Prototype mismatch: sub main::append: none vs (;@) at (eval 6) line 8
Prototype mismatch: sub main::i: none vs () at ./ttt line 10
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I haven't followed your code further, except noting that it announces the inverse of $MatrixM, but prints its determinant.

Anno

Thank you for identifying the problem with the variable i when using CGI and PDL simultaneously. I eliminated the CGI loads (and therefore was forced to run the PDL scripts from my shell - wish I could have it both ways). However, there is still a problem.

Let's suppose we want to solve two (2) complex simultaneous equations in two unknowns:

Equation 1: (1+i)*Xsub1 + (2+i)*Xsub2 = 5+10i

Equation 2: (1-2i)*Xsub1 + (2-i)*Xsub2 = 8 -5i

The following code using only real PDL variables, is well-behaved and correctly solves for the variables Xsub1 and Xsub2 as 3+i, and 2+i respectively as the execution demonstrated forthwith after the code prooves.

.

#! /usr/bin/perl -w
use warnings;
use strict;    
use PDL;
my $matrixM = pdl  [ [ 1, 2,-1,-1],
                     [ 1, 2, 2, 1],
                     [ 1, 1, 1, 2],
                     [-2,-1, 1, 2] ];
my $matrixB = pdl [ [5],[10],
                    [8],[-5] ];
my $matrixX;
print "\$matrixM = ", $matrixM,"<br>\n";
print "\$matrixB = ", $matrixB,"<br>\n";
print "\$matrixX = ", $matrixM->inv x $matrixB,"<br>\n";
exit(0);
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The results from running the above script are:


$matrixM =
[ [ 1  2 -1 -1] 
 [ 1  2  2  1]
 [ 1  1  1  2]
 [-2 -1  1  2]]
$matrixB =
[ [ 5]
 [10]
 [ 8]
 [-5]]
$matrixX =
[ [         3] [         2]
  [         1] [         1]]
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This says that Xsub1 = 3+i, and Xsub2 = 2+i .....which is the correct result!

Now, in an effort to simplify, let's use the following functionally equivalent (?) PDL with complex matrices to solve the same two same simultaneous equations; observe the results after the following code:



#! /usr/bin/perl -w
use warnings;
use strict;    
use PDL;
use PDL::Complex;
my $matrixM = pdl [ [ 1+1*i, 2+1*i], [ 1-2*i, 2-1*i] ];<br>
my $matrixB = pdl [ 5+8*i, 10-5*i ];
my $matrixX;
print "\$matrixM = ",$matrixM,"<br>\n";
print "\$matrixB = ", $matrixB,"<br>\n";
print "\$matrixX = ", $matrixM->inv x $matrixB,"<br>\n";
exit(0);
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The results from running the above script are:


$matrixM =[   [  [1 1] [2 1] ]    [ [ 1 -2] [ 2 -1] ]   ]
$matrixB =[  [ 5  8] [10 -5] ]
$matrixX =
[ [
  [  5 -13]
  [  0  21] ]
 [ [ 5 -6]
  [ 0 -7] ] ]
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So my question is why am I getting such a clearly erroneous result when I run the second piece of code?

Ugh. Please update your writeup and put <code> tags around your code and the results. The square brackets are unreadable the way it is.

Anno

You wrote:

Equation 1: (1+i)*Xsub1 + (2+i)*Xsub2 = 5+10i

Equation 2: (1-2i)*Xsub1 + (2-i)*Xsub2 = 8 -5i
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[...]

This says that Xsub1 = 3+i, and Xsub2 = 2+i .....which is the correct result!

No, it isn't! I checked your result manually and couldn't believe what I found. So I took out PDL (which I'm not particularly familiar with) and used Math::Complex to run the following:

use Math::Complex;

my ( $m11, $m12) = ( 1 +   i, 2 + i);
my ( $m21, $m22) = ( 1 - 2*i, 2 - i);
my $b1 = 5 + 10*i;
my $b2 = 8 - 5*i;

my $xsub1 = 3 + i;
my $xsub2 = 2 + i;

my $r1 = $m11*$xsub1 + $m12*$xsub2;
my $r2 = $m21*$xsub1 + $m22*$xsub2;

print "$r1 (should be $b1)\n";
print "$r2 (should be $b2)\n";
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which prints

5+8i (should be 5+10i)
10-5i (should be 8-5i)
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Pardon me for being blunt, but you should have checked your result yourself instead of sending me (and who knows how many venerable monks more) on a wild-goose chase.

Apart from that, I don't see how you arrive at the real 4x4 matrix that you use to represent a complex 2x2 matrix. I think there is such a representation, but the one you're using is obviously wrong.

I have not followed your calculations any further. Very probably the result Math::Pari gave you is the correct one.

Anno

Update: Corrected mistaken reference to Math::Pari