Привет, Хабр.
Имеется алгоритм Штрассена умножения матриц, но скоростью он не блещет. Буду рад увидеть ваши замечания по оптимизации кода.
int Strassen(int N, int **MatrixA, int **MatrixB, int **MatrixC)
{
int HalfSize = N/2;
int newSize = N/2;
if ( N <= 32 )//choosing the threshold is extremely important, try N<=2 to see the result
{
MUL(MatrixA,MatrixB,MatrixC,N);
}
else
{
int** A11;
int** A12;
int** A21;
int** A22;
int** B11;
int** B12;
int** B21;
int** B22;
int** C11;
int** C12;
int** C21;
int** C22;
int** M1;
int** M2;
int** M3;
int** M4;
int** M5;
int** M6;
int** M7;
int** AResult;
int** BResult;
//making a 1 diminsional pointer based array.
A11 = new int *[newSize];
A12 = new int *[newSize];
A21 = new int *[newSize];
A22 = new int *[newSize];
B11 = new int *[newSize];
B12 = new int *[newSize];
B21 = new int *[newSize];
B22 = new int *[newSize];
C11 = new int *[newSize];
C12 = new int *[newSize];
C21 = new int *[newSize];
C22 = new int *[newSize];
M1 = new int *[newSize];
M2 = new int *[newSize];
M3 = new int *[newSize];
M4 = new int *[newSize];
M5 = new int *[newSize];
M6 = new int *[newSize];
M7 = new int *[newSize];
AResult = new int *[newSize];
BResult = new int *[newSize];
int newLength = newSize;
//making that 1 diminsional pointer based array , a 2D pointer based array
for ( int i = 0; i < newSize; i++)
{
A11[i] = new int[newLength];
A12[i] = new int[newLength];
A21[i] = new int[newLength];
A22[i] = new int[newLength];
B11[i] = new int[newLength];
B12[i] = new int[newLength];
B21[i] = new int[newLength];
B22[i] = new int[newLength];
C11[i] = new int[newLength];
C12[i] = new int[newLength];
C21[i] = new int[newLength];
C22[i] = new int[newLength];
M1[i] = new int[newLength];
M2[i] = new int[newLength];
M3[i] = new int[newLength];
M4[i] = new int[newLength];
M5[i] = new int[newLength];
M6[i] = new int[newLength];
M7[i] = new int[newLength];
AResult[i] = new int[newLength];
BResult[i] = new int[newLength];
}
//splitting input Matrixes, into 4 submatrices each.
for (int i = 0; i < N / 2; i++)
{
for (int j = 0; j < N / 2; j++)
{
A11[i][j] = MatrixA[i][j];
A12[i][j] = MatrixA[i][j + N / 2];
A21[i][j] = MatrixA[i + N / 2][j];
A22[i][j] = MatrixA[i + N / 2][j + N / 2];
B11[i][j] = MatrixB[i][j];
B12[i][j] = MatrixB[i][j + N / 2];
B21[i][j] = MatrixB[i + N / 2][j];
B22[i][j] = MatrixB[i + N / 2][j + N / 2];
}
}
//here we calculate M1..M7 matrices .
//M1[][]
ADD( A11,A22,AResult, HalfSize);
ADD( B11,B22,BResult, HalfSize);
Strassen( HalfSize, AResult, BResult, M1 ); //now that we need to multiply this , we use the strassen itself .
//M2[][]
ADD( A21,A22,AResult, HalfSize); //M2=(A21+A22)B11
Strassen(HalfSize, AResult, B11, M2); //Mul(AResult,B11,M2);
//M3[][]
SUB( B12,B22,BResult, HalfSize); //M3=A11(B12-B22)
Strassen(HalfSize, A11, BResult, M3); //Mul(A11,BResult,M3);
//M4[][]
SUB( B21, B11, BResult, HalfSize); //M4=A22(B21-B11)
Strassen(HalfSize, A22, BResult, M4); //Mul(A22,BResult,M4);
//M5[][]
ADD( A11, A12, AResult, HalfSize); //M5=(A11+A12)B22
Strassen(HalfSize, AResult, B22, M5); //Mul(AResult,B22,M5);
//M6[][]
SUB( A21, A11, AResult, HalfSize);
ADD( B11, B12, BResult, HalfSize); //M6=(A21-A11)(B11+B12)
Strassen( HalfSize, AResult, BResult, M6); //Mul(AResult,BResult,M6);
//M7[][]
SUB(A12, A22, AResult, HalfSize);
ADD(B21, B22, BResult, HalfSize); //M7=(A12-A22)(B21+B22)
Strassen(HalfSize, AResult, BResult, M7); //Mul(AResult,BResult,M7);
//C11 = M1 + M4 - M5 + M7;
ADD( M1, M4, AResult, HalfSize);
SUB( M7, M5, BResult, HalfSize);
ADD( AResult, BResult, C11, HalfSize);
//C12 = M3 + M5;
ADD( M3, M5, C12, HalfSize);
//C21 = M2 + M4;
ADD( M2, M4, C21, HalfSize);
//C22 = M1 + M3 - M2 + M6;
ADD( M1, M3, AResult, HalfSize);
SUB( M6, M2, BResult, HalfSize);
ADD( AResult, BResult, C22, HalfSize);
//at this point , we have calculated the c11..c22 matrices, and now we are going to
//put them together and make a unit matrix which would describe our resulting Matrix.
for (int i = 0; i < N/2 ; i++)
{
for (int j = 0 ; j < N/2 ; j++)
{
MatrixC[i][j] = C11[i][j];
MatrixC[i][j + N / 2] = C12[i][j];
MatrixC[i + N / 2][j] = C21[i][j];
MatrixC[i + N / 2][j + N / 2] = C22[i][j];
}
}
// dont forget to free the space we alocated for matrices,
for (int i = 0; i < newLength; i++)
{
delete[] A11[i];delete[] A12[i];delete[] A21[i];
delete[] A22[i];
delete[] B11[i];delete[] B12[i];delete[] B21[i];
delete[] B22[i];
delete[] C11[i];delete[] C12[i];delete[] C21[i];
delete[] C22[i];
delete[] M1[i];delete[] M2[i];delete[] M3[i];delete[] M4[i];
delete[] M5[i];delete[] M6[i];delete[] M7[i];
delete[] AResult[i];delete[] BResult[i] ;
}
delete[] A11;delete[] A12;delete[] A21;delete[] A22;
delete[] B11;delete[] B12;delete[] B21;delete[] B22;
delete[] C11;delete[] C12;delete[] C21;delete[] C22;
delete[] M1;delete[] M2;delete[] M3;delete[] M4;delete[] M5;
delete[] M6;delete[] M7;
delete[] AResult;
delete[] BResult ;
}//end of else
return 0;
}
int ADD(int** MatrixA, int** MatrixB, int** MatrixResult, int MatrixSize )
{
for ( int i = 0; i < MatrixSize; i++)
{
for ( int j = 0; j < MatrixSize; j++)
{
MatrixResult[i][j] = MatrixA[i][j] + MatrixB[i][j];
}
}
return 0;
}
int SUB(int** MatrixA, int** MatrixB, int** MatrixResult, int MatrixSize )
{
for ( int i = 0; i < MatrixSize; i++)
{
for ( int j = 0; j < MatrixSize; j++)
{
MatrixResult[i][j] = MatrixA[i][j] - MatrixB[i][j];
}
}
return 0;
}
int MUL( int** MatrixA, int** MatrixB, int** MatrixResult, int MatrixSize )
{
for (int i=0;i<MatrixSize ;i++)
{
for (int j=0;j<MatrixSize ;j++)
{
MatrixResult[i][j]=0;
for (int k=0;k<MatrixSize ;k++)
{
MatrixResult[i][j]=MatrixResult[i][j]+MatrixA[i][k]*MatrixB[k][j];
}
}
}
return 0;
}
