Because you invoked "least squares fitting", I assume what you want is a planar least-squares fitting in 3d, analogous to the linear least-squares in 2d, and that z is supposed be be linearly dependent on the others: ax+by+c = z

You can see the algebra in this math.stackexchange answer, but basically you are solving A*X=B, where A is a matrix of the x and y data, X are the column-vector of the coefficients a,b,c from the above equation, and B is the column-vector of the z values for each x,y input.

I haven't looked up the exact PDL syntax, but: An exact solution for 3 sets of (x,y,z) data would have PDL akin to $coeff_X = $matrix_A->inverse * $column_B;. But since you presumably have many points, not just three, since you invoked best-fit, you have to use the "left pseudo inverse", which would have a PDL implementation akin to $coeff_X = ($matrix_A->transpose * $matrix_A)->inverse * ($matrix_A->transpose) * $column_B;

#!/usr/bin/perl
use strict;
use warnings;
use PDL;
use PDL::Matrix;

# example: 2x + 3y + 4 = z, plug in known exact values; make sure my c
+oefficients end up 2,3,4

my $matrix_A = mpdl [
    [1,1,1],
    [3,7,1],
    [5,1,1],
    [1,5,1],
];

print "A => ", $matrix_A;
print "B => ", my $column_B = vpdl [9,31,17,21];
print "X => ", my $coeff_X = (($matrix_A->transpose x $matrix_A)->inv 
+x $matrix_A->transpose) x $column_B;
[download]

prints:

A => 
[
 [1 1 1]
 [3 7 1]
 [5 1 1]
 [1 5 1]
]
B => 
[
 [ 9]
 [31]
 [17]
 [21]
]
X => 
[
 [         2]
 [         3]
 [         4]
]
[download]