direct_smoothing_operator.py 6.53 KB
 Theo Steininger committed May 15, 2017 1 2 ``````# -*- coding: utf8 -*- `````` Martin Reinecke committed Jun 30, 2017 3 4 ``````from __future__ import division from builtins import range `````` Theo Steininger committed May 15, 2017 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ``````import numpy as np from .smoothing_operator import SmoothingOperator class DirectSmoothingOperator(SmoothingOperator): def __init__(self, domain, sigma, log_distances=False, default_spaces=None): super(DirectSmoothingOperator, self).__init__(domain, sigma, log_distances, default_spaces) self.effective_smoothing_width = 3.01 `````` Theo Steininger committed Aug 26, 2017 19 20 21 22 23 24 25 `````` def _add_attributes_to_copy(self, copy, **kwargs): copy.effective_smoothing_width = self.effective_smoothing_width copy = super(DirectSmoothingOperator, self)._add_attributes_to_copy( copy, **kwargs) return copy `````` Theo Steininger committed May 15, 2017 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 `````` def _precompute(self, x, sigma, dxmax=None): """ Does precomputations for Gaussian smoothing on a 1D irregular grid. Parameters ---------- x: 1D floating point array or list containing the individual grid positions. Points must be given in ascending order. sigma: The sigma of the Gaussian with which the function living on x should be smoothed, in the same units as x. dxmax: (optional) The maximum distance up to which smoothing is performed, in the same units as x. Default is 3.01*sigma. Returns ------- ibegin: integer array of the same size as x ibegin[i] is the minimum grid index to consider when computing the smoothed value at grid index i nval: integer array of the same size as x nval[i] is the number of indices to consider when computing the smoothed value at grid index i. wgt: list with the same number of entries as x wgt[i] is an array with nval[i] entries containing the normalized smoothing weights. """ if dxmax is None: dxmax = self.effective_smoothing_width*sigma x = np.asarray(x) ibegin = np.searchsorted(x, x-dxmax) nval = np.searchsorted(x, x+dxmax) - ibegin wgt = [] expfac = 1. / (2. * sigma*sigma) for i in range(x.size): `````` Theo Steininger committed Jun 23, 2017 63 `````` if nval[i] > 0: `````` Martin Reinecke committed May 29, 2017 64 65 66 67 68 69 `````` t = x[ibegin[i]:ibegin[i]+nval[i]]-x[i] t = np.exp(-t*t*expfac) t *= 1./np.sum(t) wgt.append(t) else: wgt.append(np.array([])) `````` Theo Steininger committed May 15, 2017 70 71 72 73 74 75 76 77 78 79 80 `````` return ibegin, nval, wgt def _apply_kernel_along_array(self, power, startindex, endindex, distances, smooth_length, smoothing_width, ibegin, nval, wgt): if smooth_length == 0.0: return power[startindex:endindex] p_smooth = np.zeros(endindex-startindex, dtype=power.dtype) `````` Martin Reinecke committed Jun 30, 2017 81 `````` for i in range(startindex, endindex): `````` Theo Steininger committed May 15, 2017 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 `````` imin = max(startindex, ibegin[i]) imax = min(endindex, ibegin[i]+nval[i]) p_smooth[imin:imax] += (power[i] * wgt[i][imin-ibegin[i]:imax-imin+ibegin[i]]) return p_smooth def _apply_along_axis(self, axis, arr, startindex, endindex, distances, smooth_length, smoothing_width): nd = arr.ndim if axis < 0: axis += nd if (axis >= nd): raise ValueError( "axis must be less than arr.ndim; axis=%d, rank=%d." % (axis, nd)) ibegin, nval, wgt = self._precompute( distances, smooth_length, smooth_length*smoothing_width) ind = np.zeros(nd-1, dtype=np.int) i = np.zeros(nd, dtype=object) shape = arr.shape `````` Martin Reinecke committed Jun 30, 2017 105 `````` indlist = np.asarray(list(range(nd))) `````` Theo Steininger committed May 15, 2017 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 `````` indlist = np.delete(indlist, axis) i[axis] = slice(None, None) outshape = np.asarray(shape).take(indlist) i.put(indlist, ind) Ntot = np.product(outshape) holdshape = outshape slicedArr = arr[tuple(i.tolist())] res = self._apply_kernel_along_array( slicedArr, startindex, endindex, distances, smooth_length, smoothing_width, ibegin, nval, wgt) outshape = np.asarray(arr.shape) outshape[axis] = endindex - startindex outarr = np.zeros(outshape, dtype=arr.dtype) outarr[tuple(i.tolist())] = res k = 1 while k < Ntot: # increment the index ind[nd-1] += 1 n = -1 while (ind[n] >= holdshape[n]) and (n > (1-nd)): ind[n-1] += 1 ind[n] = 0 n -= 1 i.put(indlist, ind) slicedArr = arr[tuple(i.tolist())] res = self._apply_kernel_along_array( slicedArr, startindex, endindex, distances, smooth_length, smoothing_width, ibegin, nval, wgt) outarr[tuple(i.tolist())] = res k += 1 return outarr def _smooth(self, x, spaces, inverse): # infer affected axes # we rely on the knowledge, that `spaces` is a tuple with length 1. affected_axes = x.domain_axes[spaces[0]] if len(affected_axes) > 1: raise ValueError("By this implementation only one-dimensional " "spaces can be smoothed directly.") affected_axis = affected_axes[0] `````` Martin Reinecke committed Aug 31, 2017 153 `````` distance_array = x.domain[spaces[0]].get_distance_array() `````` Theo Steininger committed May 15, 2017 154 `````` `````` Martin Reinecke committed May 21, 2017 155 `````` #MR FIXME: this causes calls of log(0.) which should probably be avoided `````` Theo Steininger committed May 15, 2017 156 `````` if self.log_distances: `````` Martin Reinecke committed May 29, 2017 157 `````` np.log(np.maximum(distance_array,1e-15), out=distance_array) `````` Theo Steininger committed May 15, 2017 158 `````` `````` Martin Reinecke committed Aug 31, 2017 159 160 161 162 `````` augmented_data = x.val augmented_distance_array = distance_array true_start = 0 true_end = x.shape[affected_axis] `````` Theo Steininger committed May 15, 2017 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 `````` # perform the convolution along the affected axes # currently only one axis is supported data_axis = affected_axes[0] if inverse: true_sigma = 1. / self.sigma else: true_sigma = self.sigma local_result = self._apply_along_axis( data_axis, augmented_data, startindex=true_start, endindex=true_end, distances=augmented_distance_array, smooth_length=true_sigma, smoothing_width=self.effective_smoothing_width) `````` Martin Reinecke committed Aug 31, 2017 182 `` return local_result``