矩阵乘法，求解Ax = b求解x [英] Matrix multiplication, solve Ax = b solve for x

问题描述

因此，我得到了一项家庭作业，需要解决三次样条曲线的系数.现在，我清楚地了解了如何在纸上以及MatLab上进行数学运算，我想用Python解决问题.给定一个方程Ax = b，我知道A和b的值，我希望能够用Python求解x，而我很难找到一个好的资源来做这样的事情.

So I was given a homework assignment that requires solving the coefficients of cubic splines. Now I clearly understand how to do the math on paper as well as with MatLab, I want to solve the problem with Python. Given an equation Ax = b where I know the values of A and b, I want to be able to solve for x with Python and I am having trouble finding a good resource to do such a thing.

例如.

A = |1 0 0|
    |1 4 1|
    |0 0 1|

x = Unknown 3x1 matrix

b = |0 |
    |24| 
    |0 |

解决x

推荐答案

在一般情况下，请使用solve:

In a general case, use solve:

>>> import numpy as np
>>> from scipy.linalg import solve
>>> 
>>> A = np.random.random((3, 3))
>>> b = np.random.random(3)
>>> 
>>> x = solve(A, b)
>>> x
array([ 0.98323512,  0.0205734 ,  0.06424613])
>>> 
>>> np.dot(A, x) - b
array([ 0.,  0.,  0.])

如果您的问题是有条带的(通常是三次样条)，则有 http://docs.scipy.org/doc/scipy/reference/genic/scipy.linalg.solve_banded.html

If your problem is banded (which cubic splines it often are), then there's http://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_banded.html

要对问题的某些评论进行评论:更好的 not 可以使用inv求解线性系统. numpy.lstsq有点不同，它对拟合更有用.

To comment on some of the comments to the question: better not use inv for solving linear systems. numpy.lstsq is a bit different, it's more useful for fitting.

因为这是家庭作业，所以至少在阅读解决三对角线性系统的方法上确实会更好.

As this is homework, you're really better off at least reading up on ways of solving tridiagonal linear systems.

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