In [1]:

    

%pylab inline

import numpy
import astrohack_projections
import matplotlib.pyplot as plt

plt.rcParams['figure.figsize'] = 16, 16
plot_kwargs = {"interpolation": "nearest",
          "cmap": "afmhot",
          "origin": "lower"}

file_path = "/Users/dalyabaron/Downloads/cutout_242959.hdf5"
illustris_gal = astrohack_projections.illustris_model_and_image(file_path)
illustris_gal.set_image_shape((60, 80))

for i in xrange(16):
    xi_hat, eta_hat = astrohack_projections.choose_random_projection()
    alpha, beta, gamma = numpy.random.uniform(0.0, 360.0, 3)
    intensity = 1.5
    scale = 0.015 * numpy.exp(numpy.random.uniform())
    xshift = numpy.random.uniform(29., 31.)
    yshift = numpy.random.uniform(39., 41.)
    psf_size = 1.5
    bg = 0.
    
    kwargs = {'alpha':alpha, 'beta':beta, 'gamma':gamma, 'intensity':intensity, 'scale':scale, 'xshift': xshift, 'yshift': yshift, 'bg':0.0, 'psf_size':psf_size}
    illustris_gal.set_image_parameters(**kwargs)
    illustris_gal.construct_image()
    
    plt.subplot(4, 4, i+1)
    a, mid = numpy.percentile(illustris_gal.get_image(), [15., 85.])
    ran = mid - a
    vmin = mid - 5. * ran
    vmax = mid + 20. * ran
    plt.imshow(numpy.log10(illustris_gal.get_image()+1), **plot_kwargs)


    

    




Populating the interactive namespace from numpy and matplotlib






    

In [2]:

    

# create an album of 32 such objects with random projection + normaly distributed noise

# plot parameters
plt.rcParams['figure.figsize'] = 16, 16
plot_kwargs = {"interpolation": "nearest",
          "cmap": "afmhot",
          "origin": "lower"}

# initial galaxy data
file_path = "/Users/dalyabaron/Downloads/cutout_242959.hdf5"
illustris_gal = astrohack_projections.illustris_model_and_image(file_path)
illustris_gal.set_image_shape((60, 80))

# album and PSF initialisation
album = astrohack_projections.album_and_model()
psf = astrohack_projections.mixture_of_gaussians(2)
psf.add_gaussian(1., numpy.array([0., 0.]), numpy.eye(2)*1.)

# galaxy model I fit with
basevar = 0.5 * numpy.eye(3)
gal_model = astrohack_projections.galaxy_model_3d()
v = [3., 0., 0.]
gal_model.add_gaussian(1.0, numpy.array([0., -1., 0.]), basevar + numpy.outer(v,v))
v = [-1., 3., 0.]
gal_model.add_gaussian(1.0, numpy.array([2., 1., 0.]), basevar + numpy.outer(v,v))
v = [1., 3., 0.]
gal_model.add_gaussian(1.0, numpy.array([-2., 1., 0.]), basevar + numpy.outer(v,v))

for i in xrange(32):
    # projection parameters
    xi_hat, eta_hat = astrohack_projections.choose_random_projection()
    alpha, beta, gamma = numpy.random.uniform(0.0, 360.0, 3)
    intensity = 20
    scale = 0.015 * numpy.exp(numpy.random.uniform())
    xshift = numpy.random.uniform(29.5, 31.)
    yshift = numpy.random.uniform(39.5, 41.)
    psf_size = 1.5
    bg = 0.
    # illustris galaxy
    kwargs = {'alpha':alpha, 'beta':beta, 'gamma':gamma, 'intensity':intensity, 'scale':scale, 'xshift': xshift, 'yshift': yshift, 'bg':0.0, 'psf_size':psf_size}
    illustris_gal.set_image_parameters(**kwargs)
    illustris_gal.construct_image(xi_hat, eta_hat)
    # image
    image = astrohack_projections.image_and_model()
    image.set_shape((60, 80))
    image.set_psf(psf)
    kwargs = {'alpha':alpha, 'beta':beta, 'gamma':gamma, 'intensity':intensity, 'scale':scale, 'xshift': xshift, 'yshift': yshift, 'bg':0.0}
    image.set_parameters(**kwargs)
    image.set_galaxy(gal_model)
    image.set_ivar(numpy.ones(image.get_shape()))
    image.set_data(illustris_gal.get_image() + numpy.random.normal(size=image.get_shape())/ numpy.sqrt(image.ivar))
    # album
    album.add_image(image)
    
print len(album)


    

    




32






    




astrohack_projections.py:519: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.
  if xi_hat == None and eta_hat == None:

In [3]:

    

def showme(album):
    plt.rcParams['figure.figsize'] = 20, 80
    plot_kwargs = {"interpolation": "nearest",
          "cmap": "afmhot",
          "origin": "lower"}
    for i in xrange(len(album)):
        image = album.get_all_images()[i]
        plt.subplot(16, 4, 2*i+1)
        vmin = -5. / numpy.sqrt(numpy.median(image.get_ivar())) # assumes bg = 0
        vmax = -2. * vmin # assumes bg = 0
        plt.imshow(numpy.nan_to_num(numpy.sqrt(image.get_data())), **plot_kwargs)
        plt.colorbar()
        plt.subplot(16, 4, 2*i+2)
        plt.imshow(numpy.nan_to_num(numpy.sqrt(image.get_synthetic())), **plot_kwargs)
        plt.colorbar()
        
showme(album)


    

    




/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/ipykernel/__main__.py:11: RuntimeWarning: invalid value encountered in sqrt






    

In [7]:

    

basevar = 0.1 * numpy.eye(3)
gal_model = astrohack_projections.galaxy_model_3d()
num_of_gaussians = 10

for i in xrange(num_of_gaussians - 1):
    mu = numpy.random.uniform(10, 50, size=3)
    v = numpy.random.uniform(-1, 1, size=3)
    fi = basevar + numpy.outer(v, v)
    gal_model.add_gaussian(1.0, mu, fi)
    
gal_model.add_gaussian(10.0, numpy.array((15, 15, 15)), 5*numpy.eye(3))

# album and PSF initialisation
album_new = astrohack_projections.album_and_model()
psf = astrohack_projections.mixture_of_gaussians(2)
psf.add_gaussian(1., numpy.array([0., 0.]), numpy.eye(2)*1.)

for i in xrange(32):
    image = album.get_all_images()[i]
    data = image.get_data()
    parameters = image.get_parameters()
    print parameters
    # image
    image = astrohack_projections.image_and_model()
    image.set_shape((60, 80))
    image.set_psf(psf)
    parameters['scale'] = 1
    image.set_parameters(**parameters)
    image.set_galaxy(gal_model)
    image.set_ivar(numpy.ones(image.get_shape()))
    image.set_data(data)
    # album
    album_new.add_image(image)
    
showme(album_new)
album_new.set_galaxy(gal_model)
plt.savefig("./fitting_pngs/illustris_242959_complex2/initialisation.pdf")


    

    




{'beta': 51.232167005586263, 'scale': 1, 'bg': 0.0, 'yshift': 40.66364170432902, 'xshift': 30.23967726027996, 'alpha': 33.039304262559206, 'intensity': 20, 'gamma': 332.08766647984862}
{'beta': 269.05760249898043, 'scale': 1, 'bg': 0.0, 'yshift': 40.46434716815094, 'xshift': 29.681506938355994, 'alpha': 359.42251541683532, 'intensity': 20, 'gamma': 100.77772523808864}
{'beta': 86.960304795069732, 'scale': 1, 'bg': 0.0, 'yshift': 39.99934302872261, 'xshift': 30.608077992663574, 'alpha': 204.72091887562951, 'intensity': 20, 'gamma': 87.083274111293775}
{'beta': 170.79102864186979, 'scale': 1, 'bg': 0.0, 'yshift': 39.686318841503606, 'xshift': 30.507207091277987, 'alpha': 350.4932301653065, 'intensity': 20, 'gamma': 279.06206536226483}
{'beta': 2.9942822562065174, 'scale': 1, 'bg': 0.0, 'yshift': 40.0900289145379, 'xshift': 30.49398327358088, 'alpha': 213.9066337655353, 'intensity': 20, 'gamma': 253.83891976087781}
{'beta': 136.82866879971652, 'scale': 1, 'bg': 0.0, 'yshift': 40.191561849572835, 'xshift': 30.965644389105538, 'alpha': 6.6268733660004031, 'intensity': 20, 'gamma': 145.94013953927058}
{'beta': 261.35203328508828, 'scale': 1, 'bg': 0.0, 'yshift': 39.78311896001456, 'xshift': 30.99758942598634, 'alpha': 54.723504150139263, 'intensity': 20, 'gamma': 56.944498973142196}
{'beta': 74.076660513090857, 'scale': 1, 'bg': 0.0, 'yshift': 40.073363510914405, 'xshift': 30.214083928612197, 'alpha': 70.970648653571246, 'intensity': 20, 'gamma': 224.4097678114673}
{'beta': 46.123968317018495, 'scale': 1, 'bg': 0.0, 'yshift': 40.096238103165696, 'xshift': 29.961446489933792, 'alpha': 273.40689774992848, 'intensity': 20, 'gamma': 186.81029668118532}
{'beta': 346.32577249491675, 'scale': 1, 'bg': 0.0, 'yshift': 39.87368081682815, 'xshift': 29.97823397609284, 'alpha': 334.25609178529322, 'intensity': 20, 'gamma': 5.4689058162132875}
{'beta': 325.10702949339117, 'scale': 1, 'bg': 0.0, 'yshift': 40.05347750480568, 'xshift': 29.75762126337672, 'alpha': 78.453564301519123, 'intensity': 20, 'gamma': 144.41261779584227}
{'beta': 246.56595278900832, 'scale': 1, 'bg': 0.0, 'yshift': 40.97509529646623, 'xshift': 30.016131502989715, 'alpha': 205.70266773579306, 'intensity': 20, 'gamma': 3.7134591387106353}
{'beta': 257.43072972102078, 'scale': 1, 'bg': 0.0, 'yshift': 40.94268477269879, 'xshift': 30.602962775115202, 'alpha': 132.32212602418926, 'intensity': 20, 'gamma': 68.10596021493825}
{'beta': 193.57885657531102, 'scale': 1, 'bg': 0.0, 'yshift': 40.604115309414375, 'xshift': 30.81488484871529, 'alpha': 295.70874002253436, 'intensity': 20, 'gamma': 14.4145415754884}
{'beta': 39.588636568444194, 'scale': 1, 'bg': 0.0, 'yshift': 39.98152231097814, 'xshift': 30.782932602040525, 'alpha': 30.654611275507673, 'intensity': 20, 'gamma': 180.78623829862542}
{'beta': 9.2792120702754985, 'scale': 1, 'bg': 0.0, 'yshift': 40.27347573205639, 'xshift': 29.93787012543212, 'alpha': 39.638912637494258, 'intensity': 20, 'gamma': 228.52319926808315}
{'beta': 123.43445818099934, 'scale': 1, 'bg': 0.0, 'yshift': 40.73412802455406, 'xshift': 29.640676690803325, 'alpha': 339.97969949642038, 'intensity': 20, 'gamma': 225.55944264316668}
{'beta': 213.87424586132343, 'scale': 1, 'bg': 0.0, 'yshift': 39.69246599673718, 'xshift': 30.167642645205163, 'alpha': 90.122185537731184, 'intensity': 20, 'gamma': 119.77508763742014}
{'beta': 233.42928266172686, 'scale': 1, 'bg': 0.0, 'yshift': 40.44014694533738, 'xshift': 29.688547637871856, 'alpha': 198.23777642500283, 'intensity': 20, 'gamma': 311.95908991678164}
{'beta': 1.7758822775682015, 'scale': 1, 'bg': 0.0, 'yshift': 40.97578532272115, 'xshift': 30.43284546675178, 'alpha': 0.74793267027954524, 'intensity': 20, 'gamma': 137.94767515161226}
{'beta': 114.62834162532555, 'scale': 1, 'bg': 0.0, 'yshift': 40.492852811108364, 'xshift': 30.44047893838428, 'alpha': 6.3849985358472638, 'intensity': 20, 'gamma': 84.207942630801313}
{'beta': 174.4875776073329, 'scale': 1, 'bg': 0.0, 'yshift': 40.77587592650575, 'xshift': 29.544918703091643, 'alpha': 265.15309980340697, 'intensity': 20, 'gamma': 3.939544220123512}
{'beta': 240.39540157449139, 'scale': 1, 'bg': 0.0, 'yshift': 40.01750141451756, 'xshift': 30.16419548910987, 'alpha': 17.339313922539926, 'intensity': 20, 'gamma': 311.99536386930964}
{'beta': 230.35770805714472, 'scale': 1, 'bg': 0.0, 'yshift': 39.90487479558989, 'xshift': 30.760980854413933, 'alpha': 177.14430568264586, 'intensity': 20, 'gamma': 181.83394986929261}
{'beta': 22.919860921699879, 'scale': 1, 'bg': 0.0, 'yshift': 40.01969159852675, 'xshift': 29.899379467725556, 'alpha': 211.24793343060691, 'intensity': 20, 'gamma': 333.4461333473489}
{'beta': 245.43396574679215, 'scale': 1, 'bg': 0.0, 'yshift': 40.351480204298625, 'xshift': 29.905510538370045, 'alpha': 341.40442036050678, 'intensity': 20, 'gamma': 324.00913882035621}
{'beta': 337.10042264423799, 'scale': 1, 'bg': 0.0, 'yshift': 40.612460161228775, 'xshift': 30.000722043555346, 'alpha': 95.370004554256582, 'intensity': 20, 'gamma': 62.722222335106402}
{'beta': 189.99582123551576, 'scale': 1, 'bg': 0.0, 'yshift': 40.00437326294882, 'xshift': 29.97120479902282, 'alpha': 250.54994979045756, 'intensity': 20, 'gamma': 123.98583712742128}
{'beta': 80.599029999258363, 'scale': 1, 'bg': 0.0, 'yshift': 40.01985300815489, 'xshift': 29.720412558451883, 'alpha': 11.683329338043794, 'intensity': 20, 'gamma': 284.38497915636589}
{'beta': 128.91117721200047, 'scale': 1, 'bg': 0.0, 'yshift': 40.81431461368351, 'xshift': 30.949626012916404, 'alpha': 336.20155589936678, 'intensity': 20, 'gamma': 180.99561612575928}
{'beta': 170.60050668438211, 'scale': 1, 'bg': 0.0, 'yshift': 40.92181513015649, 'xshift': 30.316452714060738, 'alpha': 100.66536633639227, 'intensity': 20, 'gamma': 10.709726870254679}
{'beta': 217.81363092933944, 'scale': 1, 'bg': 0.0, 'yshift': 40.01118034622436, 'xshift': 29.889627970092032, 'alpha': 278.41749902231152, 'intensity': 20, 'gamma': 229.21087650914046}






    




/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/ipykernel/__main__.py:11: RuntimeWarning: invalid value encountered in sqrt






    

In [8]:

    

# run the thing!
import scipy.optimize as op
num_runs = 20

for i in xrange(num_runs):
    # album optimisation
    galpar0 = album_new.galaxy.get_parameters_vector()
    print "album before", album_new(galpar0)
    result = op.minimize(album_new, galpar0, method="Powell")
    galpar = result['x']
    print "album after", album_new(galpar)
    
    showme(album_new)
    plt.savefig("./fitting_pngs/illustris_242959_complex2/run_%s_album.pdf" % str(2*i).zfill(2))
    plt.close()
    
    
    # image optimisation
    for image in album_new:
        imgpar0 = image.get_parameters_vector()
        print "image before", image(imgpar0)
        result = op.minimize(image, imgpar0)
        imgpar = result['x']
        print "image after", image(imgpar)

    showme(album_new)
    plt.savefig("./fitting_pngs/illustris_242959_complex2/run_%s_image.pdf" % str(2*i+1).zfill(2))
    plt.close()


    

    




album before 





    




/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.py:1778: RuntimeWarning: invalid value encountered in double_scalars
  tmp2 = (x - v) * (fx - fw)
/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.py:1779: RuntimeWarning: invalid value encountered in double_scalars
  p = (x - v) * tmp2 - (x - w) * tmp1
/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.py:1780: RuntimeWarning: invalid value encountered in double_scalars
  tmp2 = 2.0 * (tmp2 - tmp1)
/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.py:2108: RuntimeWarning: invalid value encountered in double_scalars
  w = xb - ((xb - xc) * tmp2 - (xb - xa) * tmp1) / denom






    




100411489.045
album after





    




/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/ipykernel/__main__.py:11: RuntimeWarning: invalid value encountered in sqrt
/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/ipykernel/__main__.py:14: RuntimeWarning: invalid value encountered in sqrt






    




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/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.py:891: RuntimeWarning: divide by zero encountered in double_scalars
  rhok = 1.0 / (numpy.dot(yk, sk))






    




---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-8-397f39c41bd6> in <module>()
      7     galpar0 = album_new.galaxy.get_parameters_vector()
      8     print "album before", album_new(galpar0)
----> 9     result = op.minimize(album_new, galpar0, method="Powell")
     10     galpar = result['x']
     11     print "album after", album_new(galpar)

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/_minimize.pyc in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
    432         return _minimize_neldermead(fun, x0, args, callback, **options)
    433     elif meth == 'powell':
--> 434         return _minimize_powell(fun, x0, args, callback, **options)
    435     elif meth == 'cg':
    436         return _minimize_cg(fun, x0, args, jac, callback, **options)

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in _minimize_powell(func, x0, args, callback, xtol, ftol, maxiter, maxfev, disp, direc, return_all, **unknown_options)
   2341             fx2 = fval
   2342             fval, x, direc1 = _linesearch_powell(func, x, direc1,
-> 2343                                                  tol=xtol * 100)
   2344             if (fx2 - fval) > delta:
   2345                 delta = fx2 - fval

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in _linesearch_powell(func, p, xi, tol)
   2163     def myfunc(alpha):
   2164         return func(p + alpha*xi)
-> 2165     alpha_min, fret, iter, num = brent(myfunc, full_output=1, tol=tol)
   2166     xi = alpha_min*xi
   2167     return squeeze(fret), p + xi, xi

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in brent(func, args, brack, tol, full_output, maxiter)
   1903     options = {'xtol': tol,
   1904                'maxiter': maxiter}
-> 1905     res = _minimize_scalar_brent(func, brack, args, **options)
   1906     if full_output:
   1907         return res['x'], res['fun'], res['nit'], res['nfev']

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in _minimize_scalar_brent(func, brack, args, xtol, maxiter, **unknown_options)
   1935                   full_output=True, maxiter=maxiter)
   1936     brent.set_bracket(brack)
-> 1937     brent.optimize()
   1938     x, fval, nit, nfev = brent.get_result(full_output=True)
   1939     return OptimizeResult(fun=fval, x=x, nit=nit, nfev=nfev)

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in optimize(self)
   1748         #################################
   1749         x = w = v = xb
-> 1750         fw = fv = fx = func(*((x,) + self.args))
   1751         if (xa < xc):
   1752             a = xa

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in myfunc(alpha)
   2162     """
   2163     def myfunc(alpha):
-> 2164         return func(p + alpha*xi)
   2165     alpha_min, fret, iter, num = brent(myfunc, full_output=1, tol=tol)
   2166     xi = alpha_min*xi

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in function_wrapper(*wrapper_args)
    283     def function_wrapper(*wrapper_args):
    284         ncalls[0] += 1
--> 285         return function(*(wrapper_args + args))
    286 
    287     return ncalls, function_wrapper

/Users/dalyabaron/Copy/Astrophysics/python/new_scripts/new_scripts/DeprojectAllGalaxies/astrohack_projections.pyc in __call__(self, galparvec)
    444                 galaxy.set_parameters_from_vector(galparvec)
    445                 self.set_galaxy(galaxy) # must use `set_galaxy()` to propagate to images
--> 446                 return -2. * self.get_ln_posterior()
    447 
    448 

/Users/dalyabaron/Copy/Astrophysics/python/new_scripts/new_scripts/DeprojectAllGalaxies/astrohack_projections.pyc in get_ln_posterior(self)
    434                 lnp = self.get_ln_prior()
    435                 if numpy.isfinite(lnp):
--> 436                         lnp += self.get_ln_likelihood()
    437                 return lnp
    438 

/Users/dalyabaron/Copy/Astrophysics/python/new_scripts/new_scripts/DeprojectAllGalaxies/astrohack_projections.pyc in get_ln_likelihood(self)
    422                 lnlike = 0.
    423                 for image in self.images:
--> 424                         lnlike += image.get_ln_likelihood()
    425                 return lnlike
    426 

/Users/dalyabaron/Copy/Astrophysics/python/new_scripts/new_scripts/DeprojectAllGalaxies/astrohack_projections.pyc in get_ln_likelihood(self)
    373 
    374         def get_ln_likelihood(self):
--> 375                 return -0.5 * self.get_chi_squared()
    376 
    377         def get_ln_prior(self):

/Users/dalyabaron/Copy/Astrophysics/python/new_scripts/new_scripts/DeprojectAllGalaxies/astrohack_projections.pyc in get_chi_squared(self)
    367 
    368         def get_chi_squared(self):
--> 369                 return numpy.sum(self.ivar * (self.data - self.get_synthetic()) ** 2)
    370 
    371         def get_chi_vector(self):

/Users/dalyabaron/Copy/Astrophysics/python/new_scripts/new_scripts/DeprojectAllGalaxies/astrohack_projections.pyc in get_synthetic(self)
    323                         if self.synthetic != 0.0:
    324                                 self.synthetic = 0
--> 325                         self.construct_synthetic()
    326                 return self.synthetic
    327 

/Users/dalyabaron/Copy/Astrophysics/python/new_scripts/new_scripts/DeprojectAllGalaxies/astrohack_projections.pyc in construct_synthetic(self, xi_hat, eta_hat)
    364 		self._add_to_synthetic(self.galaxy.render_2d_image(xi_hat, eta_hat, xs, ys,
    365                                                intensity=self.parameters['intensity'],
--> 366 				               psf=self.psf.rescale(self.parameters['scale'])))
    367 
    368         def get_chi_squared(self):

/Users/dalyabaron/Copy/Astrophysics/python/new_scripts/new_scripts/DeprojectAllGalaxies/astrohack_projections.pyc in render_2d_image(self, xi_hat, eta_hat, xs, ys, intensity, psf)
    185                 if psf is not None:
    186                         mixture_2d = mixture_2d.convolve(psf)
--> 187                 densities_flatten = mixture_2d.render(positions_flatten)
    188                 densities = numpy.reshape(densities_flatten, X.shape)
    189                 return densities

/Users/dalyabaron/Copy/Astrophysics/python/new_scripts/new_scripts/DeprojectAllGalaxies/astrohack_projections.pyc in render(self, positions)
    137                 densities= numpy.zeros(N)
    138                 for k in range(self.K):
--> 139                         gaus_k = multivariate_normal(mean=self.mus[k], cov=self.fis[k])
    140                         pdf_k = gaus_k.pdf(positions)
    141                         densities += self.alphas[k] * pdf_k

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/stats/_multivariate.pyc in __call__(self, mean, cov, allow_singular, seed)
    421         return multivariate_normal_frozen(mean, cov,
    422                                           allow_singular=allow_singular,
--> 423                                           seed=seed)
    424 
    425     def _logpdf(self, x, mean, prec_U, log_det_cov, rank):

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/stats/_multivariate.pyc in __init__(self, mean, cov, allow_singular, seed)
    592         self.dim, self.mean, self.cov = _process_parameters(None, mean, cov)
    593         self.cov_info = _PSD(self.cov, allow_singular=allow_singular)
--> 594         self._dist = multivariate_normal_gen(seed)
    595 
    596     def logpdf(self, x):

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/stats/_multivariate.pyc in __init__(self, seed)
    410     def __init__(self, seed=None):
    411         super(multivariate_normal_gen, self).__init__(seed)
--> 412         self.__doc__ = doccer.docformat(self.__doc__, docdict_params)
    413 
    414     def __call__(self, mean=None, cov=1, allow_singular=False, seed=None):

/Users/dalyabaron/.virtualenvs/astro/lib/python2.7/site-packages/scipy/misc/doccer.pyc in docformat(docstring, docdict)
     48     if not docdict:
     49         return docstring
---> 50     lines = docstring.expandtabs().splitlines()
     51     # Find the minimum indent of the main docstring, after first line
     52     if len(lines) < 2:

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