[SciPy-dev] Is this a bugfix for scipy.hilbert?

Ariel Rokem arokem@berkeley....
Fri Jan 15 13:34:34 CST 2010


Hi -

attached is a file with a couple of tests. I am not sure this tests the
issues we were dealing with previously (the axis issues, etc.), but it has
some sensible test-cases, which compare to what Matlab would give you (not
quite 10by3 or 10by6, but as you can see, they make sense). Also - all the
assertions are assert_almost_equal. Do you think that's OK? I think there
are float-precision issues here, which would make assert_equal fail, but I
am not sure - I would be happy to get any general comments on these tests,
in case I am doing this all wrong.

Cheers,

Ariel

On Thu, Jan 14, 2010 at 11:10 PM, <josef.pktd@gmail.com> wrote:

> On Fri, Jan 15, 2010 at 1:44 AM, Ariel Rokem <arokem@berkeley.edu> wrote:
> > Yes - looks good. Except I would prefer to eventually set the axis to
> > default to -1, to be consistent with signal.fft (and also np.fft.fft)
> which
> > has axis=-1.
>
> I'm indifferent to the default axis, from a quick look and my
> experience there are not many functions with axis arguments in signal.
> So I'm fine with switching to axis=-1. We should do it with this
> bugfix, since until now the function wasn't correct anyway for 2d.
>
> >
> > As for whether it's doing what it's supposed to do, for what it's worth -
> it
> > seems to do similar things to what Matlab's 'hilbert' function does on a
> few
> > simple examples I tried out.
>
> I was reading briefly on wikipedia, and checked with fftpack.hilbert,
> which returns the same array as signal.hilbert(a).imag, but I didn't
> manage to figure out why fftpack.hilbert only allows 1d (i got lost
> starting at convolve.pyf)
>
> Could you write a simple test case compared to matlab, e.g. 10by3 as
> in my example, for both axis, or 10by6 if 10by3 doesn't make sense?
>
> If nobody objects, I can commit the change with axis=-1.
>
> Josef
>
> >
> > Cheers,
> >
> > Ariel
> >
> >
> >
> > On Thu, Jan 14, 2010 at 8:53 PM, <josef.pktd@gmail.com> wrote:
> >>
> >> On Thu, Jan 14, 2010 at 11:27 PM,  <josef.pktd@gmail.com> wrote:
> >> > On Thu, Jan 14, 2010 at 11:02 PM,  <josef.pktd@gmail.com> wrote:
> >> >> On Thu, Jan 14, 2010 at 10:54 PM,  <josef.pktd@gmail.com> wrote:
> >> >>> On Thu, Jan 14, 2010 at 10:24 PM, Ariel Rokem <arokem@berkeley.edu>
> >> >>> wrote:
> >> >>>> Hi everyone,
> >> >>>>
> >> >>>> I have been trying to use scipy.signal.hilbert and I got the
> >> >>>> following
> >> >>>> puzzling result:
> >> >>>>
> >> >>>> In [22]: import scipy
> >> >>>>
> >> >>>> In [23]: scipy.__version__ #I have r6182
> >> >>>> Out[23]: '0.8.0.dev'
> >> >>>>
> >> >>>> In [24]: import scipy.signal as signal
> >> >>>>
> >> >>>> In [25]: a = np.random.rand(100,100)
> >> >>>>
> >> >>>> In [26]: np.abs(signal.hilbert(a[-1]))
> >> >>>> Out[26]:
> >> >>>> array([ 0.57567681,  0.25918624,  0.50207097,  0.51834052,
> >> >>>> 0.24293389,
> >> >>>>         0.5779464 ,  0.6515758 ,  0.89973173,  1.00275444,
> >> >>>> 0.37352935,
> >> >>>>         0.62332717,  0.93599749,  0.40651376,  0.65088756,
> 0.8332281
> >> >>>> ,
> >> >>>>         0.5770101 ,  0.9288512 ,  0.46671906,  0.41536055,
> >> >>>> 0.71418068,
> >> >>>>         0.81250913,  0.07652627,  0.72939072,  0.26755626,
> >> >>>> 0.36396146,
> >> >>>>         0.59725999,  1.02264694,  0.41227986,  0.98122853,
> >> >>>> 0.71906675,
> >> >>>>         0.58582611,  0.77288117,  0.3217015 ,  0.65261394,
> >> >>>> 0.11947618,
> >> >>>>         0.75632703,  0.43432935,  0.52182485,  1.0277177 ,
> >> >>>> 1.01104986,
> >> >>>>         0.3023265 ,  0.6024772 ,  0.69257548,  0.55418735,
> >> >>>> 0.46259052,
> >> >>>>         0.25832231,  0.38278355,  0.45508532,  0.26215872,
> >> >>>> 0.34207947,
> >> >>>>         0.80704729,  0.80755477,  0.95317178,  0.97458885,
> >> >>>> 0.58762294,
> >> >>>>         0.82540618,  0.62005585,  0.82494646,  1.04221293,
> >> >>>> 0.14983027,
> >> >>>>         1.01571579,  0.99381328,  0.24158714,  0.84256569,
> >> >>>> 0.53418924,
> >> >>>>         0.24067628,  0.90489883,  1.02217747,  0.34988034,
> 0.5310065
> >> >>>> ,
> >> >>>>         0.48135002,  1.03020269,  0.6013679 ,  0.46062485,
> 0.3918485
> >> >>>> ,
> >> >>>>         0.21554545,  0.31704519,  0.04868385,  0.1787766 ,
> >> >>>> 0.37361852,
> >> >>>>         0.21977912,  0.7649772 ,  0.77867281,  0.37684278,
> >> >>>> 0.64432638,
> >> >>>>         0.77494951,  0.87106309,  0.77611484,  0.52666801,
> >> >>>> 0.88683667,
> >> >>>>         0.69164967,  0.98618191,  0.84811375,  0.35934198,
> >> >>>> 0.32650478,
> >> >>>>         0.1752677 ,  0.60574454,  0.5109132 ,  0.52332287,
> >> >>>> 0.99777805])
> >> >>>>
> >> >>>> In [27]: np.abs(signal.hilbert(a))[-1]
> >> >>>> Out[27]:
> >> >>>> array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
> >> >>>> 0.,
> >> >>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
> >> >>>> 0.,
> >> >>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
> >> >>>> 0.,
> >> >>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
> >> >>>> 0.,
> >> >>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
> >> >>>> 0.,
> >> >>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
> >> >>>> 0.,
> >> >>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
> >> >>>> 0.,
> >> >>>>         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])
> >> >>>>
> >> >>>>
> >> >>>>
> >> >>>>
> ----------------------------------------------------------------------
> >> >>>>
> >> >>>> I was expecting both of these to have the same values - am I
> missing
> >> >>>> something?
> >> >>>>
> >> >>>> I think that the following solves this issue, but now I am not that
> >> >>>> sure
> >> >>>> whether it does what it is supposed to do and I couldn't find a
> test
> >> >>>> for
> >> >>>> this in test_signaltools.py. Does anyone know of a good test-case
> for
> >> >>>> the
> >> >>>> analytic signal, that I could create for this?
> >> >>>>
> >> >>>> Index: scipy/signal/signaltools.py
> >> >>>> ===================================================================
> >> >>>> --- scipy/signal/signaltools.py    (revision 6182)
> >> >>>> +++ scipy/signal/signaltools.py    (working copy)
> >> >>>> @@ -1062,13 +1062,13 @@
> >> >>>>      """
> >> >>>>      x = asarray(x)
> >> >>>>      if N is None:
> >> >>>> -        N = len(x)
> >> >>>> +        N = x.shape[-1]
> >> >>>>      if N <=0:
> >> >>>>          raise ValueError, "N must be positive."
> >> >>>>      if iscomplexobj(x):
> >> >>>>          print "Warning: imaginary part of x ignored."
> >> >>>>          x = real(x)
> >> >>>> -    Xf = fft(x,N,axis=0)
> >> >>>> +    Xf = fft(x,N,axis=-1)
> >> >>>>      h = zeros(N)
> >> >>>>      if N % 2 == 0:
> >> >>>>          h[0] = h[N/2] = 1
> >> >>>> @@ -1078,7 +1078,7 @@
> >> >>>>          h[1:(N+1)/2] = 2
> >> >>>>
> >> >>>>      if len(x.shape) > 1:
> >> >>>> -        h = h[:, newaxis]
> >> >>>> +        h = h[newaxis,:]
> >> >>>>      x = ifft(Xf*h)
> >> >>>>      return x
> >> >>>
> >> >>> I think your change would break the currently advertised behavior,
> >> >>> axis=0 (The transformation is done along the first axis)
> >> >>>
> >> >>> but fft and ifft have default axis=-1
> >> >>>
> >> >>> fft in hilbert uses axis=0 as in docstring
> >> >>> but ifft uses default axis=-1
> >> >>>
> >> >>> so, I would think the fix should be  x = ifft(Xf*h, axis=0)
> >> >>>
> >> >>> But as it currently looks like the axis argument doesn't work
> anyway,
> >> >>> there wouldn't be much breakage if the axis would be included as an
> >> >>> argument and default to -1.
> >> >>> However, I don't know what the "standard" for scipy.signal is for
> >> >>> default axis.
> >> >>>
> >> >>> Josef
> >> >>
> >> >> after adding axis to ifft:
> >> >>>>> print hilbert(aa).real
> >> >> [[ 0.82584851  0.15215031  0.14767381]
> >> >>  [ 0.95021675  0.16803995  0.43562964]
> >> >>  [ 0.13033881  0.06198952  0.70729614]
> >> >>  [ 0.69409563  0.06962778  0.72552601]
> >> >>  [ 0.34297612  0.50579001  0.86463304]
> >> >>  [ 0.28355261  0.21626889  0.85165102]
> >> >>  [ 0.49481491  0.21290645  0.71416814]
> >> >>  [ 0.2645843   0.95783096  0.77514016]
> >> >>  [ 0.38735994  0.14274852  0.56344808]
> >> >>  [ 0.88084015  0.39879649  0.64949951]]
> >> >>>>> print hilbert(aa[:,:1]).real
> >> >> [[ 0.82584851]
> >> >>  [ 0.95021675]
> >> >>  [ 0.13033881]
> >> >>  [ 0.69409563]
> >> >>  [ 0.34297612]
> >> >>  [ 0.28355261]
> >> >>  [ 0.49481491]
> >> >>  [ 0.2645843 ]
> >> >>  [ 0.38735994]
> >> >>  [ 0.88084015]]
> >> >>
> >> >> but it treats a 1d array as row vector and transforms along zero axis
> >> >> of length 1, and not along the length of the array.
> >> >> so another fix to handle 1d arrays correctly should be done
> >> >>
> >> >>>>> print hilbert(aa[:,1]).real
> >> >> [ 0.15215031  0.16803995  0.06198952  0.06962778  0.50579001
> >> >>  0.21626889
> >> >>  0.21290645  0.95783096  0.14274852  0.39879649]
> >> >>>>> aa[:,1]
> >> >> array([ 0.15215031,  0.16803995,  0.06198952,  0.06962778,
>  0.50579001,
> >> >>        0.21626889,  0.21290645,  0.95783096,  0.14274852,
>  0.39879649])
> >> >>>>>
> >> >
> >> > there's something wrong with my example, the real part is the same
> >> > which confused me
> >> >
> >> > it works correctly with 1d
> >> >
> >> >>>> np.abs(hilbert(aa[:,0]))
> >> > array([ 0.83251128,  1.04487091,  0.27702083,  0.69901499,
>  0.49170197,
> >> >        0.31227114,  0.49505637,  0.26461488,  0.61385196,
>  0.90716272])
> >> >
> >> >>>> np.abs(hilbert(aa[:,:1])).T
> >> > array([[ 0.83251128,  1.04487091,  0.27702083,  0.69901499,
>  0.49170197,
> >> >         0.31227114,  0.49505637,  0.26461488,  0.61385196,
> >> >  0.90716272]])
> >> >
> >> >>>> np.abs(hilbert(aa))[:,0]
> >> > array([ 0.83251128,  1.04487091,  0.27702083,  0.69901499,
>  0.49170197,
> >> >        0.31227114,  0.49505637,  0.26461488,  0.61385196,
>  0.90716272])
> >> >
> >> > besides reading the docstring, I don't know what hilbert is supposed
> >> > to be good for.
> >>
> >> Would something like the function in the attachment do ?
> >>
> >>
> >>
> >> > Josef
> >> >
> >> >
> >> >> Josef
> >> >>
> >> >>
> >> >>>
> >> >>>>
> >> >>>>
> >> >>>> Cheers,
> >> >>>>
> >> >>>> Ariel
> >> >>>> --
> >> >>>> Ariel Rokem
> >> >>>> Helen Wills Neuroscience Institute
> >> >>>> University of California, Berkeley
> >> >>>> http://argentum.ucbso.berkeley.edu/ariel
> >> >>>>
> >> >>>> _______________________________________________
> >> >>>> SciPy-Dev mailing list
> >> >>>> SciPy-Dev@scipy.org
> >> >>>> http://mail.scipy.org/mailman/listinfo/scipy-dev
> >> >>>>
> >> >>>>
> >> >>>
> >> >>
> >> >
> >>
> >> _______________________________________________
> >> SciPy-Dev mailing list
> >> SciPy-Dev@scipy.org
> >> http://mail.scipy.org/mailman/listinfo/scipy-dev
> >>
> >
> >
> >
> > --
> > Ariel Rokem
> > Helen Wills Neuroscience Institute
> > University of California, Berkeley
> > http://argentum.ucbso.berkeley.edu/ariel
> >
> > _______________________________________________
> > SciPy-Dev mailing list
> > SciPy-Dev@scipy.org
> > http://mail.scipy.org/mailman/listinfo/scipy-dev
> >
> >
> _______________________________________________
> SciPy-Dev mailing list
> SciPy-Dev@scipy.org
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>



-- 
Ariel Rokem
Helen Wills Neuroscience Institute
University of California, Berkeley
http://argentum.ucbso.berkeley.edu/ariel
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