annotate libinterp/corefcn/__lin_interpn__.cc @ 27919:1891570abac8

update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2020.
author John W. Eaton <jwe@octave.org>
date Mon, 06 Jan 2020 22:29:51 -0500
parents b442ec6dda5c
children bd51beb6205e
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1 /*
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2
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1891570abac8 update Octave Project Developers copyright for the new year
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3 Copyright (C) 2007-2020 The Octave Project Developers
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4
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5 See the file COPYRIGHT.md in the top-level directory of this distribution
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6 or <https://octave.org/COPYRIGHT.html/>.
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7
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8
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9 This file is part of Octave.
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10
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11 Octave is free software: you can redistribute it and/or modify it
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12 under the terms of the GNU General Public License as published by
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13 the Free Software Foundation, either version 3 of the License, or
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14 (at your option) any later version.
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15
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16 Octave is distributed in the hope that it will be useful, but
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17 WITHOUT ANY WARRANTY; without even the implied warranty of
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18 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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19 GNU General Public License for more details.
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20
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21 You should have received a copy of the GNU General Public License
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22 along with Octave; see the file COPYING. If not, see
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23 <https://www.gnu.org/licenses/>.
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24
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25 */
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26
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27 #if defined (HAVE_CONFIG_H)
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28 # include "config.h"
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29 #endif
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30
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31 #include "lo-ieee.h"
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32 #include "dNDArray.h"
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33 #include "oct-locbuf.h"
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34
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35 #include "defun.h"
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36 #include "error.h"
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37 #include "ovl.h"
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38
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39 // equivalent to isvector.m
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40
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41 template <typename T>
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42 bool
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43 isvector (const T& array)
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44 {
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45 const dim_vector dv = array.dims ();
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46 return dv.ndims () == 2 && (dv(0) == 1 || dv(1) == 1);
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47 }
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48
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49 // lookup a value in a sorted table (lookup.m)
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50 template <typename T>
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51 octave_idx_type
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52 lookup (const T *x, octave_idx_type n, T y)
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53 {
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54 octave_idx_type j;
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55
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56 if (x[0] < x[n-1])
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57 {
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58 // increasing x
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59
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60 if (y > x[n-1] || y < x[0])
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61 return -1;
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62
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63 #if defined (EXHAUSTIF)
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64 for (j = 0; j < n - 1; j++)
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65 {
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66 if (x[j] <= y && y <= x[j+1])
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67 return j;
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68 }
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69 #else
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70 octave_idx_type j0 = 0;
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71 octave_idx_type j1 = n - 1;
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72
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73 while (true)
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74 {
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75 j = (j0+j1)/2;
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76
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77 if (y <= x[j+1])
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78 {
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79 if (x[j] <= y)
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80 return j;
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81
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82 j1 = j;
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83 }
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84
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85 if (x[j] <= y)
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86 j0 = j;
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87 }
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88 #endif
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89 }
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90 else
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91 {
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92 // decreasing x
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93 // previous code with x -> -x and y -> -y
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94
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95 if (y > x[0] || y < x[n-1])
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96 return -1;
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97
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98 #if defined (EXHAUSTIF)
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99 for (j = 0; j < n - 1; j++)
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100 {
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101 if (x[j+1] <= y && y <= x[j])
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102 return j;
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103 }
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104 #else
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105 octave_idx_type j0 = 0;
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106 octave_idx_type j1 = n - 1;
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107
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108 while (true)
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109 {
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110 j = (j0+j1)/2;
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111
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112 if (y >= x[j+1])
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113 {
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114 if (x[j] >= y)
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115 return j;
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116
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117 j1 = j;
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118 }
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119
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120 if (x[j] >= y)
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121 j0 = j;
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122 }
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123 #endif
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124 }
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125 }
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126
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127 // n-dimensional linear interpolation
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128
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129 template <typename T>
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130 void
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131 lin_interpn (int n, const octave_idx_type *size, const octave_idx_type *scale,
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132 octave_idx_type Ni, T extrapval, const T **x,
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133 const T *v, const T **y, T *vi)
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134 {
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135 bool out = false;
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136 int bit;
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137
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138 OCTAVE_LOCAL_BUFFER (T, coef, 2*n);
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139 OCTAVE_LOCAL_BUFFER (octave_idx_type, index, n);
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140
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141 // loop over all points
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142 for (octave_idx_type m = 0; m < Ni; m++)
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143 {
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144 // loop over all dimensions
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145 for (int i = 0; i < n; i++)
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146 {
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147 index[i] = lookup (x[i], size[i], y[i][m]);
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148 out = index[i] == -1;
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149
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150 if (out)
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151 break;
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152 else
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153 {
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154 octave_idx_type j = index[i];
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155 coef[2*i+1] = (y[i][m] - x[i][j])/(x[i][j+1] - x[i][j]);
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156 coef[2*i] = 1 - coef[2*i+1];
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157 }
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158 }
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159
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160 if (out)
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161 vi[m] = extrapval;
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162 else
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163 {
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164 vi[m] = 0;
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165
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166 // loop over all corners of hypercube (1<<n = 2^n)
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167 for (int i = 0; i < (1 << n); i++)
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168 {
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169 T c = 1;
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170 octave_idx_type l = 0;
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171
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172 // loop over all dimensions
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173 for (int j = 0; j < n; j++)
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174 {
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175 // test if the jth bit in i is set
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176 bit = i >> j & 1;
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177 l += scale[j] * (index[j] + bit);
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178 c *= coef[2*j+bit];
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179 }
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180
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181 vi[m] += c * v[l];
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182 }
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183 }
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184 }
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185 }
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186
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187 template <typename T, typename M>
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188 octave_value
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189 lin_interpn (int n, M *X, const M V, M *Y)
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190 {
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191 octave_value retval;
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192
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193 M Vi = M (Y[0].dims ());
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194
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195 OCTAVE_LOCAL_BUFFER (const T *, y, n);
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196 OCTAVE_LOCAL_BUFFER (octave_idx_type, size, n);
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197
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198 for (int i = 0; i < n; i++)
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199 {
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200 y[i] = Y[i].data ();
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201 size[i] = V.dims ()(i);
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202 }
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203
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204 OCTAVE_LOCAL_BUFFER (const T *, x, n);
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205 OCTAVE_LOCAL_BUFFER (octave_idx_type, scale, n);
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206
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207 const T *v = V.data ();
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208 T *vi = Vi.fortran_vec ();
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209 octave_idx_type Ni = Vi.numel ();
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210
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211 T extrapval = octave_NA;
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212
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213 // offset in memory of each dimension
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214
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215 scale[0] = 1;
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216
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217 for (int i = 1; i < n; i++)
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218 scale[i] = scale[i-1] * size[i-1];
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219
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220 // tests if X[0] is a vector, if yes, assume that all elements of X are
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221 // in the ndgrid format.
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222
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223 if (! isvector (X[0]))
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224 {
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225 for (int i = 0; i < n; i++)
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226 {
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227 if (X[i].dims () != V.dims ())
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228 error ("interpn: incompatible size of argument number %d", i+1);
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229
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230 M tmp = M (dim_vector (size[i], 1));
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231
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232 for (octave_idx_type j = 0; j < size[i]; j++)
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233 tmp(j) = X[i](scale[i]*j);
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234
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235 X[i] = tmp;
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236 }
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237 }
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238
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239 for (int i = 0; i < n; i++)
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240 {
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241 if (! isvector (X[i]) && X[i].numel () != size[i])
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242 error ("interpn: incompatible size of argument number %d", i+1);
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243
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244 x[i] = X[i].data ();
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245 }
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246
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247 lin_interpn (n, size, scale, Ni, extrapval, x, v, y, vi);
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248
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249 retval = Vi;
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250
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251 return retval;
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252 }
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253
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254 // Perform @var{n}-dimensional interpolation. Each element of then
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255 // @var{n}-dimensional array @var{v} represents a value at a location
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256 // given by the parameters @var{x1}, @var{x2},...,@var{xn}. The parameters
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257 // @var{x1}, @var{x2}, @dots{}, @var{xn} are either @var{n}-dimensional
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258 // arrays of the same size as the array @var{v} in the "ndgrid" format
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259 // or vectors. The parameters @var{y1}, @var{y2}, @dots{}, @var{yn} are
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260 // all @var{n}-dimensional arrays of the same size and represent the
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261 // points at which the array @var{vi} is interpolated.
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262 //
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263 //This function only performs linear interpolation.
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264
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265 DEFUN (__lin_interpn__, args, ,
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266 doc: /* -*- texinfo -*-
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diff changeset
267 @deftypefn {} {@var{vi} =} __lin_interpn__ (@var{x1}, @var{x2}, @dots{}, @var{xn}, @var{v}, @var{y1}, @var{y2}, @dots{}, @var{yn})
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diff changeset
268 Undocumented internal function.
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269 @end deftypefn */)
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270 {
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271 int nargin = args.length ();
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272
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273 if (nargin < 2 || nargin % 2 == 0)
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274 print_usage ();
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275
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276 octave_value retval;
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277
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278 // dimension of the problem
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279 int n = (nargin-1)/2;
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280
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281 if (args(n).is_single_type ())
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282 {
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283 OCTAVE_LOCAL_BUFFER (FloatNDArray, X, n);
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284 OCTAVE_LOCAL_BUFFER (FloatNDArray, Y, n);
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285
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286 const FloatNDArray V = args(n).float_array_value ();
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287
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288 for (int i = 0; i < n; i++)
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289 {
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290 X[i] = args(i).float_array_value ();
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291 Y[i] = args(n+i+1).float_array_value ();
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292
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293 if (Y[0].dims () != Y[i].dims ())
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294 error ("interpn: incompatible size of argument number %d", n+i+2);
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295 }
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296
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297 retval = lin_interpn<float, FloatNDArray> (n, X, V, Y);
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298 }
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299 else
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300 {
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301 OCTAVE_LOCAL_BUFFER (NDArray, X, n);
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302 OCTAVE_LOCAL_BUFFER (NDArray, Y, n);
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303
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304 const NDArray V = args(n).array_value ();
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305
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306 for (int i = 0; i < n; i++)
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307 {
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308 X[i] = args(i).array_value ();
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309 Y[i] = args(n+i+1).array_value ();
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310
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311 if (Y[0].dims () != Y[i].dims ())
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312 error ("interpn: incompatible size of argument number %d", n+i+2);
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313 }
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314
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315 retval = lin_interpn<double, NDArray> (n, X, V, Y);
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316 }
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317
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318 return retval;
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319 }
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320
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321 /*
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322 ## No test needed for internal helper function.
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323 %!assert (1)
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324 */