strassen算法之Python實現

strassen算法

strassen算法是矩陣相乘的算法，這個算法降低了時間複雜度，通常暴力破解法的時間複雜度爲O(),這種方法的時間爲O()

Python3實現

#strassen.py
#python3
#Yanglin Tu

def matrix_add(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]
			matrix_c[i].append(matrix_c_temp)
	return matrix_c

def matrix_minus(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]
			matrix_c[i].append(matrix_c_temp)
	return matrix_c

def matrix_divide(matrix_a,row,column):
	length = len(matrix_a)
	matrix_b = [list() for i in range(length//2)]
	k = 0
	for i in range((row-1)*length//2,row*length//2):
		for j in range((column-1)*length//2,column*length//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):
	length = len(matrix_11)
	matrix_all = [list() for i in range(length*2)]
	for i in range(length):
		matrix_all[i] = matrix_11[i] + matrix_12[i]
	for j in range(length):
		matrix_all[length+j] = matrix_21[j] + matrix_22[j]
	return matrix_all

def strassen(matrix_a,matrix_b):
	rows = len(matrix_a)
	if rows == 1:
		matrix_all = [list() for i in range(rows)]
		matrix_all[0].append(matrix_a[0][0] * matrix_b[0][0])
	else:
		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)))
		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)
		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)
	return matrix_all

def main():
	a = [[1,1,1,1],[2,2,2,2],[3,3,3,3],[4,4,4,4]]
	b = [[5,5,5,5],[6,6,6,6],[7,7,7,7],[8,8,8,8]]
	c = strassen(a,b)
	print(c)
if __name__ == '__main__':
	main()