/// <summary>
/// Strassen`s multiply, use when matrix rows > 32.
/// </summary>
/// <param name="a">the matrix a.</param>
/// <param name="b">the matrix b.</param>
/// <typeparam name="T">unmanaged type.</typeparam>
/// <returns>the new matrix from multiply of two matrices.</returns>
public static Matrix <T> MultiplyStrassen <T>(Matrix <T> a, Matrix <T> b) where T : unmanaged
{
if (a.Rows < 32)
{
return(a * b);
}
a.SplitMatrix(out var a11, out var a12, out var a21, out var a22);
b.SplitMatrix(out var b11, out var b12, out var b21, out var b22);
Matrix <T> p1 = MultiplyStrassen(a11 + a22, b11 + b22);
Matrix <T> p2 = MultiplyStrassen(a21 + a22, b11);
Matrix <T> p3 = MultiplyStrassen(a11, b12 - b22);
Matrix <T> p4 = MultiplyStrassen(a22, b21 - b11);
Matrix <T> p5 = MultiplyStrassen(a11 + a12, b22);
Matrix <T> p6 = MultiplyStrassen(a21 - a22, b11 + b12);
Matrix <T> p7 = MultiplyStrassen(a12 - a22, b21 + b22);
Matrix <T> c11 = p1 + p4 - p5 + p7;
Matrix <T> c12 = p3 + p5;
Matrix <T> c21 = p2 + p4;
Matrix <T> c22 = p1 + p3 - p2 + p6;
return(MatrixConverter.CollectMatrix(c11, c12, c21, c22));
}
private static ValueTask <Matrix <T> > MultiplyStrassenParallel <T>(Matrix <T> a, Matrix <T> b)
where T : unmanaged
{
if (a.Rows <= 64)
{
return(new ValueTask <Matrix <T> >(a * b));
}
a.SplitMatrix(out var a11, out var a12, out var a21, out var a22);
b.SplitMatrix(out var b11, out var b12, out var b21, out var b22);
var p1 = Task.Run(() => MultiplyStrassen(a11 + a22, b11 + b22));
var p2 = Task.Run(() => MultiplyStrassen(a21 + a22, b11));
var p3 = Task.Run(() => MultiplyStrassen(a11, b12 - b22));
var p4 = Task.Run(() => MultiplyStrassen(a22, b21 - b11));
var p5 = Task.Run(() => MultiplyStrassen(a11 + a12, b22));
var p6 = Task.Run(() => MultiplyStrassen(a21 - a11, b11 + b12));
var p7 = MultiplyStrassen(a12 - a22, b21 + b22);
Task.WhenAll(p1, p2, p3, p4, p5, p6);
var c11 = p1.Result + p4.Result - p5.Result + p7;
var c12 = p3.Result + p5.Result;
var c21 = p2.Result + p4.Result;
var c22 = p1.Result + p3.Result - p2.Result + p6.Result;
return(new ValueTask <Matrix <T> >(MatrixConverter.CollectMatrix(c11, c12, c21, c22)));
}
