Python numpy 在我的电脑中产生了错误的特征值和特征向量
Python numpy produces wrong eigenvalues and eigenvectors in my computer
我正在使用 numpy 计算矩阵的特征值和特征向量，但我在本地计算机上总是得到错误的结果。我的输入数组是：
ATA =np.array([[ 56100, 33750, 350, 0, 0, 0, -13434400, -6298800, -67340]
[ 33750, 39025, 365, 0, 0, 0, -6298800, -4105800, -40530]
[ 350, 365, 4, 0, 0, 0, -67340, -40530, -421]
[ 0, 0, 0, 56100, 33750, 350, -6297800, -4104300, -40480]
[ 0, 0, 0, 33750, 39025, 365, -4104300, -5323650, -46800]
[ 0, 0, 0, 350, 365, 4, -40480, -46800, -437]
[ -13434400, -6298800, -67340, -6297800, -4104300, -40480, -143294096, 1988812200, 21046240]
[ -6298800, -4105800, -40530, -4104300, -5323650, -46800, 1988812200, 1463802300, 13946640]
[ -67340, -40530, -421, -40480, -46800, -437, 21046240, 13946640, 136958]])
所以当我 运行 np.linalg.eig(ATA) 输出应该是：
(array([ 5.20824997e+09, 4.07454810e+08, 7.42539687e+04, 2.15085782e+04,
1.47325883e+03, 6.95623993e+02, 1.00620174e+00, -2.34183896e-10,
4.89068886e-03]), array([[ 2.84539953e-03, 1.81479448e-03, -4.03677749e-01,
8.40141629e-02, -1.62954584e-01, 6.55925095e-01,
-4.22667744e-01, 4.28089963e-01, 1.06176905e-01],
[ 1.43790972e-03, -1.64731179e-03, -4.11218161e-01,
8.20390032e-01, -1.04799961e-01, -3.83178690e-01,
-2.95123482e-03, -3.17384527e-03, -5.22638141e-03],
[ 1.50694971e-05, -1.03183136e-05, -3.89314681e-03,
7.14037036e-03, -1.10215138e-02, 5.07017350e-03,
5.91938347e-01, 3.92898770e-01, 7.03580978e-01],
[ 1.43759890e-03, -1.64599502e-03, 7.08867672e-01,
5.61266733e-01, 1.50187808e-01, 3.99898006e-01,
-1.95860586e-03, 1.11445719e-03, -1.27734452e-03],
[ 1.17548483e-03, -6.81423034e-03, 4.06683631e-01,
-6.55054431e-02, -5.23337672e-01, -4.35335264e-01,
-4.11520452e-01, 4.32430093e-01, 1.02594642e-01],
[ 1.10796389e-05, -5.48396552e-05, 4.32865661e-03,
5.41689188e-04, -1.94131236e-02, 6.27255853e-04,
-4.22766929e-01, -5.91916200e-01, 6.85935194e-01],
[-8.83129590e-01, -4.69109327e-01, -2.08350880e-03,
1.14444168e-03, -5.76087521e-04, 3.54706596e-03,
-1.71586709e-05, 6.93819107e-06, -3.51316614e-05],
[-4.69089792e-01, 8.83088500e-01, 3.43558431e-03,
2.66295777e-03, -9.46771468e-03, -9.51037214e-04,
3.67021032e-05, 2.30158491e-05, -1.70205343e-04],
[-4.82500030e-03, 5.99890239e-03, -2.98470711e-03,
-2.30397046e-02, 8.15742461e-01, -2.71037947e-01,
-3.50524557e-01, 3.53550068e-01, 1.12421281e-01]]))
但在我的环境中，它达到：
(array([ 2.80556520e+09, -1.48486833e+09, 8.91358635e+04, 3.12310662e+04,
1.67293828e+04, 1.45256927e+03, 1.02287725e+00, 1.71486141e-04,
7.14907196e-02]), array([[ 4.53911407e-03, -5.12844789e-03, 5.81815676e-01,
4.03075138e-01, -3.54070037e-01, 5.22579137e-02,
-4.18346581e-01, -4.39977631e-01, 4.77848175e-02],
[ 2.46880709e-03, -1.97041290e-03, 3.86847218e-01,
1.97085313e-01, 8.84776717e-01, 1.69008001e-01,
-4.91082887e-03, 4.02327384e-03, -7.92374720e-03],
[ 2.53995133e-05, -2.23326997e-05, 3.95854042e-03,
2.45012019e-03, 6.76807972e-03, 1.08295840e-02,
6.12610346e-01, -5.13976174e-01, 6.00293512e-01],
[ 2.46815358e-03, -1.97050701e-03, -5.08932001e-01,
8.30051437e-01, 7.85246368e-02, -2.14057675e-01,
-7.15437012e-05, -8.15717096e-04, 2.31896436e-03],
[ 2.39125344e-03, -2.86679627e-04, -4.90583621e-01,
-1.62932815e-01, 1.38557602e-01, 5.87624795e-01,
-4.12659947e-01, -4.43735069e-01, 3.29341124e-02],
[ 2.18983860e-05, -4.97622085e-06, -4.62793574e-03,
2.95201534e-04, 1.07051252e-03, 1.95471546e-02,
-3.95612985e-01, 4.58193429e-01, 7.95703714e-01],
[-5.59185122e-01, -8.29039916e-01, -1.58639818e-03,
-1.34262675e-03, 7.05133701e-04, 8.24587719e-06,
2.26139620e-07, 5.65965747e-09, 4.33823831e-07],
[-8.28977882e-01, 5.59121133e-01, 3.58122146e-03,
8.59258680e-03, -1.73055059e-03, 9.46280078e-03,
2.88384523e-05, 8.09952365e-06, -1.76507697e-04],
[-8.31631249e-03, 6.49815429e-03, -1.10014765e-01,
-2.88224906e-01, 2.57662176e-01, -7.59600488e-01,
-3.50532044e-01, -3.67952844e-01, 5.53810458e-02]]))
这与我的意图大相径庭。有谁知道为什么我可能会得到不同的结果？我在在线编译器中仔细检查了第一个输出，我确信它是正确的答案，那么为什么相同的代码会得到不同的结果？
嗯，这很愚蠢。显然，我在 Windows 中将 ATA 声明为一个 int 数组，而我 运行 在 macOS 和 Linux 中进行的所有其他测试，所以这可能与这些操作系统如何存储大量数字有关.因此，当我将 ATA 更改为浮点数组时，我得到了正确的特征值。
我正在使用 numpy 计算矩阵的特征值和特征向量，但我在本地计算机上总是得到错误的结果。我的输入数组是：
ATA =np.array([[ 56100, 33750, 350, 0, 0, 0, -13434400, -6298800, -67340]
[ 33750, 39025, 365, 0, 0, 0, -6298800, -4105800, -40530]
[ 350, 365, 4, 0, 0, 0, -67340, -40530, -421]
[ 0, 0, 0, 56100, 33750, 350, -6297800, -4104300, -40480]
[ 0, 0, 0, 33750, 39025, 365, -4104300, -5323650, -46800]
[ 0, 0, 0, 350, 365, 4, -40480, -46800, -437]
[ -13434400, -6298800, -67340, -6297800, -4104300, -40480, -143294096, 1988812200, 21046240]
[ -6298800, -4105800, -40530, -4104300, -5323650, -46800, 1988812200, 1463802300, 13946640]
[ -67340, -40530, -421, -40480, -46800, -437, 21046240, 13946640, 136958]])
所以当我 运行 np.linalg.eig(ATA) 输出应该是：
(array([ 5.20824997e+09, 4.07454810e+08, 7.42539687e+04, 2.15085782e+04,
1.47325883e+03, 6.95623993e+02, 1.00620174e+00, -2.34183896e-10,
4.89068886e-03]), array([[ 2.84539953e-03, 1.81479448e-03, -4.03677749e-01,
8.40141629e-02, -1.62954584e-01, 6.55925095e-01,
-4.22667744e-01, 4.28089963e-01, 1.06176905e-01],
[ 1.43790972e-03, -1.64731179e-03, -4.11218161e-01,
8.20390032e-01, -1.04799961e-01, -3.83178690e-01,
-2.95123482e-03, -3.17384527e-03, -5.22638141e-03],
[ 1.50694971e-05, -1.03183136e-05, -3.89314681e-03,
7.14037036e-03, -1.10215138e-02, 5.07017350e-03,
5.91938347e-01, 3.92898770e-01, 7.03580978e-01],
[ 1.43759890e-03, -1.64599502e-03, 7.08867672e-01,
5.61266733e-01, 1.50187808e-01, 3.99898006e-01,
-1.95860586e-03, 1.11445719e-03, -1.27734452e-03],
[ 1.17548483e-03, -6.81423034e-03, 4.06683631e-01,
-6.55054431e-02, -5.23337672e-01, -4.35335264e-01,
-4.11520452e-01, 4.32430093e-01, 1.02594642e-01],
[ 1.10796389e-05, -5.48396552e-05, 4.32865661e-03,
5.41689188e-04, -1.94131236e-02, 6.27255853e-04,
-4.22766929e-01, -5.91916200e-01, 6.85935194e-01],
[-8.83129590e-01, -4.69109327e-01, -2.08350880e-03,
1.14444168e-03, -5.76087521e-04, 3.54706596e-03,
-1.71586709e-05, 6.93819107e-06, -3.51316614e-05],
[-4.69089792e-01, 8.83088500e-01, 3.43558431e-03,
2.66295777e-03, -9.46771468e-03, -9.51037214e-04,
3.67021032e-05, 2.30158491e-05, -1.70205343e-04],
[-4.82500030e-03, 5.99890239e-03, -2.98470711e-03,
-2.30397046e-02, 8.15742461e-01, -2.71037947e-01,
-3.50524557e-01, 3.53550068e-01, 1.12421281e-01]]))
但在我的环境中，它达到：
(array([ 2.80556520e+09, -1.48486833e+09, 8.91358635e+04, 3.12310662e+04,
1.67293828e+04, 1.45256927e+03, 1.02287725e+00, 1.71486141e-04,
7.14907196e-02]), array([[ 4.53911407e-03, -5.12844789e-03, 5.81815676e-01,
4.03075138e-01, -3.54070037e-01, 5.22579137e-02,
-4.18346581e-01, -4.39977631e-01, 4.77848175e-02],
[ 2.46880709e-03, -1.97041290e-03, 3.86847218e-01,
1.97085313e-01, 8.84776717e-01, 1.69008001e-01,
-4.91082887e-03, 4.02327384e-03, -7.92374720e-03],
[ 2.53995133e-05, -2.23326997e-05, 3.95854042e-03,
2.45012019e-03, 6.76807972e-03, 1.08295840e-02,
6.12610346e-01, -5.13976174e-01, 6.00293512e-01],
[ 2.46815358e-03, -1.97050701e-03, -5.08932001e-01,
8.30051437e-01, 7.85246368e-02, -2.14057675e-01,
-7.15437012e-05, -8.15717096e-04, 2.31896436e-03],
[ 2.39125344e-03, -2.86679627e-04, -4.90583621e-01,
-1.62932815e-01, 1.38557602e-01, 5.87624795e-01,
-4.12659947e-01, -4.43735069e-01, 3.29341124e-02],
[ 2.18983860e-05, -4.97622085e-06, -4.62793574e-03,
2.95201534e-04, 1.07051252e-03, 1.95471546e-02,
-3.95612985e-01, 4.58193429e-01, 7.95703714e-01],
[-5.59185122e-01, -8.29039916e-01, -1.58639818e-03,
-1.34262675e-03, 7.05133701e-04, 8.24587719e-06,
2.26139620e-07, 5.65965747e-09, 4.33823831e-07],
[-8.28977882e-01, 5.59121133e-01, 3.58122146e-03,
8.59258680e-03, -1.73055059e-03, 9.46280078e-03,
2.88384523e-05, 8.09952365e-06, -1.76507697e-04],
[-8.31631249e-03, 6.49815429e-03, -1.10014765e-01,
-2.88224906e-01, 2.57662176e-01, -7.59600488e-01,
-3.50532044e-01, -3.67952844e-01, 5.53810458e-02]]))
这与我的意图大相径庭。有谁知道为什么我可能会得到不同的结果？我在在线编译器中仔细检查了第一个输出，我确信它是正确的答案，那么为什么相同的代码会得到不同的结果？
嗯，这很愚蠢。显然，我在 Windows 中将 ATA 声明为一个 int 数组，而我 运行 在 macOS 和 Linux 中进行的所有其他测试，所以这可能与这些操作系统如何存储大量数字有关.因此，当我将 ATA 更改为浮点数组时，我得到了正确的特征值。