[SciPy-dev] Is this a bugfix for scipy.hilbert?
Ariel Rokem
arokem at berkeley.edu
Fri Jan 15 01:44:54 EST 2010
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.
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.
Cheers,
Ariel
On Thu, Jan 14, 2010 at 8:53 PM, <josef.pktd at gmail.com> wrote:
> On Thu, Jan 14, 2010 at 11:27 PM, <josef.pktd at gmail.com> wrote:
> > On Thu, Jan 14, 2010 at 11:02 PM, <josef.pktd at gmail.com> wrote:
> >> On Thu, Jan 14, 2010 at 10:54 PM, <josef.pktd at gmail.com> wrote:
> >>> On Thu, Jan 14, 2010 at 10:24 PM, Ariel Rokem <arokem at 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 at scipy.org
> >>>> http://mail.scipy.org/mailman/listinfo/scipy-dev
> >>>>
> >>>>
> >>>
> >>
> >
>
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>
--
Ariel Rokem
Helen Wills Neuroscience Institute
University of California, Berkeley
http://argentum.ucbso.berkeley.edu/ariel
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