矩阵乘法，求解Ax = b求解x

本文介绍了矩阵乘法，求解Ax = b求解x的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！ 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 docs.scipy/doc/scipy/reference/genic/scipy.linalg.solve_banded.html

If your problem is banded (which cubic splines it often are), then there's docs.scipy/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.