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from __future__ import division # confidence high
import math
import numpy
MAX_REJECT = 0.5
MIN_NPIXELS = 5
GOOD_PIXEL = 0
BAD_PIXEL = 1
KREJ = 2.5
MAX_ITERATIONS = 5
def zscale (image, nsamples=1000, contrast=0.25, bpmask=None, zmask=None):
"""Implement IRAF zscale algorithm
Parameters
----------
image : arr
2-d numpy array
nsamples : int (Default: 1000)
Number of points in array to sample for determining scaling factors
contrast : float (Default: 0.25)
Scaling factor for determining min and max. Larger values increase the
difference between min and max values used for display.
bpmask : None
Not used at this time
zmask : None
Not used at this time
Returns
-------
(z1, z2)
"""
# Sample the image
samples = zsc_sample (image, nsamples, bpmask, zmask)
npix = len(samples)
samples.sort()
zmin = samples[0]
zmax = samples[-1]
# For a zero-indexed array
center_pixel = (npix - 1) // 2
if npix%2 == 1:
median = samples[center_pixel]
else:
median = 0.5 * (samples[center_pixel] + samples[center_pixel + 1])
#
# Fit a line to the sorted array of samples
minpix = max(MIN_NPIXELS, int(npix * MAX_REJECT))
ngrow = max (1, int (npix * 0.01))
ngoodpix, zstart, zslope = zsc_fit_line (samples, npix, KREJ, ngrow,
MAX_ITERATIONS)
if ngoodpix < minpix:
z1 = zmin
z2 = zmax
else:
if contrast > 0: zslope = zslope / contrast
z1 = max (zmin, median - (center_pixel - 1) * zslope)
z2 = min (zmax, median + (npix - center_pixel) * zslope)
return z1, z2
def zsc_sample (image, maxpix, bpmask=None, zmask=None):
# Figure out which pixels to use for the zscale algorithm
# Returns the 1-d array samples
# Don't worry about the bad pixel mask or zmask for the moment
# Sample in a square grid, and return the first maxpix in the sample
nc = image.shape[0]
nl = image.shape[1]
stride = max (1.0, math.sqrt((nc - 1) * (nl - 1) / float(maxpix)))
stride = int (stride)
samples = image[::stride,::stride].flatten()
return samples[:maxpix]
def zsc_fit_line (samples, npix, krej, ngrow, maxiter):
#
# First re-map indices from -1.0 to 1.0
xscale = 2.0 / (npix - 1)
xnorm = numpy.arange(npix)
xnorm = xnorm * xscale - 1.0
ngoodpix = npix
minpix = max (MIN_NPIXELS, int (npix*MAX_REJECT))
last_ngoodpix = npix + 1
# This is the mask used in k-sigma clipping. 0 is good, 1 is bad
badpix = numpy.zeros(npix, dtype="int32")
#
# Iterate
for niter in range(maxiter):
if (ngoodpix >= last_ngoodpix) or (ngoodpix < minpix):
break
# Accumulate sums to calculate straight line fit
goodpixels = numpy.where(badpix == GOOD_PIXEL)
sumx = xnorm[goodpixels].sum()
sumxx = (xnorm[goodpixels]*xnorm[goodpixels]).sum()
sumxy = (xnorm[goodpixels]*samples[goodpixels]).sum()
sumy = samples[goodpixels].sum()
sum = len(goodpixels[0])
delta = sum * sumxx - sumx * sumx
# Slope and intercept
intercept = (sumxx * sumy - sumx * sumxy) / delta
slope = (sum * sumxy - sumx * sumy) / delta
# Subtract fitted line from the data array
fitted = xnorm*slope + intercept
flat = samples - fitted
# Compute the k-sigma rejection threshold
ngoodpix, mean, sigma = zsc_compute_sigma (flat, badpix, npix)
threshold = sigma * krej
# Detect and reject pixels further than k*sigma from the fitted line
lcut = -threshold
hcut = threshold
below = numpy.where(flat < lcut)
above = numpy.where(flat > hcut)
badpix[below] = BAD_PIXEL
badpix[above] = BAD_PIXEL
# Convolve with a kernel of length ngrow
kernel = numpy.ones(ngrow,dtype="int32")
badpix = numpy.convolve(badpix, kernel, mode='same')
ngoodpix = len(numpy.where(badpix == GOOD_PIXEL)[0])
niter += 1
# Transform the line coefficients back to the X range [0:npix-1]
zstart = intercept - slope
zslope = slope * xscale
return ngoodpix, zstart, zslope
def zsc_compute_sigma (flat, badpix, npix):
# Compute the rms deviation from the mean of a flattened array.
# Ignore rejected pixels
# Accumulate sum and sum of squares
goodpixels = numpy.where(badpix == GOOD_PIXEL)
sumz = flat[goodpixels].sum()
sumsq = (flat[goodpixels]*flat[goodpixels]).sum()
ngoodpix = len(goodpixels[0])
if ngoodpix == 0:
mean = None
sigma = None
elif ngoodpix == 1:
mean = sumz
sigma = None
else:
mean = sumz / ngoodpix
temp = sumsq / (ngoodpix - 1) - sumz*sumz / (ngoodpix * (ngoodpix - 1))
if temp < 0:
sigma = 0.0
else:
sigma = math.sqrt (temp)
return ngoodpix, mean, sigma
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