Scipy的fftpack dct和id

Question

假设您使用dct函数，然后不操作数据并使用逆变换；逆变换的数据是否与预转换的数据相同？为什么会出现浮点问题？是报告的问题还是正常的行为？

In [21]: a = [1.2, 3.4, 5.1, 2.3, 4.5]

In [22]: b = dct(a)

In [23]: b
Out[23]: array([ 33.        ,  -4.98384545,  -4.5       ,  -5.971707  ,   4.5       ])

In [24]: c = idct(b)

In [25]: c
Out[25]: array([ 12.,  34.,  51.,  23.,  45.])

有人能解释为什么吗？当然，一个简单的c*10**-1就可以了，但是如果您在多个维度上重复调用函数来使用它，那么错误会变得更大：

In [37]: a = np.random.rand(3,3,3)

In [38]: d = dct(dct(dct(a).transpose(0,2,1)).transpose(2,1,0)).transpose(2,1,0).transpose(0,2,1)

In [39]: e = idct(idct(idct(d).transpose(0,2,1)).transpose(2,1,0)).transpose(2,1,0).transpose(0,2,1)

In [40]: a
Out[40]: 
array([[[ 0.48709809,  0.50624831,  0.91190972],
        [ 0.56545798,  0.85695062,  0.62484782],
        [ 0.96092354,  0.17453537,  0.17884233]],

       [[ 0.29433402,  0.08540074,  0.18574437],
        [ 0.09942075,  0.78902363,  0.62663572],
        [ 0.20372951,  0.67039551,  0.52292875]],

       [[ 0.79952289,  0.48221372,  0.43838685],
        [ 0.25559683,  0.39549153,  0.84129493],
        [ 0.69093533,  0.71522961,  0.16522915]]])

In [41]: e
Out[41]: 
array([[[ 105.21318703,  109.34963575,  196.97249887],
        [ 122.13892469,  185.10133376,  134.96712825],
        [ 207.55948396,   37.69964085,   38.62994399]],

       [[  63.57614855,   18.44656009,   40.12078466],
        [  21.47488098,  170.42910452,  135.35331646],
        [  44.00557341,  144.80543099,  112.95260949]],

       [[ 172.69694529,  104.15816275,   94.69156014],
        [  55.20891593,   85.42617016,  181.71970442],
        [ 149.2420308 ,  154.48959477,   35.68949734]]])

这里有一个指向doc的链接。