numpy.dot手动输入矩阵时，对于相同矩阵的不同输出

我想知道为什么np.dot（U，SV）！= np.dot（A，B）当我相信A = U且B = SV时，甚至尽管我在使用SVD恢复矩阵U和SV时手动输入A和B的条目。下面的代码重现了怪异。numpy.dot手动输入矩阵时，对于相同矩阵的不同输出

import numpy 
from numpy.linalg import svd 
    In [121]: fullSet = np.array([[100,50,50],[50,100,100],[20,130,130],[50,100,100]]) 

In [122]: print fullSet 
[[100 50 50] 
[ 50 100 100] 
[ 20 130 130] 
[ 50 100 100]] 

In [123]: 

In [123]: U,s,V = svd(fullSet,full_matrices=True) 

In [124]: print 'U' 
U 

In [125]: print U.round() 
[[ 0. 1. -0. -0.] 
[ 1. 0. 1. -0.] 
[ 1. -0. -1. -0.] 
[ 1. 0. 0. 1.]] 

In [126]: 

In [126]: S = np.zeros((U.shape[1],V.shape[0])) 

In [127]: S[:s.shape[0],:s.shape[0]] = np.diag(s) 

In [128]: print 'S' 
S 

In [129]: print S.round() 
[[ 296. 0. 0.] 
[ 0. 82. 0.] 
[ 0. 0. 0.] 
[ 0. 0. 0.]] 

In [130]: 

In [130]: print 'V' 
V 

In [131]: print V.round() 
[[ 0. 1. 1.] 
[ 1. -0. -0.] 
[-0. 1. -1.]] 

In [132]: 

In [132]: print 'SV' 
SV 

In [133]: print np.dot(S,V).round() 
[[ 97. 198. 198.] 
[ 78. -19. -19.] 
[ 0. 0. -0.] 
[ 0. 0. 0.]] 

In [134]: print 'SV' 
SV 

In [135]: print np.dot(S,V).round() 
[[ 97. 198. 198.] 
[ 78. -19. -19.] 
[ 0. 0. -0.] 
[ 0. 0. 0.]] 

In [136]: print 'USV' 
USV 

In [137]: SV=np.dot(S,V) 

In [138]: print np.dot(U,SV) 
[[ 100. 50. 50.] 
[ 50. 100. 100.] 
[ 20. 130. 130.] 
[ 50. 100. 100.]] 

In [139]: 

In [139]: 

In [139]: A = np.array([[0,1,0,0],[1,0,-1,0],[1,0,1,0],[1,0,0,1]]) 

In [140]: B = np.array([[97,198,198],[78,-19,-19],[0,0,0],[0,0,0]]) 

In [141]: print "A" 
A 

In [142]: print A 
[[ 0 1 0 0] 
[ 1 0 -1 0] 
[ 1 0 1 0] 
[ 1 0 0 1]] 

In [143]: print "B" 
B 

In [144]: print B 
[[ 97 198 198] 
[ 78 -19 -19] 
[ 0 0 0] 
[ 0 0 0]] 

In [145]: print "AdotB" 
AdotB 

In [146]: print np.dot(A,B) 
[[ 78 -19 -19] 
[ 97 198 198] 
[ 97 198 198] 
[ 97 198 198]] 

In [147]: print np.allclose(A,U.round()) 
False 

In [148]: print np.allclose(B,SV.round()) 
True 

In [149]: print A[0,0] 
0 

In [150]: print U[0,0] 
0.33656051104

来源

2016-12-05 user86895

是什么原因舍入输出？ 'A'和'U'和'B'和'SV'不是相同的矩阵。似乎很明显，除非'U'和'SV'是整数矩阵，否则在舍入矩阵上的操作给出的结果与在非舍入矩阵上的相同操作的结果不同。 – Forzaa

重塑你的U和SV：

In [627]: U 
Out[627]: 
array([[ -3.36560511e-01, 8.66235179e-01, -3.69274473e-01, 
     -4.61618492e-16], 
     [ -5.07358551e-01, 1.27694290e-02, 4.92365964e-01, 
     -7.07106781e-01], 
     [ -6.09837375e-01, -4.99310021e-01, -6.15457455e-01, 
     -1.06278764e-15], 
     [ -5.07358551e-01, 1.27694290e-02, 4.92365964e-01, 
      7.07106781e-01]]) 
In [628]: SV 
Out[628]: 
array([[ -9.65886537e+01, -1.97578594e+02, -1.97578594e+02], 
     [ 7.79142604e+01, -1.90446580e+01, -1.90446580e+01], 
     [ 0.00000000e+00, 4.63542263e-15, -4.63542263e-15], 
     [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]]) 
In [629]: np.dot(U,SV) 
Out[629]: 
array([[ 100., 50., 50.], 
     [ 50., 100., 100.], 
     [ 20., 130., 130.], 
     [ 50., 100., 100.]])

的dot与舍入值不会产生相同的结果：

In [630]: np.dot(U.round(),SV.round()) 
Out[630]: 
array([[ 78., -19., -19.], 
     [ 97., 198., 198.], 
     [ 97., 198., 198.], 
     [ 97., 198., 198.]])

的的U和SV全浮点值进行显着差异。记住一个dot是产品的总和 - 这些是

来源

2016-12-05 18:06:43 hpaulj

numpy.dot手动输入矩阵时，对于相同矩阵的不同输出

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