
[1,]    3
[2,]    7
    
##</code><code>##

use Math::Cephes::Matrix qw(mat);
$mat = mat [[1, 2, 3], [4, 5, 6], [7, 8, 9]];
$mat = $mat->coef;
for my $i (1..2) {   # 0 first index
	print "@{$mat->[$i]}[1..2]\n";
}
# print "5 6
#        8 9"
    
##</code><code>##

use  Math::MatrixReal;
$mat = Math::MatrixReal->new_from_rows( 
	[[1, 2, 3], [4, 5, 6], [7, 8, 9]] );
for my $i (2..3) {   # 1 first index
	for my $j (2..3) {
		print $mat->element($i, $j), " ";
	}
	print "\n";
}
# print "5 6
#        8 9"
    
##</code><code>##

use PDL;
$mat = pdl [[1, 2, 3], [4, 5, 6], [7, 8, 9]];
print $mat->slice("1:2,1:2");   # 0 first index
# print "[
#         [5 6]
#         [8 9]
#        ]"
    
##</code><code>##

mat = [1,2,3; 4,5,6; 7,8,9];
mat(2:3, 2:3)
ans =

        5        6
        8        9
    
##</code><code>##

> mat = matrix(1:9, ncol=3, byrow=T)
> mat[2:3, 2:3]
     [,1] [,2]
[1,]    5    6
[2,]    8    9
    
##</code><code>##

> vec = 1:10
> vec
 [1]  1  2  3  4  5  6  7  8  9 10
> vec %% 2
 [1] 1 0 1 0 1 0 1 0 1 0
> vec[vec %% 2 == 1]
[1] 1 3 5 7 9
> vec[vec %% 2 == 1] + 1
[1]  2  4  6  8 10

##</code><code>##

#! /usr/local/bin/perl -w
use strict;
# -----------------------------------------------------------
# 	RSA algorithm -- assymetrical\public-key cryptography
# ----------------------------------------------------------- 
use Math::Pari qw(gcd PARI) ;
# ----------------------------------------------------------- 

# m -- message 
my $m = 'Perl' ;
print "original: $m\n" ;
my $tmpl = 'C*' ;
my @m = unpack($tmpl, $m) ;	   # string -> unsigned char values
print "coded: @m\n" ;

# n = pq -- in RSA, p & q = prime, each 1024 bits/308 digits long
my $p = PARI("prime(".int(rand 50).")") ;
my $q = PARI("prime(".int(rand 50).")") ;
my $n = $p*$q ;			# $n = Pari's obj

# choose a random number r, s.t.
# 	1 < r < (p-1)(q-1) = b
# 	gcd(r, b) = 1 -- relative prime
my $b = ($p-1)*($q-1) ;
my $r ;
do {$r = int rand $b ; } until (gcd($r,$b) == 1) ;
$r = PARI $r ;

# rk = 1 mod (p-1)(q-1) -- k = private key; (n, r) public
my $k = (1/$r)%$b ;		# Pari's math operators, since vars = Pari

# encrypt -- c = (m ^ r) mod n
my @c ;
map { $c[$_] = ($m[$_]**$r)%$n } 0..$#m ;   # Perl: ** for power
print "ciphered: @c\n" ;

# decrypt -- m = (c ^ k) mod n
my @d ; 
map { $d[$_] = PARI("($c[$_]^$k)%$n") } 0..$#c ;   # Pari: ^ for power
print "deciphered: @d\n" ;
print "decoded: " . pack($tmpl, @d) . "\n" ; 


__END__
original: Perl
coded: 80 101 114 108
ciphered: 18431 6512 5843 7236
deciphered: 80 101 114 108
decoded: Perl

##</code><code>##

#! /usr/local/bin/perl -w
use strict ;

R("getwd()");

sub R {
	my $Rpath = "C:\\R\\rw\\bin\\" ;
	my $Rcmd = $Rpath . "rterm --vanilla --quiet --slave" ;
	my $Rscript = shift ;
	$Rscript =~ s/(\r|;\r)/ ;/gm ; 
	$Rscript =~ s/<-/=/gm ; # \r or <- will break "echo"
	return `echo $Rscript | $Rcmd` ;
}

##</code><code>##

my $dir = 'D:\\tmp\\prog\\math\\lp32';
my $lp_solve = "d:\\mydir\\lp_solve.exe";
my $lpfile = "d:\\mydir\\model.lp";
(my $lp = << "	EOF") =~ s/^\s+//gm;
	min: 8  x1 + 15 x2       ;
	c1:  10 x1 + 21 x2 > 156 ;
	c2:  2  x1 +    x2 > 22  ;
EOF
open OUTFILE, "+>$lpfile";
print OUTFILE $lp;
close OUTFILE;
$output = qx($lp_solve < $lpfile);
$output =~ s/\r//gm;
print $lp;
print $output;
system("del $lpfile");

##</code><code>##

use strict;
use warnings;

my ($a1,$a2,$a3,$ref);

for my $x (0..20) {
	for my $y (0..20) {
		$ref->[$x][$y] = rand 100;
	}
}

use Math::Cephes::Matrix qw(mat);
$a1 = mat $ref;

use  Math::MatrixReal;
$a2 = Math::MatrixReal->new_from_rows( $ref );

use PDL;
use PDL::Slatec;
$a3 = pdl $ref;

use Benchmark qw(cmpthese);
cmpthese(100,
	{
		cephes=>sub{$a1->inv()},
		matrixreal=>sub{$a2->inverse()},
		pdl=>sub{matinv($a3)}
	}
);

__END__
             Rate matrixreal     cephes        pdl
matrixreal 5.28/s         --       -94%       -99%
cephes     83.3/s      1479%         --       -87%
pdl         625/s     11744%       650%         --