PDL::Primitive 2.4.3

PDL::Primitive Perl module contains primitive operations for pdl.

This module provides some primitive and useful functions defined using PDL::PP and able to use the new indexing tricks.

See PDL::Indexing for how to use indices creatively. For explanation of the signature format, see PDL::PP.

Inner product over one dimension

c = sum_i a_i * b_i
, BadDoc => If a() * b() contains only bad data, c() is set bad. Otherwise c() will have its bad flag cleared, as it will not contain any bad values., ); # pp_def( inner )

pp_def( outer, HandleBad => 1, Pars => a(n); b(m); [o]c(n,m);, Code => loop(n,m) %{ $c() = $a() * $b(); %}, BadCode => loop(n,m) %{ if ( $ISBAD(a()) || $ISBAD(b()) ) { $SETBAD(c()); } else { $c() = $a() * $b(); } %}, Doc => =for ref

outer product over one dimension

Naturally, it is possible to achieve the effects of outer product simply by threading over the "*" operator but this function is provided for convenience.
); # pp_def( outer )

pp_addpm(<<EOD); =head2 x
Signature: (a(i,x), b(z,i),[o]c(x,z))

Matrix multiplication

PDL overloads the x operator (normally the repeat operator) for matrix multiplication. The number of columns (size of the 0 dimension) in the left-hand argument must normally equal the number of rows (size of the 1 dimension) in the right-hand argument.

Row vectors are represented as (N x 1) two-dimensional PDLs, or you may be sloppy and use a one-dimensional PDL. Column vectors are represented as (1 x N) two-dimensional PDLs.

Threading occurs in the usual way, but as both the 0 and 1 dimension (if present) are included in the operation, you must be sure that you dont try to thread over either of those dims.

EXAMPLES:

Here are some simple ways to define vectors and matrices:
perldl> $r = pdl(1,2); # A row vector
perldl> $c = pdl([[3],[4]]); # A column vector
perldl> $c = pdl(3,4)->(*1); # A column vector, using NiceSlice
perldl> $m = pdl([[1,2],[3,4]]); # A 2x2 matrix
Now that we have a few objects prepared, here is how to matrix-multiply them:
perldl> print $r x $m # row x matrix = row
[
[ 7 10]
]

perldl> print $m x $r # matrix x row = ERROR
PDL: Dim mismatch in matmult of [2x2] x [2x1]: 2 != 1

perldl> print $m x $c # matrix x column = column
[
[ 5]
[11]
]

perldl> print $m x 2 # Trivial case: scalar mult.
[
[2 4]
[6 8]
]

perldl> print $r x $c # row x column = scalar
[
[11]
]

perldl> print $c x $r # column x row = matrix
[
[3 6]
[4 8]
]