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Which Dwarf Are You?

Bash can only handle integer arithmetic. To process floats, you need to shell out to 'bc' or some other external utility. The core multiplication changes to: result=`echo "$result + $m * $n" | bc`; Boy, does that slow things down! For each multiplication, you're launching a shell, invoking a program, returning results. The result is 800 multiplications a second. Note this is running on integer matrices, there remain unresolved problems processing floats. One obvious problem is shelling out for every multiplication. More efficient is to accumulate the expression to calculate, and just invoke the external calculator once. Now we only shell out N^2 times, instead of N^3, so increasing matrix size leads to better performance, up to a limit. the 32x32 matrix gives 18x performance compared to the simpler version. This implies the 32x reduction in shelling out is offset by the cost of building the expression. By the time we reach 100x100, overhead costs are...

tl;dr Bash is not the language for math-intensive operations. REPS=$1; FILE_1=$2; FILE_2=$3 OUTFILENAME=$4; readonly COLS=`head -1 $FILE_1 | wc -w`; readonly ROWS=`cat $FILE_1 | wc -l`; # echo "rows is $ROWS; cols is $COLS" if [[ $ROWS != $COLS ]]; then echo "Expecting square matrices, " \ "but rows = $ROWS, cols = $COLS\n"; exit 1; fi # -------------------------------------------------- # SUBROUTINES # function outputMatrix() { local matrixname=$1; local matrix; local elem; echo "matrix is '$matrixname'."; eval matrix=\( \${${matrixname}[@]} \); local i=0; for elem in "${matrix[@]}"; do echo -n "$elem "; if (( ++i == $COLS )); then echo ''; i=0; fi done } function multiply() { declare -a product; local M=$1 N=$2; local i j k idx1 idx2 idx3; for ((i=0; i < $ROWS; i++ )); do for ((j=0; j<$COLS; j++)); do ...

Both Perl and Javascript implement only one-dimensional arrays. To represent a matrix you need to nest arrays within arrays, typically one array for each row, within the overall matrix array. Each element of the result matrix is the product of one row from the first matrix, and one column from the second. Going from one element to the next in the same row is much quicker than going to another row. The first matrix only changes rows once for each row, N changes, but the second matrix has N^3 changes of row, one for each multiplication. If we were to transpose the second array, turn the rows into columns and columns into rows, the multiplication could be carried out by by scanning along a row instead of going from row to row.That reduces the cost to N^2. How much will that save us? I transposed the second array while reading it in: for my $size ( keys %vars ) { my $filestub = q{M_} . $size . q{x} . $size . q{.}; my ( $f1, $f2 ) = ( $filestub . '1', $filestub . '...

The numbers I've been reporting for Javascript and Perl performance need a context. Are they running on a Commodore 64, or a super-computer? Nope, it's my laptop, and here's what Linpack has to report about it: 4 core, 8 thread (Intel core i7) at 3.389 GHz. Peak performance is 46 GFLOPS. Javascript and Perl are both single-threaded, so you only get 1/8 peak performance, 5 3/4 GFLOPS. That's still 1000 times the performance we actually achieve on more convenient languages. You have to sacrifice some things to gain benefits. On the optimistic side, a moderately fast modern computer sunning Perl or Javascript is almost as fast as  Sparc-10 running LINPACK. Intel(R) LINPACK data Current date/time: Fri Jun 12 01:19:06 2015 CPU frequency: 3.389 GHz Number of CPUs: 1 Number of cores: 4 Number of threads: 8 Parameters are set to: Number of tests : 15 Number of equations to solve (problem size) : 1000 2000 5000 10000 15000 18000 20000 2...

I was worried whether I was making basic errors in testing the Perl version, so I decided to use the Benchmark module to get the numbers. I copied the matmult.pl file and added use Benchmark ':all'  to the header of the file. The main() routine got changed to : my $time = $ARGV[0] || 5; my %vars = ( 2 => [], 5 => [], 10 => [], 32 => [], 100 => [], ); for my $size ( keys %vars ) { my $filestub = q{F_} . $size . q{x} . $size . q{.}; $vars{$size}[0] = readMatrix( $filestub . '1' ); $vars{$size}[1] = readMatrix( $filestub . '2' ); } say "Processing for $time seconds each size ", "will take @{[5 * $time]} seconds."; say scalar localtime; cmpthese( -$time, { 'F_2x2' => sub { matmult( $vars{2}[0], $vars{2}[1]); }, 'F_5x5...

Floating point performance compared to integer multiplication on Perl This is much the same as Perl Integer performance, and disappointly inferior to Javascript. Not a whole lot worse, comparable, really, but MY language should be better than the OTHER language! :-)

Here's the Perl script for matrix multiplication. It's derived from the RosettaCode site with slight modifications ... I didn't like some things about their way of doing things, but it's much the same in the end. #! /usr/bin/perl5.20.2 use 5.020; use warnings; use strict; use English; use Time::HiRes qw(gettimeofday tv_interval); use autodie; use Data::Dumper; # ------------------------------------------------------- # SUBROUTINES # # ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ # matmult - multiple matrices. Copied from # RosettaCode.orgwiki/Matrix_multiplication#Perl. # sub matmult { my ( $M, $N ) = @_; my ( $rows, $cols ) = (scalar @$M, scalar @{$N->[0]} ); my $prod = []; my $k = @$N - 1; for my $i ( 0..$rows - 1 ) { for my $j ( 0 .. $cols - 1 ) { $prod->[$i][$j] += $M->[$i][$_] * $N->[$_][$j] for 0..$k; } } return $prod; } # ⋯ ⋯ ⋯ ...