public function strassenMultiply(LL_Matrix $matrix)
{
if ($this->columns() != $matrix->rows()) {
// impossible operation.
return false;
}
if ($this->columns() < 32) {
return $this->naiveMultiply($matrix);
}
// get these from $this.
$subdivisions = $this->subdivide($this, 2, 2);
if ($subdivisions === false) {
return $this->naiveMultiply($matrix);
}
$a11 = new LL_Matrix($subdivisions[0][0]);
$a12 = new LL_Matrix($subdivisions[0][1]);
$a21 = new LL_Matrix($subdivisions[1][0]);
$a22 = new LL_Matrix($subdivisions[1][1]);
// get these from $matrix
$subdivisions = $this->subdivide($matrix, 2, 2);
if ($subdivisions === false) {
// fall back on naïve if even subdivide isn't possible.
return $this->naiveMultiply($matrix);
}
$b11 = new LL_Matrix($subdivisions[0][0]);
$b12 = new LL_Matrix($subdivisions[0][1]);
$b21 = new LL_Matrix($subdivisions[1][0]);
$b22 = new LL_Matrix($subdivisions[1][1]);
// intermediaries
/*
M1 = (A11 + A22) (B11 + B22)
M2 = (A21 + A22) B11
M3 = A11 (B12 – B22)
M4 = A22 (B21 – B11)
M5 = (A11 + A12) B22
M6 = (A21 – A11) (B11 + B12) M7 = (A12 – A22) (B21 + B22)
*/
$m1_1 = $a11->add($a22);
$m1_2 = $b11->add($b22);
$m1 = $m1_1->strassenMultiply($m1_2);
unset($m1_1);
unset($m1_2);
$m2_1 = $a21->add($a22);
$m2 = $m2_1->strassenMultiply($b11);
unset($m2_1);
$m3_1 = $b12->subtract($b22);
$m3 = $a11->strassenMultiply($m3_1);
unset($m3_1);
$m4_1 = $b21->subtract($b11);
$m4 = $a22->strassenMultiply($m4_1);
$m5_1 = $a11->add($a12);
$m5 = $m5_1->strassenMultiply($b22);
$m6_1 = $a21->subtract($a11);
$m6_2 = $b11->add($b12);
$m6 = $m6_1->strassenMultiply($m6_2);
$m7_1 = $a12->add($a22);
$m7_2 = $b21->add($b22);
$m7 = $m7_1->strassenMultiply($m7_2);
// result
$c11 = $m1->add($m1);
$c11 = $c11->add($m4);
$c11 = $c11->subtract($m5);
$c11 = $c11->add($m7);
$c12 = $m3->add($m5);
$c21 = $m2->add($m4);
$c22 = $m1->subtract($m2);
$c22 = $c22->add($m3);
$c22 = $c22->add($m6);
$result = array(array($c11, $c12), array($c21, $c22));
return $this->rebuild($result);
}
