numpy-discussion

[Numpy-discussion] Weird (wrong?) real fft 2d behavior

[Andrew J. <a.h...@gm...>]

If I start with what I thought was an appropriate (n, n/2+1) complex 
matrix which should have a real inverse fft, and then take its real fft, 
I don't get back the original matrix.

Note the presence of very small but nonzero reals in the final matrix, 
and the fact that the 2d and 4th rows are duplicates. This seems to be a 
  mistake somewhere.

Or am I just misunderstanding/misremembering something about 2d real ffts?

Andrew


In [41]: dims=(4,4)

In [42]: delta_k = aniso.dft_realizn(dims, P)
          #### this just makes an appropriate matrix

In [43]: delta_k
Out[43]:
array([[-0.    +0.j    ,  0.5904+0.0429j,  0.9063+0.j    ],
        [-0.221 +0.j    ,  0.4169+0.4602j, -0.6909+0.j    ],
        [ 0.9059+0.j    , -0.8037+0.2604j,  1.835 +0.j    ],
        [ 1.7436+0.j    , -0.2382+0.221j , -0.0607+0.j    ]])
        #### 16 real numbers

In [44]: delta_r = N.dft.inverse_real_fft2d(delta_k)

In [45]: delta_r
Out[45]:
array([[ 0.2718, -0.0956,  0.2805,  0.1505],
        [ 0.0297, -0.0533, -0.259 ,  0.0561],
        [ 0.1308, -0.2096,  0.2288, -0.3041],
        [ 0.0895,  0.1105, -0.3188, -0.1076]])

In [46]: delta_kp = N.dft.real_fft2d(delta_r)

In [47]: delta_kp
Out[47]:
array([[ 0.     +0.00e+00j,  0.5904 +4.2938e-02j,  0.9063 +0.0000e+00j],
        [ 0.7613 +5.5511e-17j,0.4169 +4.6020e-01j, -0.3758 +5.5511e-17j],
        [ 0.9059 +0.0000e+00j,-0.8037+2.6038e-01j, 1.835  +0.0000e+00j],
        [ 0.7613 -5.5511e-17j,-0.2382+2.2099e-01j,-0.3758-5.5511e-17j]])

In [48]: N.__version__
Out[48]: '0.9.5.1982'
------------------------

[Numpy-discussion] Re: Weird (wrong?) real fft 2d behavior

[Andrew J. <a.h...@gm...>]

Andrew Jaffe wrote:
> If I start with what I thought was an appropriate (n, n/2+1) complex 
> matrix which should have a real inverse fft, and then take its real fft, 
> I don't get back the original matrix.
> 
> Note the presence of very small but nonzero reals in the final matrix, 
> and the fact that the 2d and 4th rows are duplicates. This seems to be a 
>  mistake somewhere.
> 
> Or am I just misunderstanding/misremembering something about 2d real ffts?

and I should point out that
	delta_rp = N.dft.real_fft2d(delta_kp)
is 'allclose' to the original delta_r (which leads me to believe that I 
may indeed be misunderstanding something).

Andrew


> 
> Andrew
> 
> 
> In [41]: dims=(4,4)
> 
> In [42]: delta_k = aniso.dft_realizn(dims, P)
>          #### this just makes an appropriate matrix
> 
> In [43]: delta_k
> Out[43]:
> array([[-0.    +0.j    ,  0.5904+0.0429j,  0.9063+0.j    ],
>        [-0.221 +0.j    ,  0.4169+0.4602j, -0.6909+0.j    ],
>        [ 0.9059+0.j    , -0.8037+0.2604j,  1.835 +0.j    ],
>        [ 1.7436+0.j    , -0.2382+0.221j , -0.0607+0.j    ]])
>        #### 16 real numbers
> 
> In [44]: delta_r = N.dft.inverse_real_fft2d(delta_k)
> 
> In [45]: delta_r
> Out[45]:
> array([[ 0.2718, -0.0956,  0.2805,  0.1505],
>        [ 0.0297, -0.0533, -0.259 ,  0.0561],
>        [ 0.1308, -0.2096,  0.2288, -0.3041],
>        [ 0.0895,  0.1105, -0.3188, -0.1076]])
> 
> In [46]: delta_kp = N.dft.real_fft2d(delta_r)
> 
> In [47]: delta_kp
> Out[47]:
> array([[ 0.     +0.00e+00j,  0.5904 +4.2938e-02j,  0.9063 +0.0000e+00j],
>        [ 0.7613 +5.5511e-17j,0.4169 +4.6020e-01j, -0.3758 +5.5511e-17j],
>        [ 0.9059 +0.0000e+00j,-0.8037+2.6038e-01j, 1.835  +0.0000e+00j],
>        [ 0.7613 -5.5511e-17j,-0.2382+2.2099e-01j,-0.3758-5.5511e-17j]])
> 
> In [48]: N.__version__
> Out[48]: '0.9.5.1982'
> ------------------------

Re: [Numpy-discussion] Re: Weird (wrong?) real fft 2d behavior

[Warren F. <fo...@sl...>]

On Wed, 25 Jan 2006, Andrew Jaffe wrote:

> Andrew Jaffe wrote:
> > If I start with what I thought was an appropriate (n, n/2+1) complex
> > matrix which should have a real inverse fft, and then take its real fft,
> > I don't get back the original matrix.
> >
> > Note the presence of very small but nonzero reals in the final matrix,

That's just roundoff.

> > and the fact that the 2d and 4th rows are duplicates. This seems to be a
> >  mistake somewhere.
> >
> > Or am I just misunderstanding/misremembering something about 2d real ffts?

It looks wrong to me, and I think I wrote those functions.  I get the same
results in Numeric.  I'll try to look into the problem.

> and I should point out that
> 	delta_rp = N.dft.real_fft2d(delta_kp)
> is 'allclose' to the original delta_r (which leads me to believe that I
> may indeed be misunderstanding something).

"Stable" does not neccessarily imply "correct".

w

>
> Andrew
>
>
> >
> > Andrew
> >
> >
> > In [41]: dims=(4,4)
> >
> > In [42]: delta_k = aniso.dft_realizn(dims, P)
> >          #### this just makes an appropriate matrix
> >
> > In [43]: delta_k
> > Out[43]:
> > array([[-0.    +0.j    ,  0.5904+0.0429j,  0.9063+0.j    ],
> >        [-0.221 +0.j    ,  0.4169+0.4602j, -0.6909+0.j    ],
> >        [ 0.9059+0.j    , -0.8037+0.2604j,  1.835 +0.j    ],
> >        [ 1.7436+0.j    , -0.2382+0.221j , -0.0607+0.j    ]])
> >        #### 16 real numbers
> >
> > In [44]: delta_r = N.dft.inverse_real_fft2d(delta_k)
> >
> > In [45]: delta_r
> > Out[45]:
> > array([[ 0.2718, -0.0956,  0.2805,  0.1505],
> >        [ 0.0297, -0.0533, -0.259 ,  0.0561],
> >        [ 0.1308, -0.2096,  0.2288, -0.3041],
> >        [ 0.0895,  0.1105, -0.3188, -0.1076]])
> >
> > In [46]: delta_kp = N.dft.real_fft2d(delta_r)
> >
> > In [47]: delta_kp
> > Out[47]:
> > array([[ 0.     +0.00e+00j,  0.5904 +4.2938e-02j,  0.9063 +0.0000e+00j],
> >        [ 0.7613 +5.5511e-17j,0.4169 +4.6020e-01j, -0.3758 +5.5511e-17j],
> >        [ 0.9059 +0.0000e+00j,-0.8037+2.6038e-01j, 1.835  +0.0000e+00j],
> >        [ 0.7613 -5.5511e-17j,-0.2382+2.2099e-01j,-0.3758-5.5511e-17j]])
> >
> > In [48]: N.__version__
> > Out[48]: '0.9.5.1982'
> > ------------------------
>
>
>
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[Numpy-discussion] Re: Weird (wrong?) real fft 2d behavior

[Andrew J. <a.h...@gm...>]

Dear Warren,
 >
 > On Wed, 25 Jan 2006, Andrew Jaffe wrote:
 >
 >> Andrew Jaffe wrote:
 >>> If I start with what I thought was an appropriate (n, n/2+1) complex
 >>> matrix which should have a real inverse fft, and then take its real 
fft,
 >>> I don't get back the original matrix.
 >>>
 >>> Note the presence of very small but nonzero reals in the final matrix,
 >
 > That's just roundoff.
 >
 >>> and the fact that the 2d and 4th rows are duplicates. This seems to 
be a
 >>>  mistake somewhere.
 >>>
 >>> Or am I just misunderstanding/misremembering something about 2d 
real ffts?
 >
 > It looks wrong to me, and I think I wrote those functions.  I get the 
same
 > results in Numeric.  I'll try to look into the problem.
 >
 >> and I should point out that
 >> 	delta_rp = N.dft.real_fft2d(delta_kp)
 >> is 'allclose' to the original delta_r (which leads me to believe that I
 >> may indeed be misunderstanding something).
 >
 > "Stable" does not neccessarily imply "correct".

Indeed! And more to the point, it's actually the case that "delta_kp" 
doesn't actually have the requisite 16 (non-small) real degrees of 
freedom -- so it can't really be right.

Andrew

[Numpy-discussion] Re: Weird (wrong?) real fft 2d behavior

[Andrew J. <a.h...@gm...>]

 > On Wed, 25 Jan 2006, Andrew Jaffe wrote:
 >
 >> Andrew Jaffe wrote:
 >>> If I start with what I thought was an appropriate (n, n/2+1) complex
 >>> matrix which should have a real inverse fft, and then take its real 
fft,
 >>> I don't get back the original matrix.
 >>>
 >>> Note the presence of very small but nonzero reals in the final matrix,
 >
 > That's just roundoff.
 >
 >>> and the fact that the 2d and 4th rows are duplicates. This seems to 
be a
 >>>  mistake somewhere.
 >>>
 >>> Or am I just misunderstanding/misremembering something about 2d 
real ffts?
 >
 > It looks wrong to me, and I think I wrote those functions.  I get the 
same
 > results in Numeric.  I'll try to look into the problem.
 >
 >> and I should point out that
 >> 	delta_rp = N.dft.real_fft2d(delta_kp)
 >> is 'allclose' to the original delta_r (which leads me to believe that I
 >> may indeed be misunderstanding something).
 >
 > "Stable" does not neccessarily imply "correct".

Indeed! And more to the point, it's actually the case that "delta_kp" 
doesn't actually have the requisite 16 (non-small) real degrees of 
freedom -- so it can't really be right.

Andrew