Find modal sky on an array.

msky.py

import numpy, pylab, scipy
from scipy import optimize

# Uses MEANCLIP from above
from meanclip import meanclip

def msky(inarray, do_plot=0, verbose=0, ptitle='', func=0):
   """
   Find modal sky on an array.

   First step is determination of median value and sigma.
   Histogram of the data and fit parabola to the
   logaritmic histogram. The coefficient of the parabola
   are used to get mode and sigma of the sky on the
   assumption that it is well fitted by a gaussian or
   2nd-degree polynomial.

   .. note:: MYSKY5 routine from ACS library.

   :History:
       * 11/25/2009 Created by PLL based on IDL routine by MS.
       * 01/29/2010 PLL fixed broken where statement for histogram.

   Parameters
   ----------
   inarray: array_like
       Input data.

   do_plot: {0, 1}
       Do plot?

   verbose: {0, 1}
       Print info to screen?

   ptitle: string
       Title of plot. Only used if `do_plot`=1.

   func: {0, 1}
       Function for fitting:
           * 0: 2nd degree polynomial
           * 1: Gaussian

   Returns
   -------
   mmean: float
       Mode of fitted function.

   sigma: float
       Sigma of fitted function.

   """
   # Constants
   func_name = 'MSKY'
   nsig = 8.0
   c1 = 2.5 # 2.8
   c2 = 0.8 # 1.3

   # Min/max of input array
   arr_min = numpy.min(inarray)
   arr_max = numpy.max(inarray)

   # Get sigma
   mmean, sigma = meanclip(inarray, clipsig=5.0, maxiter=10, verbose=verbose)
   if sigma <= 0:
       print ' '
       print '%s: Weird distribution' % func_name
       print '%-6s: %.6f' % ('MEAN', mmean)
       print '%-6s: %.6f' % ('STDDEV', sigma)
       print '%-6s: %.6f' % ('MIN', arr_min)
       print '%-6s: %.6f' % ('MAX', arr_max)
       return mmean, sigma

   # Print info
   if verbose:
       print ' '
       print '%s input array info' % func_name
       print '%-6s: %.6f' % ('MIN', arr_min)
       print '%-6s: %.6f' % ('MAX', arr_max)

   # Flatten input array
   arr_1d = inarray.reshape( inarray.size, )

   # Define min and max for the histogram
   x = nsig * sigma
   mmean = numpy.median(arr_1d)
   minhist = mmean - x
   maxhist = mmean + x
   ufi = inarray[ numpy.where((inarray > minhist) & (inarray < maxhist)) ]

   # Calculate 25% and 75% percentile to get the interquartile range
   # IRQ = pc75-pc25
   # zenman, A. J. 1991.
   sixd = numpy.argsort( ufi )
   ndata = ufi.size
   pc25 = ufi[ sixd[0.25*ndata] ]
   pc75 = ufi[ sixd[0.75*ndata] ]
   irq = pc75 - pc25
   step = 2.0 * irq * ndata**(-1.0/3.0)

   # Calculate number of bins to use
   nbin = round(2*x / step - 1)

   # Histogram
   # http://www.scipy.org/Tentative_NumPy_Tutorial
   yhist, hbin = numpy.histogram(arr_1d, range=(minhist,maxhist),bins=nbin)
   xhist = 0.5 * ( hbin[1:] + hbin[:-1] )

   # Define xmin and xmax for the 2-0rder fit
   x1 = mmean - c1*sigma
   x2 = mmean + c2*sigma

   # Select the points beween x1 and x2 for the fit
   w = numpy.where((xhist > x1) & (xhist < x2) & (yhist > 0))
   count = len(w[0])
   xwg  = xhist[w]
   nywg = yhist[w]
   if count < 2:
       print ' '
       print '%s: Singular matrix' % func_name
       print '%-6s: %.6f' % ('X[W]', xwg)
       print '%-6s: %.6f' % ('NY[W]', nywg)
       print '%-6s: %.6f' % ('MEDIAN', mmean)
       return mmean, sigma

   # Change to log scale
   yhist = numpy.log10(yhist)
   iyh   = numpy.where( ~numpy.isinf(yhist) )
   xhist = xhist[iyh]
   yhist = yhist[iyh]
   nywg  = numpy.log10(nywg)

   # Calculate the fit coefficients
   ymax = nywg.max()

   # Gaussian
   # http://www.scipy.org/Cookbook/FittingData
   if func == 1:
       if verbose: print '%s: Fitting gaussian' % func_name

       # Initial guess
       ysum = numpy.sum(nywg)
       mmean = numpy.sum(xwg * nywg) / ysum
       sigma = numpy.sqrt(numpy.abs(numpy.sum((xwg-mmean)**2*nywg)/ysum))
       params = (ymax, mmean, sigma)

       # Error function to minimize
       errorfunction = lambda p: scipy.ravel(gaussian(*p)(xhist) - yhist)

       # Linear least square fitting
       a_opt, a_success = optimize.leastsq(errorfunction, params)
       ymax  = a_opt[0]
       mmean = a_opt[1]
       sigma = a_opt[2]

       # Fit to entire range
       yall = ymax * numpy.exp(-(xhist-mmean)**2/(2.0*sigma**2))

   # 2nd degree polynomial
   else:
       if verbose: print '%s: Fitting 2nd deg polynomial' % func_name

       # Polynomial
       a_opt = numpy.polyfit(xwg, nywg, 2)
       mmean = -0.5*a_opt[1]/a_opt[0]
       sigma = numpy.sqrt(-0.5 / ( a_opt[0]*numpy.log(10) ) )

       # Fit to entire range
       yall = a_opt[0]*xhist**2 + a_opt[1]*xhist + a_opt[2]

   # Print results
   if verbose:
       print ' '
       print '%s: Results' % func_name
       print '%-6s: %.6f' % ('MODE', mmean)
       print '%-6s: %.6f' % ('SIGMA', sigma)
       print ' '

   plot_y1 = 0
   plot_y2 = ymax + 0.1

   # Plot results
   if do_plot:
       pylab.clf()
       # Data points
       pylab.plot(xhist, yhist, 'ko')
       # Mark fitted region
       pylab.plot(xwg, nywg, 'bo', hold=1)
       # Draw fitted function
       pylab.plot(xhist, yall, 'r--', hold=1)
       pylab.axvline(x=mmean, color='r')
       # Plot xmin xmax for the fit
       pylab.axvline(x=x1, ymin=0, ymax=0.1, color='b')
       pylab.axvline(x=x2, ymin=0, ymax=0.1, color='b')
       # Axis limits and labels
       pylab.axis([minhist, maxhist, plot_y1, plot_y2])
       pylab.xlabel('Pix value')
       pylab.ylabel('Log num of pix')
       pylab.title(ptitle)
       #pylab.show()

       # Pause for visual examination of plot
       x_user = raw_input('ENTER ANY CHAR TO CONTINUE: ')

   return mmean, sigma

def gaussian(height, center_x, width_x):
   """
   Returns a gaussian function with the given parameters.
   This is used for least square fitting optimization.

   .. note:: This is used by `msky`.

   Parameters
   ----------
   height: float
       Peak amplitude.

   center_x: float
       Peak location.

   width_x: float
       Sigma of gaussian curve.

   Returns
   -------
   x: lambda function
       Function used for optimization.

   """
   return lambda x: height * numpy.exp(-(center_x-x)**2/(2.0*width_x**2))