Re^2: PDL works for real number matrix operations, but not working for complex number matrix operations.

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);
[download]

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]]
[download]

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);
[download]

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] ] ]
[download]

So my question is why am I getting such a clearly erroneous result when I run the second piece of code?

Comment on Re^2: PDL works for real number matrix operations, but not working for complex number matrix operations. Select or Download Code

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Re^3: PDL works for real number matrix operations, but not working for complex number matrix operations. by Anno (Deacon) on Mar 19, 2007 at 21:58 UTC
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	[reply] [d/l]
Re^3: PDL works for real number matrix operations, but not working for complex number matrix operations. by Anno (Deacon) on Mar 20, 2007 at 21:48 UTC
You wrote: `Equation 1: (1+i)Xsub1 + (2+i)Xsub2 = 5+10i Equation 2: (1-2i)Xsub1 + (2-i)Xsub2 = 8 -5i` [download] `[...]` 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 - 2i, 2 - i); my $b1 = 5 + 10i; my $b2 = 8 - 5i; 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";` [download] which prints `5+8i (should be 5+10i) 10-5i (should be 8-5i)` [download] 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`	[reply] [d/l] [select]
Re^4: PDL works for real number matrix operations, but not working for complex number matrix operations. by gmacfadden (Sexton) on Mar 21, 2007 at 17:00 UTC
Anno, please accept my sincere apology. I'm grateful for your's and all the monks' altruism in helping those of us trying to come up on the learning curve. I feel badly about whatever time the bespoke error caused you to waste. I will re-create a correct problem statement for my PDL question. If you can forgive this mistake, I would again value and invite your and the monk community's help.	[reply]
Re^5: PDL works for real number matrix operations, but not working for complex number matrix operations. by etj (Priest) on Jun 21, 2022 at 17:44 UTC
The differently-asked question was at PDL::Complex question. The answer was that PDL::Complex has severe limitations which can be partly mitigated by using PDL::LinearAlgebra; a more complete solution was part of PDL 2.040 with "native complex" number support.	[reply]