#!/usr/bin/perl
use warnings;
use Math::Matrix;

#say you have equations
# 1x   2y   3z   4w  = 17
# 5x   6y   7z   8w  = 18
# 9x   10y  11z  12w = 19
# 13x  14y  15z  16w = 20

$a = new Math::Matrix ([1,2,3,4],
                       [5,6,7,8],
                       [9,10,11,12],
                       [13,14,15,16]);

$x = new Math::Matrix ([17,18,19,20]);

print "det-> ",$a->determinant,"\n";

$a->print("A\n");
$E = $a->concat($x->transpose);
$E->print("Equation system\n");
$s = $E->solve;
$s->print("Solutions s\n");
$a->multiply($s)->print("A*s\n");


##</code><code>##

OUTPUT
det-> 0
A
1.00000    2.00000    3.00000    4.00000
5.00000    6.00000    7.00000    8.00000
9.00000   10.00000   11.00000   12.00000
13.00000  14.00000   15.00000   16.00000

Equation system
1.00000    2.00000    3.00000    4.00000   17.00000
5.00000    6.00000    7.00000    8.00000   18.00000
9.00000   10.00000   11.00000   12.00000   19.00000
13.00000  14.00000   15.00000   16.00000   20.00000

Solutions s
-16.50000
16.75000
0.00000
0.00000

A*s
17.00000
18.00000
19.00000
20.00000

##</code><code>##

#!/usr/bin/perl
use warnings;
use strict;
use Math::MatrixReal;

my ($a1, $b1, $c1, $d1, $e1,
$a2, $b2, $c2, $d2, $e2,
$a3, $b3, $c3, $d3, $e3,
$a4, $b4, $c4, $d4, $e4) =
(1,  2,  3,  4,  17,
 5,  6,  7,  8,  18,
 9,  10, 11, 12, 19,
 13, 14, 15, 16, 20);

my $A = Math::MatrixReal->new_from_string(<<EOF);
[ $a1 $b1 $c1 $d1 ]
[ $a2 $b2 $c2 $d2 ]
[ $a3 $b3 $c3 $d3 ]
[ $a4 $b4 $c4 $d4 ]
EOF

my $b = Math::MatrixReal->new_from_string(<<EOF);
[ $e1 ]
[ $e2 ]
[ $e3 ]
[ $e4 ]
EOF

print "det-> ",$A->det(),"\n";

my $LR = $A->decompose_LR();

my ($dim, $solution, $B) = $LR->solve_LR($b);

#print "dim->$dim\n\nsolution->\n$solution\n\nbase->\n$B\n\n";
print "dim->$dim\n\nsolution->\n$solution\n\nbase->\n$B\n\n";

my $out = $A * $solution;
print $out,"\n";

##</code><code>##

OUTPUT:
det-> 0
dim->2

solution->
[ -5.333333333333E+00 ]
[  0.000000000000E+00 ]
[  0.000000000000E+00 ]
[  5.583333333333E+00 ]


[  1.700000000000E+01 ]
[  1.800000000000E+01 ]
[  1.900000000000E+01 ]
[  2.000000000000E+01 ]

##</code><code>##

#!/usr/bin/perl
use warnings;
use Math::Matrix;

$a = new Math::Matrix ([1, -2,  3,  4],
                       [4, -5,  6,  7],
                       [7,  8, -9,  10],
                       [8,  9, -9, -11],
                       );

$x = new Math::Matrix ([17,18,19,20]);

print "det-> ",$a->determinant,"\n";

$a->print("A\n");
$E = $a->concat($x->transpose);
$E->print("Equation system\n");
$s = $E->solve;
$s->print("Solutions s\n");
$a->multiply($s)->print("A*s\n");


##</code><code>##

OUTPUT:
det-> -1104

A
1.00000   -2.00000    3.00000    4.00000
4.00000   -5.00000    6.00000    7.00000
7.00000    8.00000   -9.00000   10.00000
8.00000    9.00000   -9.00000  -11.00000

Equation system
1.00000   -2.00000    3.00000    4.00000   17.00000
4.00000   -5.00000    6.00000    7.00000   18.00000
7.00000    8.00000   -9.00000   10.00000   19.00000
8.00000    9.00000   -9.00000  -11.00000   20.00000

Solutions s
1.45652
18.03261
16.02899
0.88043

A*s
17.00000
18.00000
19.00000
20.00000

##</code><code>##

#!/usr/bin/perl
use warnings;
use strict;
use Math::MatrixReal;

my ($a1, $b1, $c1, $d1, $e1,
$a2, $b2, $c2, $d2, $e2,
$a3, $b3, $c3, $d3, $e3,
$a4, $b4, $c4, $d4, $e4) =
(1,  -2,   3,   4,  17,
 4,  -5,   6,   7,  18,
 7,   8,  -9,  10,  19,
 8,   9,  -9, -11,  20);


my $A = Math::MatrixReal->new_from_string(<<EOF);
[ $a1 $b1 $c1 $d1 ]
[ $a2 $b2 $c2 $d2 ]
[ $a3 $b3 $c3 $d3 ]
[ $a4 $b4 $c4 $d4 ]
EOF

my $b = Math::MatrixReal->new_from_string(<<EOF);
[ $e1 ]
[ $e2 ]
[ $e3 ]
[ $e4 ]
EOF

print "det-> ",$A->det(),"\n";

my $LR = $A->decompose_LR();

my ($dim, $solution, $B) = $LR->solve_LR($b);

#print "dim->$dim\n\nsolution->\n$solution\n\nbase->\n$B\n\n";
print "dim->$dim\n\nsolution->\n\n$solution\n\n";

my $out = $A * $solution;
print $out,"\n";

##</code><code>##

det-> -1104
dim->0

solution->

[  1.456521739130E+00 ]
[  1.803260869565E+01 ]
[  1.602898550725E+01 ]
[  8.804347826087E-01 ]


[  1.700000000000E+01 ]
[  1.800000000000E+01 ]
[  1.900000000000E+01 ]
[  2.000000000000E+01 ]

##</code><code>##

[1  0  0  0],
[0  1  0  0],
[0  0  1  0],
[0  0  0  1]

##</code><code>##

#!/usr/bin/perl
use warnings;
use Math::MatrixReal;

$a = Math::MatrixReal->new_from_rows ([
[1, -2,  3,   4],
[4, -5,  6,   7],
[7,  8, -9,  10],
[8,  9, -9, -11],
]);

print $a,"\n";

my $b = Math::MatrixReal->new_from_cols ([
[17,18,19,20]
]);
print $b,"\n";

print $a->det(),"\n";

$inva = $a->inverse();
print $inva,"\n";

$c = $inva * $b ;

print "solution->\n$c\n";


##</code><code>##

OUTPUT:
[  1.000000000000E+00 -2.000000000000E+00  3.000000000000E+00  4.000000000000E+00 ]
[  4.000000000000E+00 -5.000000000000E+00  6.000000000000E+00  7.000000000000E+00 ]
[  7.000000000000E+00  8.000000000000E+00 -9.000000000000E+00  1.000000000000E+01 ]
[  8.000000000000E+00  9.000000000000E+00 -9.000000000000E+00 -1.100000000000E+01 ]

[  1.700000000000E+01 ]
[  1.800000000000E+01 ]
[  1.900000000000E+01 ]
[  2.000000000000E+01 ]

-1104
[ -1.684782608696E-01  1.739130434783E-01  5.434782608696E-03  5.434782608696E-02 ]
[  1.595108695652E+00 -6.304347826087E-01 -3.532608695652E-02  1.467391304348E-01 ]
[  1.362318840580E+00 -4.492753623188E-01 -8.695652173913E-02  1.304347826087E-01 ]
[  6.793478260870E-02 -2.173913043478E-02  4.619565217391E-02 -3.804347826087E-02 ]

solution->
[  1.456521739130E+00 ]
[  1.803260869565E+01 ]
[  1.602898550725E+01 ]
[  8.804347826087E-01 ]