func Multiply(A *matrix.Matrix, B *matrix.Matrix) *matrix.Matrix {
n := A.CountRows()
bigN := scaleSize(n)
bigA := matrix.MakeMatrix(make([]float64, bigN*bigN), bigN, bigN)
bigB := matrix.MakeMatrix(make([]float64, bigN*bigN), bigN, bigN)
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
bigA.SetElm(i, j, A.GetElm(i, j))
bigB.SetElm(i, j, B.GetElm(i, j))
}
}
bigC := recurse(bigA, bigB)
C := matrix.MakeMatrix(make([]float64, n*n), n, n)
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
C.SetElm(i, j, bigC.GetElm(i, j))
}
}
return C
}
func BenchmarkStrassen(b *testing.B) {
a := make([]float64, 100000000, 100000000)
c := make([]float64, 100000000, 100000000)
for i := 0; i < 100000000; i++ {
a[i] = float64(i)
c[i] = float64(100000000 - i)
}
A := matrix.MakeMatrix(a, 10000, 10000)
B := matrix.MakeMatrix(c, 10000, 10000)
for i := 0; i < b.N; i++ {
Multiply(A, B)
}
}
func TestStrassen(t *testing.T) {
A := matrix.MakeMatrix([]float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}, 4, 4)
B := matrix.MakeMatrix([]float64{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}, 4, 4)
C := Multiply(A, B)
D := matrix.Multiply(A, B)
if !FloatArrayEquals(C.Elements, D.Elements) {
t.Error()
}
A = matrix.MakeMatrix([]float64{1, 1, 1, 1}, 2, 2)
B = matrix.MakeMatrix([]float64{1, 1, 1, 1}, 2, 2)
C = Multiply(A, B)
D = matrix.Multiply(A, B)
if !FloatArrayEquals(C.Elements, D.Elements) {
t.Error()
}
A = matrix.MakeMatrix([]float64{1, 1, 1, 1, 1, 1, 1, 1, 1}, 3, 3)
B = matrix.MakeMatrix([]float64{1, 1, 1, 1, 1, 1, 1, 1, 1}, 3, 3)
C = Multiply(A, B)
D = matrix.Multiply(A, B)
if !FloatArrayEquals(C.Elements, D.Elements) {
t.Error()
}
}
func recurse(A *matrix.Matrix, B *matrix.Matrix) *matrix.Matrix {
n := A.CountRows()
newSize := n / 2
if n < 2 {
return matrix.MakeMatrix([]float64{A.GetElm(0, 0) * B.GetElm(0, 0)}, 1, 1)
}
A11 := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
A12 := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
A21 := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
A22 := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
B11 := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
B12 := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
B21 := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
B22 := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
for i := 0; i < newSize; i++ {
for j := 0; j < newSize; j++ {
A11.SetElm(i, j, A.GetElm(i, j))
A12.SetElm(i, j, A.GetElm(i, j+newSize))
A21.SetElm(i, j, A.GetElm(i+newSize, j))
A22.SetElm(i, j, A.GetElm(i+newSize, j+newSize))
B11.SetElm(i, j, B.GetElm(i, j))
B12.SetElm(i, j, B.GetElm(i, j+newSize))
B21.SetElm(i, j, B.GetElm(i+newSize, j))
B22.SetElm(i, j, B.GetElm(i+newSize, j+newSize))
}
}
a := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
b := matrix.MakeMatrix(make([]float64, newSize*newSize), newSize, newSize)
// P1 = (A11 + A22) * (B11 + B22)
a = matrix.Add(A11, A22)
b = matrix.Add(B11, B22)
P1 := recurse(a, b)
// P2 = (A21 + A22) * (B11)
a = matrix.Add(A21, A22)
P2 := recurse(a, B11)
// P3 = (A11) * (B12 - B11)
b = matrix.Substract(B12, B22)
P3 := recurse(A11, b)
// P4 = A22 * (B21 - B22)
b = matrix.Substract(B21, B11)
P4 := recurse(A22, b)
// P5 = (A11 + A12) * B22
a = matrix.Add(A11, A12)
P5 := recurse(a, B22)
// P6 = (A21 - A11) * (B11 + B12)
a = matrix.Substract(A21, A11)
b = matrix.Add(B11, B12)
P6 := recurse(a, b)
// P7 = (A12 - A22) * (B21 + B22)
a = matrix.Substract(A12, A22)
b = matrix.Add(B21, B22)
P7 := recurse(a, b)
// Aggregates the result into C
C12 := matrix.Add(P3, P5)
C21 := matrix.Add(P2, P4)
a = matrix.Add(P1, P4)
b = matrix.Add(a, P7)
C11 := matrix.Substract(b, P5)
a = matrix.Add(P1, P3)
b = matrix.Add(a, P6)
C22 := matrix.Substract(b, P2)
C := matrix.MakeMatrix(make([]float64, n*n), n, n)
for i := 0; i < newSize; i++ {
for j := 0; j < newSize; j++ {
C.SetElm(i, j, C11.GetElm(i, j))
C.SetElm(i, j+newSize, C12.GetElm(i, j))
C.SetElm(i+newSize, j, C21.GetElm(i, j))
C.SetElm(i+newSize, j+newSize, C22.GetElm(i, j))
}
}
return C
}