Question

我正在尝试创建一个python程序来执行strassen和常规矩阵乘法方法。但是，当我尝试使用createRandom Matrix函数创建的随机生成的矩阵运行我的strassen函数时，得到以下错误：

Traceback (most recent call last):
  File "matrixMult.py", line 106, in <module>
    print strassen(c, d, 10)
  File "matrixMult.py", line 77, in strassen
    p1 = strassen(addMatrix(a11,a22), addMatrix(b11,b22), n/2)
  File "matrixMult.py", line 78, in strassen
    p2 = strassen(addMatrix(a21,a22), b11, n/2)
  File "matrixMult.py", line 82, in strassen
    p6 = strassen(subMatrix(a21,a11), addMatrix(b11,b12), n/2)
  File "matrixMult.py", line 62, in subMatrix
    c.append(a[i][j] - b[i][j]) 
  IndexError: list index out of range

这是代码。我随机创建一个10x10矩阵，然后尝试用它执行Strassen，我得到前面的错误。然而，当我使用最后定义的简单4x4矩阵时，strassen工作正常，似乎我的随机矩阵生成没有问题，所以我不确定问题出在哪里。有人有什么想法吗？

import random
import time

random.seed()


def createEmptyMatrix(x, y): # create empty matrix
    matrix = [[0 for row in range(x)] for col in range(y)]
    return matrix

def createRandomMatrix(size): # create matrix filled with random ints
    matrix = []
    matrix = [[random.randint(1,20) for row in range(size)] for col in range(10)]
    return matrix

def regular(a, b): # standard O(n^3) matrix multiplication
    c = createEmptyMatrix(len(a), len(b[0]))
    for i in range(len(a)):
        for j in range(len(b[0])):
            for k in range(len(b)):
                c[i][j] += a[i][k]*b[k][j]
    return c

def split(matrix): # split matrix into quarters for strassen
    a = matrix
    b = matrix
    c = matrix
    d = matrix
    while(len(a) > len(matrix)/2):
        a = a[:len(a)/2]
        b = b[:len(b)/2]
        c = c[len(c)/2:]
        d = d[len(d)/2:]
    while(len(a[0]) > len(matrix[0])/2):
        for i in range(len(a[0])/2):
            a[i] = a[i][:len(a[i])/2]
            b[i] = b[i][len(b[i])/2:]
            c[i] = c[i][:len(c[i])/2]
            d[i] = d[i][len(d[i])/2:]
    return a,b,c,d

def addMatrix(a, b): # add 2 matrices
    d = []
    for i in range(len(a)):
        c = []
        for j in range(len(a[0])):
            c.append(a[i][j] + b[i][j])
        d.append(c)
    return d

def subMatrix(a, b): # subtract 2 matrices
    d = []
    for i in range(len(a)):
        c = []
        for j in range(len(a[0])):
            c.append(a[i][j] - b[i][j])
        d.append(c)
    return d


def strassen(a, b, n): # strassen matrix multiplication method
    #base case
    if n == 1:
        d = [[0]]
        d[0][0] = a[0][0] * b[0][0]
        return d
    else:
        a11, a12, a21, a22 = split(a)
        b11, b12, b21, b22 = split(b)

        p1 = strassen(addMatrix(a11,a22), addMatrix(b11,b22), n/2)
    p2 = strassen(addMatrix(a21,a22), b11, n/2)
    p3 = strassen(a11, subMatrix(b12,b22), n/2)
    p4 = strassen(a22, subMatrix(b21,b11), n/2)
    p5 = strassen(addMatrix(a11,a12), b22, n/2)
    p6 = strassen(subMatrix(a21,a11), addMatrix(b11,b12), n/2)
    p7 = strassen(subMatrix(a12,a22), addMatrix(b21,b22), n/2)

    c11 = addMatrix(subMatrix(addMatrix(p1, p4), p5), p7)
    c12 = addMatrix(p3, p5)
    c21 = addMatrix(p2, p4)
    c22 = addMatrix(subMatrix(addMatrix(p1, p3), p2), p6)

        c = createEmptyMatrix(len(c11)*2,len(c11)*2)

    for i in range(len(c11)):
            for j in range(len(c11)):
                c[i][j]                   = c11[i][j]
                c[i][j+len(c11)]          = c12[i][j]
                c[i+len(c11)][j]          = c21[i][j]
                c[i+len(c11)][j+len(c11)] = c22[i][j]

        return c

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 = createRandomMatrix(10)
d = createRandomMatrix(10)
print "Strassen Outputs:"
#print strassen(c, d, 10)
print "Should be:"
print regular(c, d)
print c
print d

print a
print b
print strassen(a, b, 4)

Answer 1

我建议使用numpy，您可以在其中轻松使用矩阵，并且所有这些功能都已存在。

与此同时，如果您在此函数中遇到索引错误，请尝试添加类似assert的内容：

def subMatrix(a, b): # subtract 2 matrices
    assert len(a) == len(b), "Number of rows does not match!"
    assert len(a[0]) == len(b[0]), "Number of columns does not match!"
    d = []
    for i in range(len(a)):
        c = []
        for j in range(len(a[0])):
            c.append(a[i][j] - b[i][j])
        d.append(c)
    return d

但是你根本不需要写这个函数：

import numpy as np
a = np.matrix(np.random.randint(10, size=(3,3)))
b = np.matrix(np.random.randint(10, size=(3,))).T

c = a * b
d = a - b

print a
[[5 8 1]
 [7 6 1]
 [9 2 9]]

print b
[[5]
 [2]
 [4]]

print c
[[45]
 [51]
 [85]]

print d
[[ 0  3 -4]
 [ 5  4 -1]
 [ 5 -2  5]]

Answer 2

引用的最后一行告诉你出了什么问题：

  File "matrixMult.py", line 62, in subMatrix
    c.append(a[i][j] - b[i][j]) 
  IndexError: list index out of range

这一行包含4个数组索引用法，其中一个超出了数组的范围。

要调试此功能，请转到第62行，在它之前添加print i,j。您将获得大量输出，并且异常之前的输出行将告诉您哪个索引超出范围。通过这种方式，您可以跟踪此处的错误。

“只是调试它”

Python矩阵乘法，

2 个答案: