Hi Gary,
Thanks for responding. It looks like the mpmath does what I'm looking for.
Your code looks interesting, as it lowers the number of dependencies needed.
I hope I'll find the time to really incorporate this features to something
that can come as part to matplotlib.
Regarding the plots I've pointed to, I didn't make them, so I don't know how
the author did it (expect that he used Mathematica).
Thanks,
Guy
On Sat, Apr 3, 2010 at 4:29 AM, Gary Ruben <gru...@bigpond.net.au> wrote:
> Hi Guy,
>
> I am also interested in the answer to this. The cplot function in the
> mpmath module does exactly this using matplotlib, but very inefficiently, as
> it computes the colour of each pixel in the image in hls colour-space and
> generates the corresponding rgb value directly. I suspect this is how it has
> to be done, as colormaps in matplotlib are 1D sequences and the black-white
> (lightness) value is really another dimension. However mpmath's method can
> be improved by doing the mapping using array operations instead of computing
> it for each pixel.
>
> I've attached a function I wrote to reproduce the Sage cplot command in my
> own work. It's a bit old and can be improved. It takes the Arg and Abs of a
> complex array as the first two arguments - you can easily change this to
> compute these inside the function if you prefer. The line
> np.vectorize(hls_to_rgb) can be replaced - recent versions of matplotlib
> have a vectorized function called hsv_to_rgb() inside colors.py - so you
> replace the return line with the commented-out version if you first import
> hsv_to_rgb from colors.
>
> I hope this helps.
>
> I'm also curious: the plots you point to also show plots of the function
> "extrema", which are the phase singularities - does mathematica have a
> function that gives you these, or did you write your own function to find
> them?
>
> regards,
> Gary
>
>
> Guy Rutenberg wrote:
>
>> Hi,
>>
>> Is there a way to generate colormaps for complex-valued functions using
>> matplotlib? The type of plots I'm looking for are like the plots in:
>> http://commons.wikimedia.org/wiki/User:Jan_Homann/Mathematics
>>
>> Thanks in advance,
>>
>> Guy
>>
>
> def cplot_like(ph, intens=None, int_exponent=1.0, s=1.0, l_bias=1.0,
> drape=0, is_like_mpmath=False):
> '''
> Implements the mpmath cplot-like default_color_function
> The combined image is generated in hls colourspace then transformed to
> rgb
> *phase*
> A filename or 2D n x m array containing phase data in the range
> -pi->pi
> *intens*
> If None, set to 1.0
> A filename or 2D n x m array containing intensity or amplitude data
> in the range 0->max
> *int_exponent*
> Default 1.0 applies the intens mask directly to the hls
> lightness-channel
> 0.6 works well when drape==0
> *s*
> saturation. Defaults to 1.0. mpmath uses 0.8.
> *l_bias*
> biases the mean lightness value away from 0.5. mpmath uses 1.0.
> Examples are: l_bias=2 -> mean=0.33 (ie darker), l_bias=0.5 ->
> mean=0.66 (lighter)
> *drape*
> If >1, drapes a structured maximum filter of size drape x drape over
> the intensity data
> *is_like_mpmath*
> If True, sets int_exponent = 0.3, s = 0.8
> '''
> from colorsys import hls_to_rgb
>
> if type(ph) is str:
> cph = plt.imread(ph)/256.*2*pi-pi # -pi->pi
> if len(cph.shape) == 3: cph = cph[...,0] # if ph is RGB or
> RGBA, extract the R-plane
> else:
> cph = ph.copy()
>
> if intens is None:
> cintens = np.ones_like(cph)
> elif type(intens) is str:
> cintens = plt.imread(intens)/255. # 0->1
> if len(cintens.shape) == 3: cintens = cintens[...,0] # if intens
> is RGB or RGBA, extract the R-plane
> else:
> cintens = intens.copy()
> cintens /= cintens.max() # autoscale intensity
> data to 0->1
>
> if drape > 1:
> # envelope the intensity
> cintens = maximum_filter(cintens, size=drape)
>
> h = ((cph + pi) / (2*pi)) % 1.0
>
> if is_like_mpmath:
> # apply mpmath values
> int_exponent = 0.3
> s = 0.8
>
> l = 1.0 - l_bias/(l_bias+cintens**int_exponent)
> v_hls_to_rgb = np.vectorize(hls_to_rgb)
>
> #~ return hsv_to_rgb(dstack((h,np.ones_like(h),l)))
> return dstack(v_hls_to_rgb(h,l,s))
>
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