Strassen's algorithm: Difference between revisions

Content added Content deleted
(added Raku programming solution)
(→‎{{header|Raku}}: minor updates + some comments)
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use Math::Libgsl::Matrix;
use Math::Libgsl::Matrix;
use Math::Libgsl::BLAS;
use Math::Libgsl::BLAS;

my @M;
my @M;

sub SQM (\in) { # create custom sq matrix from CSV
sub SQM (\in) { # create custom sq matrix from CSV
die "Not a ■" if (my \L = in.split(/\,/)).sqrt != (my \size = L.sqrt.Int);
die "Not a ■" if (my \L = in.split(/\,/)).sqrt != (my \size = L.sqrt.Int);
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M
M
}
}

sub infix:<⊗>(\x,\y) { # custom multiplication
sub infix:<⊗>(\x,\y) { # custom multiplication
my Math::Libgsl::Matrix \z .= new: x.size1, x.size2;
my Math::Libgsl::Matrix \z .= new: x.size1, x.size2;
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z
z
}
}

sub infix:<⊕>(\x,\y) { # custom addition
sub infix:<⊕>(\x,\y) { # custom addition
my Math::Libgsl::Matrix \z .= new: x.size1, x.size2;
my Math::Libgsl::Matrix \z .= new: x.size1, x.size2;
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z
z
}
}

sub infix:<⊖>(\x,\y) { # custom subtraction
sub infix:<⊖>(\x,\y) { # custom subtraction
my Math::Libgsl::Matrix \z .= new: x.size1, x.size2;
my Math::Libgsl::Matrix \z .= new: x.size1, x.size2;
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z
z
}
}

sub Strassen($A, $B) {
sub Strassen($A, $B) {

{ return $A ⊗ $B } if (my \n = $A.size1) == 1;
{ return $A ⊗ $B } if (my \n = $A.size1) == 1;

my Math::Libgsl::Matrix ($A11,$A12,$A21,$A22,$B11,$B12,$B21,$B22);
my Math::Libgsl::Matrix ($A11,$A12,$A21,$A22,$B11,$B12,$B21,$B22);
my Math::Libgsl::Matrix ($P1,$P2,$P3,$P4,$P5,$P6,$P7);
my Math::Libgsl::Matrix ($P1,$P2,$P3,$P4,$P5,$P6,$P7);
⚫
my Math::Libgsl::Matrix ($C11,$C12,$C21,$C22);
my Math::Libgsl::Matrix::View ($mv1,$mv2,$mv3,$mv4,$mv5,$mv6,$mv7,$mv8);
my Math::Libgsl::Matrix::View ($mv1,$mv2,$mv3,$mv4,$mv5,$mv6,$mv7,$mv8);
($mv1,$mv2,$mv3,$mv4,$mv5,$mv6,$mv7,$mv8)».&{ $_ .= new };
($mv1,$mv2,$mv3,$mv4,$mv5,$mv6,$mv7,$mv8)».=new ;


my \half = n div 2; # dimension of quarter submatrices
⚫
$A11 = $mv1.submatrix($A, 0,0, n div 2,n div 2);
⚫
$A12 = $mv2.submatrix($A, 0,n div 2, n div 2,n div 2);
⚫
$A21 = $mv3.submatrix($A, n div 2,0, n div 2,n div 2);
⚫
$A22 = $mv4.submatrix($A, n div 2,n div 2, n div 2,n div 2);
⚫
$B11 = $mv5.submatrix($B, 0,0, n div 2,n div 2);
⚫
$B12 = $mv6.submatrix($B, 0,n div 2, n div 2,n div 2);
⚫
$B21 = $mv7.submatrix($B, n div 2,0, n div 2,n div 2);
$B22 = $mv8.submatrix($B, n div 2,n div 2, n div 2,n div 2);


⚫
$A11 = $mv1.submatrix($A, 0,0, half,half); #
$A12 = $mv2.submatrix($A, 0,half, half,half); # create quarter views
⚫
$A21 = $mv3.submatrix($A, half,0, half,half); # of operand matrices
⚫
$A22 = $mv4.submatrix($A, half,half, half,half); #
⚫
$B11 = $mv5.submatrix($B, 0,0, half,half); # 11 12
⚫
$B12 = $mv6.submatrix($B, 0,half, half,half); #
⚫
$B21 = $mv7.submatrix($B, half,0, half,half); # 21 22
⚫
$B22 = $mv8.submatrix($B, half,half, half,half); #
$P1 = Strassen($A12 ⊖ $A22, $B21 ⊕ $B22);
$P1 = Strassen($A12 ⊖ $A22, $B21 ⊕ $B22);
$P2 = Strassen($A11 ⊕ $A22, $B11 ⊕ $B22);
$P2 = Strassen($A11 ⊕ $A22, $B11 ⊕ $B22);
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$P6 = Strassen($A22, $B21 ⊖ $B11);
$P6 = Strassen($A22, $B21 ⊖ $B11);
$P7 = Strassen($A21 ⊕ $A22, $B11 );
$P7 = Strassen($A21 ⊕ $A22, $B11 );
⚫
my Math::Libgsl::Matrix $C .= new: n, n; # Build C from
⚫
my Math::Libgsl::Matrix::View ($mvC11,$mvC12,$mvC21,$mvC22); # C11 C12
($mvC11,$mvC12,$mvC21,$mvC22)».=new ; # C21 C22


$C11 = (($P1 ⊕ $P2) ⊖ $P4) ⊕ $P6;
given $mvC11.submatrix($C, 0,0, half,half) { .add: (($P1 ⊕ $P2) ⊖ $P4) ⊕ $P6 };
$C12 = $P4 ⊕ $P5;
given $mvC12.submatrix($C, 0,half, half,half) { .add: $P4 ⊕ $P5 };
$C21 = $P6 ⊕ $P7;
given $mvC21.submatrix($C, half,0, half,half) { .add: $P6 ⊕ $P7 };
$C22 = (($P2 ⊖ $P3) ⊕ $P5) ⊖ $P7;
given $mvC22.submatrix($C, half,half, half,half) { .add: (($P2 ⊖ $P3) ⊕ $P5) ⊖ $P7 };


⚫
my Math::Libgsl::Matrix $C .= new: n, n;
my $h = n div 2;
for ^$h X ^$h -> ($i,$j) {
$C[$i;$j] = $C11[$i;$j];
$C[$i;$j+$h] = $C12[$i;$j];
$C[$i+$h;$j] = $C21[$i;$j];
$C[$i+$h;$j+$h] = $C22[$i;$j];
}
$C
$C
}
}

for $=pod[0].contents { next if /^\n$/ ; @M.append: SQM $_ }
for $=pod[0].contents { next if /^\n$/ ; @M.append: SQM $_ }

for @M.rotor(2) {
for @M.rotor(2) {
my $product = @_[0] ⊗ @_[1];
my $product = @_[0] ⊗ @_[1];
# $product.get-row($_)».round(1).fmt('%2d').put for ^$product.size1;
# $product.get-row($_)».round(1).fmt('%2d').put for ^$product.size1;

say "Regular multiply:";
say "Regular multiply:";
$product.get-row($_)».fmt('%.10g').put for ^$product.size1;
$product.get-row($_)».fmt('%.10g').put for ^$product.size1;

$product = Strassen @_[0], @_[1];
$product = Strassen @_[0], @_[1];

say "Strassen multiply:";
say "Strassen multiply:";
$product.get-row($_)».fmt('%.10g').put for ^$product.size1;
$product.get-row($_)».fmt('%.10g').put for ^$product.size1;
}
}

=begin code
=begin code
1,2,3,4
1,2,3,4
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9 10 11 12
9 10 11 12
13 14 15 16</pre>
13 14 15 16</pre>



=={{header|Wren}}==
=={{header|Wren}}==
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