Create stressen.py

stressen.py

@@ -0,0 +1,167 @@
+
+import numpy as np
+
+num_addorsub=0
+num_mul=0
+num_assign=0
+
+def matrix_add(matrix_a, matrix_b):
+    '''
+    :param matrix_a:
+    :param matrix_b:
+    :return:matrix_c=matrix_a+matrix_b
+    '''
+    rows = len(matrix_a) # get numbers of rows
+    columns = len(matrix_a[0]) # get numbers of cols
+    matrix_c = [list() for i in range(rows)] # build matrix 2d list
+    for i in range(rows):
+        for j in range(columns):
+            matrix_c_temp = matrix_a[i][j] + matrix_b[i][j]
+            global num_addorsub,num_assign
+            num_addorsub = num_addorsub + 1
+            num_assign = num_assign + 1
+            matrix_c[i].append(matrix_c_temp)
+    return matrix_c
+
+
+def matrix_minus(matrix_a, matrix_b):
+    '''
+    :param matrix_a:
+    :param matrix_b:
+    :return:matrix_c=matrix_a-matrix_b
+    '''
+    rows = len(matrix_a)
+    columns = len(matrix_a[0])
+    matrix_c = [list() for i in range(rows)]
+    for i in range(rows):
+        for j in range(columns):
+            matrix_c_temp = matrix_a[i][j] - matrix_b[i][j]
+            global num_addorsub,num_assign
+            num_addorsub = num_addorsub + 1
+            num_assign=num_assign + 1
+            matrix_c[i].append(matrix_c_temp)
+    return matrix_c
+
+
+def matrix_divide(matrix_a, row, column):
+    '''
+    :param matrix_a:
+    :param row:
+    :param column:
+    :return: matrix_b=matrix_a(row,column) to divide matrix_a
+    '''
+    rows = len(matrix_a)
+    columns = len(matrix_a[0])
+    matrix_b = [list() for i in range(rows // 2)]
+    k = 0
+    for i in range((row - 1) * rows // 2, row * rows // 2):
+        for j in range((column - 1) * columns // 2, column * columns // 2):
+            matrix_c_temp = matrix_a[i][j]
+            matrix_b[k].append(matrix_c_temp)
+        k += 1
+    return matrix_b
+
+
+def matrix_merge(matrix_11, matrix_12, matrix_21, matrix_22):
+    '''
+    :param matrix_11:
+    :param matrix_12:
+    :param matrix_21:
+    :param matrix_22:
+    :return:mariix merged by 4 parts above
+    '''
+    length = len(matrix_11)
+    matrix_all = [list() for i in range(length * 2)]  # build a matrix of double rows
+    for i in range(length):
+        # for each row. matrix_all list contain row of matrix_11 and matrix_12
+        matrix_all[i] = matrix_11[i] + matrix_12[i]
+    for j in range(length):
+        # for each row. matrix_all list contain row of matrix_21 and matrix_22
+        matrix_all[length + j] = matrix_21[j] + matrix_22[j]
+    return matrix_all
+ 
+
+def strassen(matrix_a, matrix_b):
+    '''
+    :param matrix_a:
+    :param matrix_b:
+    :return:matrix_a * matrix_b
+    '''
+    row_a = len(matrix_a)
+    col_a = len(matrix_a[0])
+    row_b = len(matrix_b)
+    col_b = len(matrix_b[0])
+    if col_a != row_b:
+        print('matrix_a and matrix_b can not be multiplied')
+        return
+    global num_mul,num_addorsub
+    if row_a == 1 or col_a == 1 or row_b == 1 or col_b == 1:
+        matrix_all = [list() for i in range(row_a)]
+        for i in range(row_a):
+            for j in range(col_b):
+                matrix_all_temp = 0
+                for k in range(col_a):
+                    matrix_all_temp += matrix_a[i][k] * matrix_b[k][j]
+                    num_mul = num_mul + 1
+                    num_addorsub = num_addorsub + 1
+                matrix_all[i].append(matrix_all_temp)
+    else:
+        # 10 first parts of computing
+        s1 = matrix_minus((matrix_divide(matrix_b, 1, 2)), (matrix_divide(matrix_b, 2, 2)))
+        s2 = matrix_add((matrix_divide(matrix_a, 1, 1)), (matrix_divide(matrix_a, 1, 2)))
+        s3 = matrix_add((matrix_divide(matrix_a, 2, 1)), (matrix_divide(matrix_a, 2, 2)))
+        s4 = matrix_minus((matrix_divide(matrix_b, 2, 1)), (matrix_divide(matrix_b, 1, 1)))
+        s5 = matrix_add((matrix_divide(matrix_a, 1, 1)), (matrix_divide(matrix_a, 2, 2)))
+        s6 = matrix_add((matrix_divide(matrix_b, 1, 1)), (matrix_divide(matrix_b, 2, 2)))
+        s7 = matrix_minus((matrix_divide(matrix_a, 1, 2)), (matrix_divide(matrix_a, 2, 2)))
+        s8 = matrix_add((matrix_divide(matrix_b, 2, 1)), (matrix_divide(matrix_b, 2, 2)))
+        s9 = matrix_minus((matrix_divide(matrix_a, 1, 1)), (matrix_divide(matrix_a, 2, 1)))
+        s10 = matrix_add((matrix_divide(matrix_b, 1, 1)), (matrix_divide(matrix_b, 1, 2)))
+        # 7 second parts of computing
+        p1 = strassen(matrix_divide(matrix_a, 1, 1), s1)
+        p2 = strassen(s2, matrix_divide(matrix_b, 2, 2))
+        p3 = strassen(s3, matrix_divide(matrix_b, 1, 1))
+        p4 = strassen(matrix_divide(matrix_a, 2, 2), s4)
+        p5 = strassen(s5, s6)
+        p6 = strassen(s7, s8)
+        p7 = strassen(s9, s10)
+        # 4 final parts of result
+        c11 = matrix_add(matrix_add(p5, p4), matrix_minus(p6, p2))
+        c12 = matrix_add(p1, p2)
+        c21 = matrix_add(p3, p4)
+        c22 = matrix_minus(matrix_add(p5, p1), matrix_add(p3, p7))
+        matrix_all = matrix_merge(c11, c12, c21, c22)
+        global num_assign
+        num_assign =num_assign+22
+    return matrix_all
+
+
+def main():
+
+    # statistical data
+    A = np.random.random_integers(-5, 5, size=(256, 64))
+    print("\nRandom Matrix A:\n", A)
+    B = np.random.random_integers(-5, 5, size=(64, 128))
+    print("\nRandom Matrix B:\n", B)
+
+    C_verification=np.dot(A,B)
+
+    result = strassen(A, B)
+    print("\n A*B Result of matrixs by generate randomly\n",np.array(result))
+
+    print("\nfrequency of add/sub",num_addorsub)
+    print("frequency of assign", num_assign)
+    print("frequency of mul", num_mul)
+
+    if (C_verification==result).all():
+        print("\nCorrect")
+    else:
+        print("\nWrong")
+
+if __name__ == '__main__':
+    main()
+
+# frequency of add/sub 4499186
+# frequency of assign 3989370
+# frequency of mul 941192
+# 2097152