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 $matrixB,"<br>\n";
exit(0);
`
The results from running the above script are:
`$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]]
`
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 $matrixB,"<br>\n";
exit(0);
`
The results from running the above script are:
`$matrixM =[ [ [1 1] [2 1] ] [ [ 1 -2] [ 2 -1] ] ]
$matrixB =[ [ 5 8] [10 -5] ]
$matrixX =
[ [
[ 5 -13]
[ 0 21] ]
[ [ 5 -6]
[ 0 -7] ] ]
`
So my question is why am I getting such a clearly erroneous result when I run the second piece of code? |
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