Question

我正在尝试编写一个程序，该程序无需部分旋转即可进行高斯消除。到目前为止，这是我所拥有的，我知道我正在弄乱某些东西，但似乎无法弄清楚。它一直打印出与开始时相同的矩阵，而不是对角线中的1而不是0。任何帮助表示赞赏！

import numpy as np
import math

#A = np.array([[1,2,-1],[5,2,2],[-3,5,-1]])
#b = np.array([[2,9,1]])
A = np.array([[8,-2,-1,0,0],[-2,9,-4,-1,0],[-1,-3,7,-1,2],[0,-4,-2,12,-5],[0,0,-7,-3,15]])
b = np.array([[5],[2],[0],[1],[5]])

def forward_elim(A, b, n):
#calculates the forward part of Gaussian elimination.

    for row in range(0, n-1):
        for i in range(row+1, n):
            factor = A[i,row] / A[row,row]
            for j in range(row, n):
                A[i,j] = A[i,j] - factor * A[row,j]

            b[i] = b[i] - factor * b[row]

        print("A = \n%s and b = %s" % (A,b))
    return A, b

def back_sub(A, b, n):
#back substitution and returns result

    x = np.zeros((n,1))
    x[n-1] = b[n-1] / A[n-1, n-1]
    for row in range(n-2, -1, -1):
        sums = b[row]
        for j in range(row+1, n):
            sums = sums - A[row,j] * x[j]
        x[row] = sums / A[row,row]
    return x

def gauss_elim(A, b):
#performs gaussian elimination without pivoting

    n = A.shape[0]
    #checks for zero diagonal elements
    if any(np.diag(A)==0):
        raise ZeroDivisionError(("Can't divide by 0")) #raise used to raise exception

    A, b = forward_elim(A, b, n)
    return back_sub(A, b, n)

print(A)

Answer 1

从给定的代码尚不清楚您是否有效地调用了函数gauss_elim(A, b)。

为帮助找出正在发生的情况，请尝试逐步完成一个非常简单的示例。最好借助调试器或打印出中间值。按照相同的示例在纸上写下步骤。

一个简单的例子可能是：

A = np.array([[2,4],[3,9]])
b = np.array([[2,30]])

问题之一是您将b声明为1xn矩阵，但后来将其仅用作向量。一个解决方案可以是将b声明为向量：

b = np.array([2,30])

高斯消除不旋转

1 个答案: