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annotate src/DLD-FUNCTIONS/__lin_interpn__.cc @ 7561:a938cd7869b2

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__lin_interpn__.cc: handle decreasing coordinate values
author Alexander Barth
date Thu, 06 Mar 2008 01:56:55 -0500
parents 93c65f2a5668
children 82be108cc558 72830070a17b
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /*
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2
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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
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29 #include "defun-dld.h"
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30 #include "error.h"
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31 #include "oct-obj.h"
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32
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33 // equivalent to isvector.m
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34
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35 bool
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36 isvector (const NDArray& array)
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37 {
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38 const dim_vector dv = array.dims ();
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39 return dv.length () == 2 && (dv(0) == 1 || dv(1) == 1);
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40 }
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41
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42 // lookup a value in a sorted table (lookup.m)
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43 octave_idx_type
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44 lookup (const double *x, octave_idx_type n, double y)
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45 {
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46 octave_idx_type j;
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47
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48 if (x[0] < x[n-1])
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49 {
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50 // increasing x
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51
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52 if (y > x[n-1] || y < x[0])
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53 return -1;
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54
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55 #ifdef EXHAUSTIF
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56 for (j = 0; j < n - 1; j++)
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57 {
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58 if (x[j] <= y && y <= x[j+1])
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59 return j;
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60 }
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61 #else
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62 octave_idx_type j0 = 0;
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63 octave_idx_type j1 = n - 1;
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64
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65 while (true)
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66 {
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67 j = (j0+j1)/2;
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68
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69 if (y <= x[j+1])
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70 {
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71 if (x[j] <= y)
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72 return j;
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73
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74 j1 = j;
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75 }
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76
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77 if (x[j] <= y)
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78 j0 = j;
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79 }
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80 #endif
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81 }
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82 else
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83 {
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84 // decreasing x
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85 // previous code with x -> -x and y -> -y
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86
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87 if (y > x[0] || y < x[n-1])
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88 return -1;
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89
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90 #ifdef EXHAUSTIF
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91 for (j = 0; j < n - 1; j++)
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92 {
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93 if (x[j+1] <= y && y <= x[j])
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94 return j;
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95 }
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96 #else
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97 octave_idx_type j0 = 0;
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98 octave_idx_type j1 = n - 1;
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99
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100 while (true)
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101 {
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102 j = (j0+j1)/2;
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103
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104 if (y >= x[j+1])
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105 {
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106 if (x[j] >= y)
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107 return j;
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108
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109 j1 = j;
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110 }
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111
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112 if (x[j] >= y)
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113 j0 = j;
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114 }
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115 #endif
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116 }
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117 }
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118
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119 // n-dimensional linear interpolation
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120
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121 void
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122 lin_interpn (int n, const octave_idx_type *size, const octave_idx_type *scale,
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123 octave_idx_type Ni, double extrapval, const double **x,
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124 const double *v, const double **y, double *vi)
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125 {
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126 bool out = false;
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127 int bit;
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128
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129 OCTAVE_LOCAL_BUFFER (double, coef, 2*n);
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130 OCTAVE_LOCAL_BUFFER (octave_idx_type, index, n);
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131
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132 // loop over all points
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133 for (octave_idx_type m = 0; m < Ni; m++)
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134 {
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135 // loop over all dimensions
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136 for (int i = 0; i < n; i++)
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137 {
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138 index[i] = lookup (x[i], size[i], y[i][m]);
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139 out = index[i] == -1;
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140
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141 if (out)
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142 break;
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143 else
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144 {
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145 octave_idx_type j = index[i];
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146 coef[2*i+1] = (y[i][m] - x[i][j])/(x[i][j+1] - x[i][j]);
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147 coef[2*i] = 1 - coef[2*i+1];
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148 }
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149 }
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150
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151
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152 if (out)
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153 vi[m] = extrapval;
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154 else
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155 {
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156 vi[m] = 0;
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157
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158 // loop over all corners of hypercube (1<<n = 2^n)
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159 for (int i = 0; i < (1 << n); i++)
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160 {
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161 double c = 1;
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162 octave_idx_type l = 0;
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163
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164 // loop over all dimensions
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165 for (int j = 0; j < n; j++)
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166 {
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167 // test if the jth bit in i is set
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168 bit = i >> j & 1;
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169 l += scale[j] * (index[j] + bit);
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170 c *= coef[2*j+bit];
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171 }
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172
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173 vi[m] += c * v[l];
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174 }
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175 }
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176 }
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177 }
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178
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179 // Perform @var{n}-dimensional interpolation. Each element of then
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180 // @var{n}-dimensional array @var{v} represents a value at a location
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181 // given by the parameters @var{x1}, @var{x2},...,@var{xn}. The parameters
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182 // @var{x1}, @var{x2}, @dots{}, @var{xn} are either @var{n}-dimensional
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183 // arrays of the same size as the array @var{v} in the \"ndgrid\" format
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184 // or vectors. The parameters @var{y1}, @var{y2}, @dots{}, @var{yn} are
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185 // all @var{n}-dimensional arrays of the same size and represent the
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186 // points at which the array @var{vi} is interpolated.
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187 //
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188 //This function only performs linear interpolation.
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189
6702
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190 DEFUN_DLD (__lin_interpn__, args, ,
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191 "-*- texinfo -*-\n\
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192 @deftypefn {Loadable Function} {@var{vi} =} __lin_interpn__ (@var{x1}, @var{x2}, @dots{}, @var{xn}, @var{v}, @var{y1}, @var{y2}, @dots{}, @var{yn})\n\
6945
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193 Undocumented internal function.\n\
6702
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194 @end deftypefn")
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195 {
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196 octave_value retval;
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197
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198 int nargin = args.length ();
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199
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200 if (nargin < 2 || nargin % 2 == 0)
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201 {
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202 print_usage ();
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203 return retval;
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204 }
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205
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206 // dimension of the problem
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207 int n = (nargin-1)/2;
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208
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209 OCTAVE_LOCAL_BUFFER (NDArray, X, n);
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210 OCTAVE_LOCAL_BUFFER (NDArray, Y, n);
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211
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212 OCTAVE_LOCAL_BUFFER (const double *, x, n);
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213 OCTAVE_LOCAL_BUFFER (const double *, y, n);
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214 OCTAVE_LOCAL_BUFFER (octave_idx_type, scale, n);
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215 OCTAVE_LOCAL_BUFFER (octave_idx_type, size, n);
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216
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217 const NDArray V = args(n).array_value ();
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218 NDArray Vi = NDArray (args(n+1).dims ());
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219
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220 if (error_state)
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221 {
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222 print_usage ();
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223 return retval;
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224 }
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225
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226 const double *v = V.data ();
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227 double *vi = Vi.fortran_vec ();
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228 octave_idx_type Ni = Vi.numel ();
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229
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230 double extrapval = octave_NA;
6702
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231
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232 for (int i = 0; i < n; i++)
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233 {
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234 X[i] = args(i).array_value ();
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235 Y[i] = args(n+i+1).array_value ();
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236
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237 if (error_state)
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238 {
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239 print_usage ();
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240 return retval;
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241 }
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242
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243 y[i] = Y[i].data ();
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244 size[i] = V.dims()(i);
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245
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246 if (Y[0].dims () != Y[i].dims ())
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247 {
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248 error ("interpn: incompatible size of argument number %d", n+i+2);
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249 return retval;
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250 }
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251 }
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252
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253 // offset in memory of each dimension
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254
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255 scale[0] = 1;
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256
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257 for (int i = 1; i < n; i++)
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258 scale[i] = scale[i-1] * size[i-1];
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259
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260 // tests if X[0] is a vector, if yes, assume that all elements of X are
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261 // in the ndgrid format.
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262
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dbateman
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263 if (! isvector (X[0]))
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dbateman
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diff changeset
264 {
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265 for (int i = 0; i < n; i++)
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parents:
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266 {
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dbateman
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267 if (X[i].dims () != V.dims ())
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268 {
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269 error ("interpn: incompatible size of argument number %d", i+1);
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270 return retval;
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271 }
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272 else
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273 {
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274 NDArray tmp = NDArray (dim_vector (size[i], 1));
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275
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276 for (octave_idx_type j = 0; j < size[i]; j++)
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277 tmp(j) = X[i](scale[i]*j);
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278
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279 X[i] = tmp;
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280 }
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281 }
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282 }
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283
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dbateman
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284 for (int i = 0; i < n; i++)
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285 {
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286 if (! isvector (X[i]) && X[i].numel () != size[i])
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287 {
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288 error ("interpn: incompatible size of argument number %d", i+1);
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289 return retval;
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290 }
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dbateman
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291 else
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292 x[i] = X[i].data ();
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293 }
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294
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295 lin_interpn (n, size, scale, Ni, extrapval, x, v, y, vi);
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296
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297 retval = Vi;
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298
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299 return retval;
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300 }