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Author: TonyQ2k3

parallel_matrix_multiply.py

@@ -0,0 +1,94 @@
+import time
+import numpy as np
+import multiprocessing
+
+
+def default_multiply(matrix_a, matrix_b):
+    dim = matrix_a.shape[0]
+    result = np.zeros((dim, dim), dtype='int')
+    matrix_b = np.transpose(matrix_b)
+    for i in range(dim):
+        result[i] = np.sum(matrix_a[i] * matrix_b, axis=1)
+    return result
+
+
+def matrix_split(matrix):
+    n = matrix.shape[0] // 2
+    return matrix[:n, :n], matrix[:n, n:], matrix[n:, :n], matrix[n:, n:]
+
+
+def strassen(matrix_a, matrix_b):
+    dim = matrix_a.shape[0]
+    if dim % 4 != 0:
+        return default_multiply(matrix_a, matrix_b)
+
+    A, B, C, D = matrix_split(matrix_a)
+    E, F, G, H = matrix_split(matrix_b)
+
+    p1 = strassen(A + D, E + H)
+    p2 = strassen(C + D, E)
+    p3 = strassen(A, F - H)
+    p4 = strassen(D, G - E)
+    p5 = strassen(A + B, H)
+    p6 = strassen(C - A, E + F)
+    p7 = strassen(B - D, G + H)
+
+    top_left = p1 + p4 - p5 + p7
+    top_right = p3 + p5
+    bot_left = p2 + p4
+    bot_right = p1 - p2 + p3 + p6
+
+    result = np.vstack((np.hstack((top_left, top_right)), np.hstack((bot_left, bot_right))))
+    return result
+
+
+def pad_zeros(matrix):
+    zeros = 0
+    size = matrix.shape[0]
+    while (size + zeros) % 4 != 0:
+        zeros += 1
+    pad_h = np.zeros((size, zeros), dtype='int')
+    pad_v = np.zeros((zeros, size + zeros), dtype='int')
+
+    matrix = np.hstack((matrix, pad_h))
+    return np.vstack((matrix, pad_v))
+
+
+def parallel_multiply_matrices(matrix_a, matrix_b):
+    dim = matrix_a.shape[0]
+    if dim % 4 != 0:
+        matrix_a = pad_zeros(matrix_a)
+        matrix_b = pad_zeros(matrix_b)
+
+    A, B, C, D = matrix_split(matrix_a)
+    E, F, G, H = matrix_split(matrix_b)
+
+    workers = [(A + D, E + H), (C + D, E), (A, F - H), (D, G - E), (A + B, H), (C - A, E + F), (B - D, G + H)]
+
+    with multiprocessing.Pool() as pool:
+        results = pool.starmap(strassen, workers)
+        pool.close()
+        pool.join()
+
+    top_left = results[0] + results[3] - results[4] + results[6]
+    top_right = results[2] + results[4]
+    bot_left = results[1] + results[3]
+    bot_right = results[0] - results[1] + results[2] + results[5]
+
+    result = np.vstack((np.hstack((top_left, top_right)), np.hstack((bot_left, bot_right))))
+    return result[:dim, :dim]
+
+
+if __name__=='__main__':
+    n = 1000
+    matrix1 = np.random.randint(0, 2, size=(n, n))
+    matrix2 = np.random.randint(0, 2, size=(n, n))
+
+    #print(matrix1, '\n')
+    #print(matrix2, '\n')
+    start = time.time()
+    result = parallel_multiply_matrices(matrix1, matrix2)
+    end = time.time()
+    print("Execution time: ", end-start)
+    print("Result:")
+    print(result, '\n')