算法导论4.2strassen

// strassen.h
#ifndef STRASSEN_HH
#define STRASSEN_HH

#include <iostream>
#include <iomanip>

template<typename T>
class Strassen_class{
public:
void ADD(T** MatrixA, T** MatrixB, T** MatrixResult, int MatrixSize );
void SUB(T** MatrixA, T** MatrixB, T** MatrixResult, int MatrixSize );
void MUL(T** MatrixA, T** MatrixB, T** MatrixResult, int MatrixSize ); // 朴素算法实现
void FillMatrix( T** MatrixA, T** MatrixB, int length);                // A,B矩阵赋值
void PrintMatrix(T **MatrixA,int MatrixSize);                          // 打印矩阵
void Strassen(int N, T **MatrixA, T **MatrixB, T **MatrixC);           // Strassen算法实现
};

template<typename T>
void Strassen_class<T>::ADD(T** MatrixA, T** MatrixB, T** 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];
}
}
}

template<typename T>
void Strassen_class<T>::SUB(T** MatrixA, T** MatrixB, T** 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];
}
}
}

template<typename T>
void Strassen_class<T>::MUL(T** MatrixA, T** MatrixB, T** 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];
}
}
}
}

/*
c++使用二维数组，申请动态内存方法
申请
int **A;
A = new int *[desired_array_row];
for ( int i = 0; i < desired_array_row; i++)
A[i] = new int [desired_column_size];

释放
for ( int i = 0; i < your_array_row; i++)
delete [] A[i];
delete[] A;

*/
template<typename T>
void Strassen_class<T>::Strassen(int N, T** MatrixA, T** MatrixB, T** MatrixC)
{
int HalfSize = N / 2;
int newSize  = N / 2;

if (N <= 64)    //分治门槛，小于这个值时不再进行递归计算，而是采用常规矩阵计算方法
{
MUL(MatrixA, MatrixB, MatrixC, N);
}
else
{
T** A11;
T** A12;
T** A21;
T** A22;

T** B11;
T** B12;
T** B21;
T** B22;

T** C11;
T** C12;
T** C21;
T** C22;

T** M1;
T** M2;
T** M3;
T** M4;
T** M5;
T** M6;
T** M7;
T** AResult;
T** BResult;

// making a 1 diminsional pointer based array.
A11 = new T*[newSize];
A12 = new T*[newSize];
A21 = new T*[newSize];
A22 = new T*[newSize];

B11 = new T*[newSize];
B12 = new T*[newSize];
B21 = new T*[newSize];
B22 = new T*[newSize];

C11 = new T*[newSize];
C12 = new T*[newSize];
C21 = new T*[newSize];
C22 = new T*[newSize];

M1 = new T*[newSize];
M2 = new T*[newSize];
M3 = new T*[newSize];
M4 = new T*[newSize];
M5 = new T*[newSize];
M6 = new T*[newSize];
M7 = new T*[newSize];

AResult = new T*[newSize];
BResult = new T*[newSize];

int newLength = newSize;

//making that 1 dimensional pointer based array , a 2D pointer based array
for ( int i = 0; i < newSize; i++)
{
A11[i] = new T[newLength];
A12[i] = new T[newLength];
A21[i] = new T[newLength];
A22[i] = new T[newLength];

B11[i] = new T[newLength];
B12[i] = new T[newLength];
B21[i] = new T[newLength];
B22[i] = new T[newLength];

C11[i] = new T[newLength];
C12[i] = new T[newLength];
C21[i] = new T[newLength];
C22[i] = new T[newLength];

M1[i] = new T[newLength];
M2[i] = new T[newLength];
M3[i] = new T[newLength];
M4[i] = new T[newLength];
M5[i] = new T[newLength];
M6[i] = new T[newLength];
M7[i] = new T[newLength];

AResult[i] = new T[newLength];
BResult[i] = new T[newLength];
}
// splitting input Matrices, into 4 sub matrices 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);         // p5=(a+d)*(e+h)
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   p3=(c+d)*e
Strassen(HalfSize, AResult, B11, M2);       // Mul(AResult,B11,M2);

//M3[][]
SUB(B12, B22, BResult, HalfSize);           // M3=A11(B12-B22)   p1=a*(f-h)
Strassen(HalfSize, A11, BResult, M3);       // Mul(A11,BResult,M3);

//M4[][]
SUB(B21, B11, BResult, HalfSize);           // M4=A22(B21-B11)    p4=d*(g-e)
Strassen(HalfSize, A22, BResult, M4);       // Mul(A22,BResult,M4);

//M5[][]
ADD(A11, A12, AResult, HalfSize);           // M5=(A11+A12)B22   p2=(a+b)*h
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)   p7=(c-a)(e+f)
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)    p6=(b-d)*(g+h)
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.
// 组合小矩阵到一个大矩阵
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];
}
}

// 释放矩阵内存空间
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
}

template<typename T>
void Strassen_class<T>::FillMatrix(T** MatrixA, T** MatrixB, int length)
{
for(int row = 0; row < length; row++)
{
for(int column = 0; column < length; column++)
{
// MatrixB[row][column] = (MatrixA[row][column] = rand() % 5);
MatrixB[row][column] = (MatrixA[row][column] = rand() % 2);
//matrix2[row][column] = rand() % 2;//ba hazfe in khat 50% afzayeshe soorat khahim dasht
}
}
}

template<typename T>
void Strassen_class<T>::PrintMatrix(T** MatrixA, int MatrixSize)
{
std::cout.setf(std::ios::right, std::ios::adjustfield);
std::cout.fill('0');
std::cout << std::endl;
for(int row = 0; row < MatrixSize; row++)
{
for(int column = 0; column < MatrixSize; column++)
{
std::cout << std::setw(4) << MatrixA[row][column] << "\t";
if ((column + 1) % ((MatrixSize)) == 0)
std::cout << std::endl;
}
}
std::cout << std::endl;
}

#endif

// strassen.cpp
#include <ctime>
#include "strassen.h"

using std::cout;
using std::cin;
using std::endl;

int main()
{
Strassen_class<int> stra; // 定义Strassen_class类对象
int MatrixSize = 0;

int** MatrixA;            // 存放矩阵A
int** MatrixB;            // 存放矩阵B
int** MatrixC;            // 存放结果矩阵

clock_t startTime_For_Normal_Multipilication ;
clock_t endTime_For_Normal_Multipilication ;

clock_t startTime_For_Strassen ;
clock_t endTime_For_Strassen ;
srand(static_cast<unsigned int>(time(0)));

cout << "\n请输入矩阵大小(必须是2的幂指数值(例如:32,64,512,..): ";
cin >> MatrixSize;
cout << endl;
int N = MatrixSize; // for readiblity.

// 申请内存
MatrixA = new int*[MatrixSize];
MatrixB = new int*[MatrixSize];
MatrixC = new int*[MatrixSize];

for (int i = 0; i < MatrixSize; i++)
{
MatrixA[i] = new int[MatrixSize];
MatrixB[i] = new int[MatrixSize];
MatrixC[i] = new int[MatrixSize];
}

stra.FillMatrix(MatrixA, MatrixB, MatrixSize);  // 矩阵赋值

//*******************conventional multiplication test
cout << "朴素矩阵算法开始时钟: " << (startTime_For_Normal_Multipilication = clock());

stra.MUL(MatrixA, MatrixB, MatrixC, MatrixSize); // 朴素矩阵相乘算法 T(n) = O(n^3)

cout << "\n朴素矩阵算法结束时钟: " << (endTime_For_Normal_Multipilication = clock());

cout << "\n矩阵运算结果... \n";
stra.PrintMatrix(MatrixC, MatrixSize);

//*******************Strassen multiplication test
cout << "\nStrassen算法开始时钟: " << (startTime_For_Strassen = clock());

stra.Strassen(N, MatrixA, MatrixB, MatrixC); // strassen矩阵相乘算法

cout << "\nStrassen算法结束时钟: " << (endTime_For_Strassen = clock());

cout << "\n矩阵运算结果... \n";
stra.PrintMatrix(MatrixC, MatrixSize);

cout << "矩阵大小 " << MatrixSize;
cout << "\n朴素矩阵算法: " << (endTime_For_Normal_Multipilication - startTime_For_Normal_Multipilication) << " Clocks.." << (endTime_For_Normal_Multipilication - startTime_For_Normal_Multipilication) / CLOCKS_PER_SEC << " Sec";
cout << "\nStrassen算法: " << (endTime_For_Strassen - startTime_For_Strassen) << " Clocks.." << (endTime_For_Strassen - startTime_For_Strassen) / CLOCKS_PER_SEC << " Sec\n";

getchar();
return 0;

}