Source code for diffpy.utils.parsers.resample

#!/usr/bin/env python
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#
# diffpy.utils      by DANSE Diffraction group
#                   Simon J. L. Billinge
#                   (c) 2010 The Trustees of Columbia University
#                   in the City of New York.  All rights reserved.
#
# File coded by:    Chris Farrow
#
# See AUTHORS.txt for a list of people who contributed.
# See LICENSE_DANSE.txt for license information.
#
##############################################################################

"""Various utilities related to data parsing and manipulation."""

import numpy


# NOTE - this should be faster than resample below and conforms more closely to
# numpy.interp. I'm keeping resample for legacy reasons.
[docs] def wsinterp(x, xp, fp, left=None, right=None): """One-dimensional Whittaker-Shannon interpolation. This uses the Whittaker-Shannon interpolation formula to interpolate the value of fp (array), which is defined over xp (array), at x (array or float). Parameters ---------- x: ndarray Desired range for interpolation. xp: ndarray Defined range for fp. fp: ndarray Function to be interpolated. left: float If given, set fp for x < xp[0] to left. Otherwise, if left is None (default) or not given, set fp for x < xp[0] to fp evaluated at xp[-1]. right: float If given, set fp for x > xp[-1] to right. Otherwise, if right is None (default) or not given, set fp for x > xp[-1] to fp evaluated at xp[-1]. Returns ------- float: If input x is a scalar (not an array), return the interpolated value at x. ndarray: If input x is an array, return the interpolated array with dimensions of x. """ scalar = numpy.isscalar(x) if scalar: x = numpy.array(x) x.resize(1) # shape = (nxp, nx), nxp copies of x data span axis 1 u = numpy.resize(x, (len(xp), len(x))) # Must take transpose of u for proper broadcasting with xp. # shape = (nx, nxp), v(xp) data spans axis 1 v = (xp - u.T) / (xp[1] - xp[0]) # shape = (nx, nxp), m(v) data spans axis 1 m = fp * numpy.sinc(v) # Sum over m(v) (axis 1) fp_at_x = numpy.sum(m, axis=1) # Enforce left and right if left is None: left = fp[0] fp_at_x[x < xp[0]] = left if right is None: right = fp[-1] fp_at_x[x > xp[-1]] = right # Return a float if we got a float if scalar: return float(fp_at_x[0]) return fp_at_x
[docs] def resample(r, s, dr): """Resample a PDF on a new grid. This uses the Whittaker-Shannon interpolation formula to put s1 on a new grid if dr is less than the sampling interval of r1, or linear interpolation if dr is greater than the sampling interval of r1. Parameters ---------- r The r-grid used for s1. s The signal to be resampled. dr The new sampling interval. Returns ------- Returns resampled (r, s). """ dr0 = r[1] - r[0] # Constant timestep if dr0 < dr: rnew = numpy.arange(r[0], r[-1]+0.5*dr, dr) snew = numpy.interp(rnew, r, s) return rnew, snew elif dr0 > dr: # Tried to pad the end of s to dampen, but nothing works. #m = (s[-1] - s[-2]) / dr0 #b = (s[-2] * r[-1] - s[-1] * r[-2]) / dr0 #rpad = r[-1] + numpy.arange(1, len(s))*dr0 #spad = rpad * m + b #spad = numpy.concatenate([s,spad]) #rnew = numpy.arange(0, rpad[-1], dr) #snew = numpy.zeros_like(rnew) ## Accomodate for the fact that r[0] might not be 0 #u = (rnew-r[0]) / dr0 #for n in range(len(spad)): # snew += spad[n] * numpy.sinc(u - n) #sel = numpy.logical_and(rnew >= r[0], rnew <= r[-1]) rnew = numpy.arange(0, r[-1], dr) snew = numpy.zeros_like(rnew) u = (rnew-r[0]) / dr0 for n in range(len(s)): snew += s[n] * numpy.sinc(u - n) sel = numpy.logical_and(rnew >= r[0], rnew <= r[-1]) return rnew[sel], snew[sel] # If we got here, then no resampling is required return r.copy(), s.copy()
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