#!/usr/bin/perl -w

# ----------------------------------------------------------------
# John Kerl
# kerl.john.r@gmail.com
# 2005-06-15
#
# Computes the Gram-Schmidt orthonormalization of a set of real vectors,
# represented as columns of a matrix.
#
# bash$ cat a.txt
#   1  4 -2
#   4  1 -2
#  -2 -2 -2
# bash$ pgramsch a.txt
#   0.2182179   0.9116846  -0.3481553
#   0.8728716  -0.3418817  -0.3481553
#  -0.4364358  -0.2279212  -0.8703883
# bash$ pgramsch a.txt > b.txt
# bash$ pmatmul -t1 b.txt b.txt
#   1.0000001   0.0000000   0.0000000
#   0.0000000   1.0000000   0.0000000
#   0.0000000   0.0000000   1.0000000
# ----------------------------------------------------------------

# Setup information:
# (1) Obtain my PMATLIB.pm;
# (2) Put PMATLIB.pm somewhere, e.g. the $HOME/bin directory;
# (3) Include that directory in the PERLLIB environment variable.
#     For bash, if PERLLIB exists:         export PERLLIB=$HOME/bin
#     For bash, if PERLLIB does not exist: export PERLLIB=$PERLLIB:$HOME/bin
#     For csh,  if PERLLIB exists:         setenv PERLLIB $HOME/bin
#     For csh,  if PERLLIB does not exist: setenv PERLLIB ${PERLLIB}:$HOME/bin
use PMATLIB;

$transpose = 0;

while (@ARGV) {
	last unless $ARGV[0] =~ m/^-/;
	if (pmatlib_opt(\@ARGV)) {
		;
	}
	elsif ($ARGV[0] eq "-t") {
		$transpose = 1;
		shift @ARGV;
	}
	else {
		usage();
	}
}

@A = (); $anr = 0; $anc = 0; 
read_matrix(\@A, \$anr, \$anc, $ARGV[0]);
transpose_in_place(\@A, \$anr, \$anc) if ($transpose);
@Q = gram_schmidt(\@A, $anr, $anc);
transpose_in_place(\@Q, \$anr, \$anc) if ($transpose);
print_matrix(\@Q, $anr, $anc);

# ----------------------------------------------------------------
sub usage
{
	die
		"Usage: $0 [options] {input file name}\n" .
		"Options:\n" .
		"  -t: Input is rows rather than columns.\n" .
		pmatlib_options_string();
}