Question

我从scipy.linalg.eigh函数得到了不一致的结果（如果我尝试使用numpy.linalg.eigh）。即使我使用相同的输入，我得到的值也是不同的。为了以防万一，我尝试将随机种子设置为常数，但仍然没有运气。

这是我的测试代码：

print('#'*50)

import numpy as np
import scipy
from scipy.linalg import eigh

# Make a random symmetric matrix
m_size = 1500
A = scipy.random.rand(m_size, m_size)
L = np.triu(A) + np.triu(A,1).T
# Verify that matrix is symmetric
print('L symmetric: %s' % np.array_equal(L,L.T))
print('')

# Just to make sure that changes to one L won't effect changes to another
# and that we are starting with the exact same input.
import copy
L1 = copy.deepcopy(L)
L2 = copy.deepcopy(L)
L3 = copy.deepcopy(L)
L4 = copy.deepcopy(L)
L5 = copy.deepcopy(L)

# Sanity check that inputs are the same
print('L == L1 (before): %s' % str(np.array_equal(L,L1)))
print('L == L2 (before): %s' % str(np.array_equal(L,L2)))
print('L == L3 (before): %s' % str(np.array_equal(L,L3)))
print('L == L4 (before): %s' % str(np.array_equal(L,L4)))
print('L == L5 (before): %s' % str(np.array_equal(L,L5)))
print('L1 == L2 (before): %s' % str(np.array_equal(L1,L2)))
print('L1 == L3 (before): %s' % str(np.array_equal(L1,L3)))
print('L1 == L4 (before): %s' % str(np.array_equal(L1,L4)))
print('L1 == L5 (before): %s' % str(np.array_equal(L1,L5)))
print('L2 == L3 (before): %s' % str(np.array_equal(L2,L3)))
print('L2 == L4 (before): %s' % str(np.array_equal(L2,L4)))
print('L2 == L5 (before): %s' % str(np.array_equal(L2,L5)))
print('L3 == L4 (before): %s' % str(np.array_equal(L3,L4)))
print('L3 == L5 (before): %s' % str(np.array_equal(L3,L5)))
print('L4 == L5 (before): %s' % str(np.array_equal(L4,L5)))
print('')

# Normally, only np.random.seed(5) should set the random generator for both
# numpy and scipy functions, but just in case, I've included both here
np.random.seed(5)
scipy.random.seed(5)
[eigval,U] = eigh(L,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval1,U1] = eigh(L1,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval2,U2] = eigh(L2,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval3,U3] = eigh(L3,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval4,U4] = eigh(L4,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval5,U5] = eigh(L5,eigvals=(0,1))

# Make sure the inputs still match each other after the function
print('L == L1 (after): %s' % str(np.array_equal(L,L1)))
print('L == L2 (after): %s' % str(np.array_equal(L,L2)))
print('L == L3 (after): %s' % str(np.array_equal(L,L3)))
print('L == L4 (after): %s' % str(np.array_equal(L,L4)))
print('L == L5 (after): %s' % str(np.array_equal(L,L5)))
print('L1 == L2 (after): %s' % str(np.array_equal(L1,L2)))
print('L1 == L3 (after): %s' % str(np.array_equal(L1,L3)))
print('L1 == L4 (after): %s' % str(np.array_equal(L1,L4)))
print('L1 == L5 (after): %s' % str(np.array_equal(L1,L5)))
print('L2 == L3 (after): %s' % str(np.array_equal(L2,L3)))
print('L2 == L4 (after): %s' % str(np.array_equal(L2,L4)))
print('L2 == L5 (after): %s' % str(np.array_equal(L2,L5)))
print('L3 == L4 (after): %s' % str(np.array_equal(L3,L4)))
print('L3 == L5 (after): %s' % str(np.array_equal(L3,L5)))
print('L4 == L5 (after): %s' % str(np.array_equal(L4,L5)))
print('')

# Check to see if the outputs match each other
print('U == U1: %s' % str(np.array_equal(U,U1)))
print('U == U2: %s' % str(np.array_equal(U,U2)))
print('U == U3: %s' % str(np.array_equal(U,U3)))
print('U == U4: %s' % str(np.array_equal(U,U4)))
print('U == U5: %s' % str(np.array_equal(U,U5)))
print('U1 == U2: %s' % str(np.array_equal(U1,U2)))
print('U1 == U3: %s' % str(np.array_equal(U1,U3)))
print('U1 == U4: %s' % str(np.array_equal(U1,U4)))
print('U1 == U5: %s' % str(np.array_equal(U1,U5)))
print('U2 == U3: %s' % str(np.array_equal(U2,U3)))
print('U2 == U4: %s' % str(np.array_equal(U2,U4)))
print('U2 == U5: %s' % str(np.array_equal(U2,U5)))
print('U3 == U4: %s' % str(np.array_equal(U3,U4)))
print('U3 == U5: %s' % str(np.array_equal(U3,U5)))
print('U4 == U5: %s' % str(np.array_equal(U4,U5)))
print('')
print('eigval == eigval1: %s' % str(np.array_equal(eigval,eigval1)))
print('eigval == eigval2: %s' % str(np.array_equal(eigval,eigval2)))
print('eigval == eigval3: %s' % str(np.array_equal(eigval,eigval3)))
print('eigval == eigval4: %s' % str(np.array_equal(eigval,eigval4)))
print('eigval == eigval5: %s' % str(np.array_equal(eigval,eigval5)))
print('eigval1 == eigval2: %s' % str(np.array_equal(eigval1,eigval2)))
print('eigval1 == eigval3: %s' % str(np.array_equal(eigval1,eigval3)))
print('eigval1 == eigval4: %s' % str(np.array_equal(eigval1,eigval4)))
print('eigval1 == eigval5: %s' % str(np.array_equal(eigval1,eigval5)))
print('eigval2 == eigval3: %s' % str(np.array_equal(eigval2,eigval3)))
print('eigval2 == eigval4: %s' % str(np.array_equal(eigval2,eigval4)))
print('eigval2 == eigval5: %s' % str(np.array_equal(eigval2,eigval5)))
print('eigval3 == eigval4: %s' % str(np.array_equal(eigval3,eigval4)))
print('eigval3 == eigval5: %s' % str(np.array_equal(eigval3,eigval5)))
print('eigval4 == eigval5: %s' % str(np.array_equal(eigval4,eigval5)))
print('')
print('#'*50)

这是输出：

##################################################
L symmetric: True

L == L1 (before): True
L == L2 (before): True
L == L3 (before): True
L == L4 (before): True
L == L5 (before): True
L1 == L2 (before): True
L1 == L3 (before): True
L1 == L4 (before): True
L1 == L5 (before): True
L2 == L3 (before): True
L2 == L4 (before): True
L2 == L5 (before): True
L3 == L4 (before): True
L3 == L5 (before): True
L4 == L5 (before): True

L == L1 (after): True
L == L2 (after): True
L == L3 (after): True
L == L4 (after): True
L == L5 (after): True
L1 == L2 (after): True
L1 == L3 (after): True
L1 == L4 (after): True
L1 == L5 (after): True
L2 == L3 (after): True
L2 == L4 (after): True
L2 == L5 (after): True
L3 == L4 (after): True
L3 == L5 (after): True
L4 == L5 (after): True

U == U1: False
U == U2: False
U == U3: False
U == U4: False
U == U5: False
U1 == U2: False
U1 == U3: False
U1 == U4: False
U1 == U5: False
U2 == U3: True
U2 == U4: True
U2 == U5: True
U3 == U4: True
U3 == U5: True
U4 == U5: True

eigval == eigval1: True
eigval == eigval2: True
eigval == eigval3: True
eigval == eigval4: True
eigval == eigval5: True
eigval1 == eigval2: True
eigval1 == eigval3: True
eigval1 == eigval4: True
eigval1 == eigval5: True
eigval2 == eigval3: True
eigval2 == eigval4: True
eigval2 == eigval5: True
eigval3 == eigval4: True
eigval3 == eigval5: True
eigval4 == eigval5: True

##################################################

如何在特征分解中获得一致的确定性结果？

Answer 1

您希望浮点计算对于相同的输入始终产生相同的结果实际上是错误的 - 即使在没有线程的单台计算机上也是如此。浮点重现性通常在没有采取某些预防措施（具有性能影响）的情况下无法在高性能计算中实现，在编写代码时需要考虑这些因素。

这有几个原因，其中一个原因是优化编译器。有关详细信息，请参阅https://software.intel.com/sites/default/files/article/164389/fp-consistency-102511.pdf。

Answer 2

所以，基于我收到的评论，我决定尝试更新我的numpy和scipy库。我将numpy从1.7.1更新到1.9.2，并将scipy从0.12.0更新为0.15.1。而这似乎已经成功了！我想这是由于在这些库的更高版本中修复了一个错误。

感谢您的评论，伙计们！如果不是这样的话，我可能不会想到更新。

Numpy / Scipy eigh函数的结果不一致

2 个答案: