annotate src/DLD-FUNCTIONS/__lin_interpn__.cc @ 8377:25bc2d31e1bf

improve OCTAVE_LOCAL_BUFFER
author Jaroslav Hajek <highegg@gmail.com>
date Wed, 29 Oct 2008 16:52:10 +0100
parents 82be108cc558
children eb63fbe60fab
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1 /*
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2
b2391d403ed2 [project @ 2007-06-12 21:39:26 by dbateman]
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3 Copyright (C) 2007 Alexander Barth
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 #ifdef HAVE_CONFIG_H
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24 #include <config.h>
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25 #endif
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26
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27 #include "dNDArray.h"
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28 #include "oct-locbuf.h"
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29
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30 #include "defun-dld.h"
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31 #include "error.h"
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32 #include "oct-obj.h"
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33
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34 // equivalent to isvector.m
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35
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36 template <class T>
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37 bool
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38 isvector (const T& array)
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39 {
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40 const dim_vector dv = array.dims ();
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41 return dv.length () == 2 && (dv(0) == 1 || dv(1) == 1);
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42 }
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43
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44 // lookup a value in a sorted table (lookup.m)
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45 template <class T>
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46 octave_idx_type
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47 lookup (const T *x, octave_idx_type n, T y)
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48 {
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49 octave_idx_type j;
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50
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51 if (x[0] < x[n-1])
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52 {
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53 // increasing x
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54
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55 if (y > x[n-1] || y < x[0])
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56 return -1;
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57
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58 #ifdef EXHAUSTIF
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59 for (j = 0; j < n - 1; j++)
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60 {
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61 if (x[j] <= y && y <= x[j+1])
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62 return j;
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63 }
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64 #else
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65 octave_idx_type j0 = 0;
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66 octave_idx_type j1 = n - 1;
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67
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68 while (true)
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69 {
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70 j = (j0+j1)/2;
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71
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72 if (y <= x[j+1])
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73 {
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74 if (x[j] <= y)
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75 return j;
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76
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77 j1 = j;
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78 }
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79
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80 if (x[j] <= y)
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81 j0 = j;
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82 }
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83 #endif
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84 }
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85 else
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86 {
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87 // decreasing x
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88 // previous code with x -> -x and y -> -y
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89
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90 if (y > x[0] || y < x[n-1])
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91 return -1;
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92
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93 #ifdef EXHAUSTIF
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94 for (j = 0; j < n - 1; j++)
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95 {
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96 if (x[j+1] <= y && y <= x[j])
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97 return j;
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98 }
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99 #else
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100 octave_idx_type j0 = 0;
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101 octave_idx_type j1 = n - 1;
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102
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103 while (true)
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104 {
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105 j = (j0+j1)/2;
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106
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107 if (y >= x[j+1])
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108 {
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109 if (x[j] >= y)
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110 return j;
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111
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112 j1 = j;
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113 }
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114
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115 if (x[j] >= y)
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116 j0 = j;
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117 }
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118 #endif
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119 }
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120 }
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121
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122 // n-dimensional linear interpolation
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123
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124 template <class T>
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125 void
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126 lin_interpn (int n, const octave_idx_type *size, const octave_idx_type *scale,
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127 octave_idx_type Ni, T extrapval, const T **x,
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128 const T *v, const T **y, T *vi)
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129 {
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130 bool out = false;
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131 int bit;
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132
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133 OCTAVE_LOCAL_BUFFER (T, coef, 2*n);
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134 OCTAVE_LOCAL_BUFFER (octave_idx_type, index, n);
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135
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136 // loop over all points
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137 for (octave_idx_type m = 0; m < Ni; m++)
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138 {
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139 // loop over all dimensions
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140 for (int i = 0; i < n; i++)
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141 {
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142 index[i] = lookup (x[i], size[i], y[i][m]);
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143 out = index[i] == -1;
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144
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145 if (out)
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146 break;
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147 else
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148 {
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149 octave_idx_type j = index[i];
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150 coef[2*i+1] = (y[i][m] - x[i][j])/(x[i][j+1] - x[i][j]);
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151 coef[2*i] = 1 - coef[2*i+1];
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152 }
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153 }
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154
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155
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156 if (out)
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157 vi[m] = extrapval;
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158 else
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159 {
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160 vi[m] = 0;
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161
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162 // loop over all corners of hypercube (1<<n = 2^n)
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163 for (int i = 0; i < (1 << n); i++)
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164 {
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165 T c = 1;
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166 octave_idx_type l = 0;
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167
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168 // loop over all dimensions
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169 for (int j = 0; j < n; j++)
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170 {
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171 // test if the jth bit in i is set
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172 bit = i >> j & 1;
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173 l += scale[j] * (index[j] + bit);
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174 c *= coef[2*j+bit];
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175 }
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176
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177 vi[m] += c * v[l];
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178 }
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179 }
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180 }
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181 }
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182
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183 template <class T, class M>
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184 octave_value
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185 lin_interpn (int n, M *X, const M V, M *Y)
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186 {
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187 octave_value retval;
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188
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189 M Vi = M (Y[0].dims ());
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190
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191 OCTAVE_LOCAL_BUFFER (const T *, y, n);
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192 OCTAVE_LOCAL_BUFFER (octave_idx_type, size, n);
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193
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194 for (int i = 0; i < n; i++)
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195 {
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196 y[i] = Y[i].data ();
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197 size[i] = V.dims()(i);
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198 }
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199
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200 OCTAVE_LOCAL_BUFFER (const T *, x, n);
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201 OCTAVE_LOCAL_BUFFER (octave_idx_type, scale, n);
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202
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203 const T *v = V.data ();
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204 T *vi = Vi.fortran_vec ();
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205 octave_idx_type Ni = Vi.numel ();
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206
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207 T extrapval = octave_NA;
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208
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209 // offset in memory of each dimension
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210
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211 scale[0] = 1;
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212
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213 for (int i = 1; i < n; i++)
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214 scale[i] = scale[i-1] * size[i-1];
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215
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216 // tests if X[0] is a vector, if yes, assume that all elements of X are
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217 // in the ndgrid format.
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218
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219 if (! isvector (X[0]))
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220 {
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221 for (int i = 0; i < n; i++)
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222 {
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223 if (X[i].dims () != V.dims ())
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224 {
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225 error ("interpn: incompatible size of argument number %d", i+1);
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226 return retval;
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227 }
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228 else
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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
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240 for (int i = 0; i < n; i++)
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241 {
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242 if (! isvector (X[i]) && X[i].numel () != size[i])
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243 {
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244 error ("interpn: incompatible size of argument number %d", i+1);
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245 return retval;
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246 }
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247 else
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248 x[i] = X[i].data ();
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249 }
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250
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251 lin_interpn (n, size, scale, Ni, extrapval, x, v, y, vi);
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252
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253 retval = Vi;
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254
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255 return retval;
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256 }
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257
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258 // Perform @var{n}-dimensional interpolation. Each element of then
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259 // @var{n}-dimensional array @var{v} represents a value at a location
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260 // given by the parameters @var{x1}, @var{x2},...,@var{xn}. The parameters
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261 // @var{x1}, @var{x2}, @dots{}, @var{xn} are either @var{n}-dimensional
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262 // arrays of the same size as the array @var{v} in the \"ndgrid\" format
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263 // or vectors. The parameters @var{y1}, @var{y2}, @dots{}, @var{yn} are
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264 // all @var{n}-dimensional arrays of the same size and represent the
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265 // points at which the array @var{vi} is interpolated.
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266 //
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267 //This function only performs linear interpolation.
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268
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269 DEFUN_DLD (__lin_interpn__, args, ,
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270 "-*- texinfo -*-\n\
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271 @deftypefn {Loadable Function} {@var{vi} =} __lin_interpn__ (@var{x1}, @var{x2}, @dots{}, @var{xn}, @var{v}, @var{y1}, @var{y2}, @dots{}, @var{yn})\n\
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272 Undocumented internal function.\n\
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273 @end deftypefn")
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274 {
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275 octave_value retval;
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276
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277 int nargin = args.length ();
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278
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279 if (nargin < 2 || nargin % 2 == 0)
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280 {
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281 print_usage ();
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282 return retval;
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283 }
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284
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285 // dimension of the problem
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286 int n = (nargin-1)/2;
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287
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288 if (args(n).is_single_type())
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289 {
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290 OCTAVE_LOCAL_BUFFER (FloatNDArray, X, n);
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291 OCTAVE_LOCAL_BUFFER (FloatNDArray, Y, n);
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292
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293 const FloatNDArray V = args(n).float_array_value ();
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294
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295 if (error_state)
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296 {
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297 print_usage ();
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298 return retval;
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299 }
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300
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301 for (int i = 0; i < n; i++)
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302 {
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303 X[i] = args(i).float_array_value ();
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304 Y[i] = args(n+i+1).float_array_value ();
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305
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306 if (error_state)
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307 {
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308 print_usage ();
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309 return retval;
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310 }
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311
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312 if (Y[0].dims () != Y[i].dims ())
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313 {
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314 error ("interpn: incompatible size of argument number %d", n+i+2);
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315 return retval;
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316 }
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317 }
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318
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319 retval = lin_interpn<float, FloatNDArray> (n, X, V, Y);
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320 }
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321 else
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322 {
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323 OCTAVE_LOCAL_BUFFER (NDArray, X, n);
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324 OCTAVE_LOCAL_BUFFER (NDArray, Y, n);
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325
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326 const NDArray V = args(n).array_value ();
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327
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328 if (error_state)
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329 {
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330 print_usage ();
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331 return retval;
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332 }
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333
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334 for (int i = 0; i < n; i++)
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335 {
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336 X[i] = args(i).array_value ();
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337 Y[i] = args(n+i+1).array_value ();
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338
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339 if (error_state)
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340 {
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341 print_usage ();
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342 return retval;
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343 }
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344
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345 if (Y[0].dims () != Y[i].dims ())
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346 {
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347 error ("interpn: incompatible size of argument number %d", n+i+2);
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348 return retval;
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349 }
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350 }
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351
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352 retval = lin_interpn<double, NDArray> (n, X, V, Y);
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353 }
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354
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355 return retval;
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356 }