Gaussian elimination: Difference between revisions

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=={{header|Raku}}==

(formerly Perl 6)

Gaussian elimination results in a matrix in row echelon form. Gaussian elimination with back-substitution (also known as Gauss-Jordan elimination) results in a matrix in reduced row echelon form. That being the case, we can reuse much of the code from the [[Reduced row echelon form]] task. Raku stores and does calculations on decimal numbers within its limit of precision using Rational numbers by default, meaning the calculations are exact.

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}

# reduced row echelon form ~~(Gauss-Jordan elimination)~~

# reduced row echelon form

sub rref (@m) {

⚫

my ($lead, $rows, $cols) = 0, @m, @m[0];

return unless @m;

⚫

my ($lead, $rows, $cols) = 0, +@m, +@m[0];

for ^$rows -> $r {

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}

@m[$i, $r] = @m[$r, $i] if $r != $i;

my $lv = @m[$r;$lead];

@m[$r] »/=» $ = @m[$r;$lead];

@m[$r] »/=» $lv;

for ^$rows -> $n {

next if $n == $r;

@m[$n] »-=» @m[$r] »*» (@m[$n;$lead] // 0);

@m[$n] »-=» @m[$r] »×» (@m[$n;$lead] // 0);

}

++$lead;

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sub rat-or-int ($num) {

return $num unless $num ~~ Rat;

return $num.narrow if $num.narrow~~.WHAT~~ ~~ Int;

return $num.narrow if $num.narrow ~~ Int;

$num.nude.join: '/';

}