线性方程组，使得 matlab 反斜杠和 numpy.linalg.solve 产生不同的解

Question

我使用 numpy 1.3.0 和 MATLAB 7.9.0 时遇到以下问题：python 代码

import numpy as np    
Lu = [[1.01250000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[-0.00250000000000000,1.01250000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,-0.00250000000000000,1.01250000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,-0.00250000000000000,1.01250000000000,0,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0,0],[-0.00250000000000000,0,0,0,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0,0],[0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0,0],[0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0,0],[0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,0,0,0,-0.00250000000000000,0,0,0,0,0,0,0,0],[0,0,0,0,-0.00250000000000000,0,0,0,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0,0],[0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0,0],[0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0,0,0],[0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,0,0,0,-0.00250000000000000,0,0,0,0],[0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,0,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0,0],[0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0,0],[0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,-0.00250000000000000,0,0,-0.00250000000000000,0],[0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01000000000000,0,0,0,-0.00250000000000000],[0,0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,0,1.01250000000000,-0.00250000000000000,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01250000000000,-0.00250000000000000,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01250000000000,-0.00250000000000000],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.00250000000000000,0,0,-0.00250000000000000,1.01250000000000]]
rhs = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0, 0,0, 0,  0, 0, 0.0050, 0.0050, 0.0050, 0.0050]

Lu = np.array(Lu)
rhs = np.array(rhs)
ans = np.linalg.solve(Lu,rhs)
print ans

产生输出

[  1.87241716e-13   1.89545264e-13   1.89545264e-13   1.87241716e-13
   7.56433496e-11   7.63890449e-11   7.63890449e-11   7.56433496e-11
   3.04833369e-08   3.07089522e-08   3.07089522e-08   3.04833369e-08
   1.22844835e-05   1.23451480e-05   1.23451480e-05   1.22844835e-05
   4.95055571e-03   4.96277946e-03   4.96277946e-03   4.95055571e-03]

而在 MATLAB 中使用反斜杠会产生输出

 0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0050    0.0050    0.0050    0.0050

我还没有发现 numpy 和 matlab 产生不同解的任何其他线性代数方程组。我目前不在城里，因此无法检查不同版本的 numpy（在不同的计算机上）是否会给出正确的结果。np.linalg.solve 不是解决该系统的正确函数（系统矩阵 Lu 是稀疏的）吗？这是我的 numpy 版本中的错误吗？我的代码有问题吗？

谢谢！

Answer 1

实际上，这些可能是相同的解决方案。MATLAB 舍入为 0.0000（至少在打印时），而 python 为您提供更详细的数字（某些问题可能来自浮点舍入错误）。唯一显示为 的数字0.0050是e-03。所有其他数字都小于 0.0005，因此可能会四舍五入为 0.0000。