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

josef.pktd@gmai... josef.pktd@gmai...
Fri Jan 15 13:48:51 CST 2010


On Fri, Jan 15, 2010 at 2:34 PM, Ariel Rokem <arokem@berkeley.edu> wrote:
> 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.

nice test cases, I like theoretical tests even better than verified
numbers from other packages.

Besides some cosmetic changes to get them into a test function, the
only part to add is the precision of the tests.
The default precision of assert_almost_equal is only 6 decimals.

For these kind of cases, I usually go to 12 to 15 depending on the
numerical precision of the algorithm. Usually, I go by trial and error
until the test breaks, or calculate max abs of the error.

I can add some tests for the axis argument.

Can you open a ticket for the record or shall I ?

Josef


>
> 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
>> 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
>
>


More information about the SciPy-Dev mailing list