78 lines
2.2 KiB
Raku
78 lines
2.2 KiB
Raku
sub deconvolve (@g, @f) {
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my $h = 1 + @g - @f;
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my @m;
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@m[^@g;^$h] >>+=>> 0;
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@m[^@g;$h] >>=<< @g;
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for ^$h -> $j { for @f.kv -> $k, $v { @m[$j + $k][$j] = $v } }
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return rref( @m )[^$h;$h];
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}
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sub convolve (@f, @h) {
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my @g = 0 xx + @f + @h - 1;
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@g[^@f X+ ^@h] >>+=<< (@f X* @h);
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return @g;
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}
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# Reduced Row Echelon Form simultaneous equation solver.
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# Can handle over-specified systems of equations.
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# (n unknowns in n + m equations)
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sub rref ($m is copy) {
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return unless $m;
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my ($lead, $rows, $cols) = 0, +$m, +$m[0];
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# Trim off over specified rows if they exist, for efficiency
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if $rows >= $cols {
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$m = trim_system($m);
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$rows = +$m;
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}
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for ^$rows -> $r {
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$lead < $cols or return $m;
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my $i = $r;
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until $m[$i][$lead] {
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++$i == $rows or next;
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$i = $r;
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++$lead == $cols and return $m;
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}
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$m[$i, $r] = $m[$r, $i] if $r != $i;
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my $lv = $m[$r][$lead];
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$m[$r] >>/=>> $lv;
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for ^$rows -> $n {
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next if $n == $r;
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$m[$n] >>-=>> $m[$r] >>*>> ($m[$n][$lead]//0);
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}
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++$lead;
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}
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return $m;
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# Reduce a system of equations to n equations with n unknowns.
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# Looks for an equation with a true value for each position.
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# If it can't find one, assumes that it has already taken one
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# and pushes in the first equation it sees. This assumtion
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# will alway be successful except in some cases where an
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# under-specified system has been supplied, in which case,
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# it would not have been able to reduce the system anyway.
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sub trim_system ($m is rw) {
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my ($vars, @t) = +$m[0]-1, ();
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for ^$vars -> $lead {
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for ^$m -> $row {
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@t.push: | $m.splice( $row, 1 ) and last if $m[$row][$lead];
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}
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}
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while (+@t < $vars) and +$m { @t.push: $m.splice( 0, 1 ) };
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return @t;
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}
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}
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my @h = (-8,-9,-3,-1,-6,7);
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my @f = (-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1);
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my @g = (24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7);
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.say for ~@g, ~convolve(@f, @h),'';
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.say for ~@h, ~deconvolve(@g, @f),'';
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.say for ~@f, ~deconvolve(@g, @h),'';
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