Андреев С.А. ЛР№1. Умножение плотных матриц. Элементы типа double. Алгоритм Штрассена.

1706-4/Andreev_SA/Strassen.cpp

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+#include <iomanip>
+#include <iostream>
+#include <ctime>
+#include <chrono>
+
+void PrintMatrix(double* matrix, int N)
+{
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+        {
+            std::cout.width(6);
+            //cout << matrix[i*N + j] << " ";
+            std::cout << matrix[i * N + j] << " " << std::setw(6);
+        }
+        std::cout << std::endl;
+    }
+    std::cout << std::endl;
+}
+
+void GenerateRandomMatrix(double* matrix1, double* matrix2, int N)
+{
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+        {
+            matrix1[i * N + j] = ((rand() % 101 - 50) / 10.0);
+            matrix2[i * N + j] = ((rand() % 101 - 50) / 10.0);
+            /*matrix1[i*N + j] = (double)rand() / (double)RAND_MAX* 5;
+            matrix2[i*N + j] = (double)rand() / (double)RAND_MAX* 5 ;*/
+        }
+    }
+}
+
+bool matComparison(double* matrix1, double* matrix2, int N)
+{
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+        {
+            if (matrix1[i * N + j] != matrix2[i * N + j])
+            {
+                return false;
+                //std::cout << "Not Equal" << std::endl;
+            }
+        }
+    }
+    return true;
+}
+
+double* CreateMatrix(int N)
+{
+    double* matrix = new double[N * N];
+    return matrix;
+}
+
+double* defaultMult(double* matrix1, double* matrix2, int N)
+{
+    double* tmp = CreateMatrix(N);
+    double sum;
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++) {
+            sum = 0;
+            for (int k = 0; k < N; k++)
+            {
+                sum += matrix1[i * N + k] * matrix2[k * N + j];
+            }
+            tmp[i * N + j] = sum;
+        }
+    }
+    return tmp;
+}
+
+double* Add(double* matrix1, double* matrix2, int N)
+{
+    double* tmp = CreateMatrix(N);
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+        {
+            tmp[i * N + j] = matrix1[i * N + j] + matrix2[i * N + j];
+        }
+    }
+    return tmp;
+}
+
+double* Add(double* matrix1, double* matrix2, double* matrix3, double* matrix4, int N)
+{
+    double* tmp = CreateMatrix(N);
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+        {
+            tmp[i * N + j] = matrix1[i * N + j] + matrix2[i * N + j] + matrix3[i * N + j] + matrix4[i * N + j];
+        }
+    }
+    return tmp;
+}
+
+double* Sub(double* matrix1, double* matrix2, int N)
+{
+    double* tmp = CreateMatrix(N);
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+        {
+            tmp[i * N + j] = matrix1[i * N + j] - matrix2[i * N + j];
+        }
+    }
+    return tmp;
+}
+
+double* Sub(double* matrix1, double* matrix2, double* matrix3, double* matrix4, int N)
+{
+    double* tmp = CreateMatrix(N);
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+        {
+            tmp[i * N + j] = matrix1[i * N + j] + matrix2[i * N + j] + matrix3[i * N + j] - matrix4[i * N + j];
+        }
+    }
+    return tmp;
+}
+
+double* Str_alg(double* matrix1, double* matrix2, int N, int threshold)
+{
+    double* Rez;
+
+    if (N <= threshold)
+        Rez = defaultMult(matrix1, matrix2, N);
+    else
+    {
+        Rez = CreateMatrix(N);
+        N = N / 2;
+
+        double* A[4]; double* B[4]; double* C[4]; double* P[7];
+
+        double* TMP1; double* TMP2; double* TMP3; double* TMP4; double* TMP5;
+        double* TMP6; double* TMP7; double* TMP8; double* TMP9; double* TMP10;
+
+        for (int i = 0; i < 4; i++)
+        {
+            A[i] = CreateMatrix(N);
+            B[i] = CreateMatrix(N);
+        }
+
+        for (int i = 0; i < N; i++)
+            for (int j = 0; j < N; j++)
+            {
+                A[0][i * N + j] = matrix1[2 * i * N + j];
+                A[1][i * N + j] = matrix1[2 * i * N + j + N];
+                A[2][i * N + j] = matrix1[2 * i * N + j + 2 * N * N];
+                A[3][i * N + j] = matrix1[2 * i * N + j + 2 * N * N + N];
+
+                B[0][i * N + j] = matrix2[2 * i * N + j];
+                B[1][i * N + j] = matrix2[2 * i * N + j + N];
+                B[2][i * N + j] = matrix2[2 * i * N + j + 2 * N * N];
+                B[3][i * N + j] = matrix2[2 * i * N + j + 2 * N * N + N];
+            }
+
+        TMP1 = Add(A[0], A[3], N);
+        TMP2 = Add(B[0], B[3], N);
+        TMP3 = Add(A[2], A[3], N);
+        TMP4 = Sub(B[1], B[3], N);
+        TMP5 = Sub(B[2], B[0], N);
+        TMP6 = Add(A[0], A[1], N);
+        TMP7 = Sub(A[2], A[0], N);
+        TMP8 = Add(B[0], B[1], N);
+        TMP9 = Sub(A[1], A[3], N);
+        TMP10 = Add(B[2], B[3], N);
+
+        P[0] = Str_alg(TMP1, TMP2, N, threshold); // (A11 + A22)*(B11 + B22)
+        P[1] = Str_alg(TMP3, B[0], N, threshold); // (A21 + A22)*B11
+        P[2] = Str_alg(A[0], TMP4, N, threshold); // A11*(B12 - B22)
+        P[3] = Str_alg(A[3], TMP5, N, threshold); // A22*(B21 - B11)
+        P[4] = Str_alg(TMP6, B[3], N, threshold); // (A11 + A12)*B22
+        P[5] = Str_alg(TMP7, TMP8, N, threshold); // (A21 - A11)*(B11 + B12)
+        P[6] = Str_alg(TMP9, TMP10, N, threshold); // (A12 - A22)*(B21 + B22)
+
+        C[0] = Sub(P[0], P[3], P[6], P[4], N); // P1 + P4 - P5 + P7
+        C[1] = Add(P[2], P[4], N); // P3 + P5
+        C[2] = Add(P[1], P[3], N); // P2 + P4
+        C[3] = Sub(P[0], P[2], P[5], P[1], N); // P1 - P2 + P3 + P6
+
+        for (int i = 0; i < N; i++)
+            for (int j = 0; j < N; j++) {
+                Rez[i * 2 * N + j] = C[0][i * N + j];
+                Rez[i * 2 * N + j + N] = C[1][i * N + j];
+                Rez[i * 2 * N + j + 2 * N * N] = C[2][i * N + j];
+                Rez[i * 2 * N + j + 2 * N * N + N] = C[3][i * N + j];
+            }
+
+        for (int i = 0; i < 4; i++) {
+            delete[] A[i];
+            delete[] B[i];
+            delete[] C[i];
+        }
+
+        for (int i = 0; i < 7; i++) {
+            delete[] P[i];
+        }
+
+        delete[]TMP1; delete[]TMP2; delete[]TMP3; delete[]TMP4; delete[]TMP5;
+        delete[]TMP6; delete[]TMP7; delete[]TMP8; delete[]TMP9; delete[]TMP10;
+    }
+
+    return Rez;
+}
+
+int main()
+{
+    int degree;
+    int Size;
+
+    std::cout << "Degree of matrix size: ";
+    std::cin >> degree;
+    Size = (int)pow(2, degree);
+    std::cout << "Size of matrix: " << Size << std::endl;
+
+    double* matA = nullptr;
+    double* matB = nullptr;
+    double* matResStrassen = nullptr;
+    double* matResDefault = nullptr;
+
+    matA = CreateMatrix(Size);
+    matB = CreateMatrix(Size);
+    matResStrassen = CreateMatrix(Size);
+    matResDefault = CreateMatrix(Size);
+
+    GenerateRandomMatrix(matA, matB, Size);
+
+    auto start_default = std::chrono::high_resolution_clock::now();
+    matResDefault = defaultMult(matA, matB, Size);
+    auto end_default = std::chrono::high_resolution_clock::now();
+    std::chrono::duration<double> duration_def = end_default - start_default;
+
+    auto start_Strassen = std::chrono::high_resolution_clock::now();
+    matResStrassen = Str_alg(matA, matB, Size, 64);
+    auto end_Strassen = std::chrono::high_resolution_clock::now();
+    std::chrono::duration<double> duration_Strassen = end_Strassen - start_Strassen;
+
+    if (matComparison(matResStrassen, matResDefault, Size) != true) { std::cout << "Mats are not equal" << std::endl << std::endl; }
+    else { std::cout << "Mats are equal" << std::endl << std::endl; }
+
+    std::cout << "Default multiplication: " << duration_def.count() << std::endl;
+    std::cout << "Strassen algorithm: " << duration_Strassen.count() << std::endl;
+
+    delete[]matA;
+    delete[]matB;
+    delete[]matResStrassen;
+    delete[]matResDefault;
+    return 0;
+}