Dear Masters,
I have the following sparse matrix A. 
       2   3   0   0   0
       3   0   4   0   6
       0  -1  -3   2   0
       0   0   1   0   0
       0   4   2   0   1

[download]
Then I would like to capture the following information from there:
  1. cumulative count of entries, as matrix is scanned columnwise. Yielding:   Ap = [ 0, 2, 5, 9, 10, 12 ];
  2. row indices of entries, as matrix is scanned columnwise. Yielding:  Ai = [0, 1, 0,  2, 4, 1,  2, 3, 4, 2, 1, 4 ];
  3. Non-zero matrix entries, as matrix is scanned columnwise. Yielding: Ax = [2, 3, 3, -1, 4, 4, -3, 1, 2, 2, 6, 1];


Since the actual matrix A is potentially very2 large, is there any efficient way in Perl that can capture those elements? Especially without slurping all matrix A into RAM.

I am stuck with the following code. Which doesn't give what I want. 
    use strict;
    use warnings;
    
    my (@Ax, @Ai, @Ap) = ();
    while (<>) {
        chomp;
        my @elements = split /\s+/;
        my $i = 0;
        my $new_line = 1;
        while (defined(my $element = shift @elements)) {
            $i++;
            if ($element) {
                push @Ax, 0 + $element;
                if ($new_line) {
                    push @Ai, scalar @Ax;
                    $new_line = 0;
                }
             
                push @JA, $i;
            }
        }
    }
    push @Ai, 1 + @Ax;
    print('@Ax  = [', join(" ", @Ax), "]\n");
    print('@Ai = [', join(" ", @Ai), "]\n");
    print('@Ap = [', join(" ", @Ap), "]\n");

[download]


---
neversaint and everlastingly indebted.......

In reply to Capturing Non-Zero Elements, Counts and Indexes of Sparse Matrix by neversaint

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.