annotate src/DLD-FUNCTIONS/__lin_interpn__.cc @ 7789:82be108cc558

First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
parents a938cd7869b2
children 25bc2d31e1bf
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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 template <class T>
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36 bool
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37 isvector (const T& array)
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38 {
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39 const dim_vector dv = array.dims ();
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40 return dv.length () == 2 && (dv(0) == 1 || dv(1) == 1);
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41 }
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42
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43 // lookup a value in a sorted table (lookup.m)
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44 template <class T>
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45 octave_idx_type
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46 lookup (const T *x, octave_idx_type n, T y)
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47 {
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48 octave_idx_type j;
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49
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50 if (x[0] < x[n-1])
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51 {
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52 // increasing x
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53
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54 if (y > x[n-1] || y < x[0])
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55 return -1;
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56
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57 #ifdef EXHAUSTIF
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58 for (j = 0; j < n - 1; j++)
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59 {
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60 if (x[j] <= y && y <= x[j+1])
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61 return j;
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62 }
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63 #else
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64 octave_idx_type j0 = 0;
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65 octave_idx_type j1 = n - 1;
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66
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67 while (true)
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68 {
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69 j = (j0+j1)/2;
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70
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71 if (y <= x[j+1])
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72 {
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73 if (x[j] <= y)
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74 return j;
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75
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76 j1 = j;
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77 }
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78
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79 if (x[j] <= y)
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80 j0 = j;
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81 }
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82 #endif
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83 }
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84 else
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85 {
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86 // decreasing x
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87 // previous code with x -> -x and y -> -y
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88
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89 if (y > x[0] || y < x[n-1])
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90 return -1;
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91
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92 #ifdef EXHAUSTIF
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93 for (j = 0; j < n - 1; j++)
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94 {
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95 if (x[j+1] <= y && y <= x[j])
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96 return j;
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97 }
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98 #else
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99 octave_idx_type j0 = 0;
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100 octave_idx_type j1 = n - 1;
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101
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102 while (true)
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103 {
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104 j = (j0+j1)/2;
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105
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106 if (y >= x[j+1])
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107 {
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108 if (x[j] >= y)
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109 return j;
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110
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111 j1 = j;
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112 }
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113
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114 if (x[j] >= y)
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115 j0 = j;
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116 }
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117 #endif
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118 }
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119 }
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120
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121 // n-dimensional linear interpolation
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122
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123 template <class T>
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124 void
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125 lin_interpn (int n, const octave_idx_type *size, const octave_idx_type *scale,
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126 octave_idx_type Ni, T extrapval, const T **x,
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127 const T *v, const T **y, T *vi)
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128 {
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129 bool out = false;
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130 int bit;
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131
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132 OCTAVE_LOCAL_BUFFER (T, coef, 2*n);
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133 OCTAVE_LOCAL_BUFFER (octave_idx_type, index, n);
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134
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135 // loop over all points
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136 for (octave_idx_type m = 0; m < Ni; m++)
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137 {
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138 // loop over all dimensions
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139 for (int i = 0; i < n; i++)
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140 {
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141 index[i] = lookup (x[i], size[i], y[i][m]);
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142 out = index[i] == -1;
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143
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144 if (out)
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145 break;
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146 else
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147 {
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148 octave_idx_type j = index[i];
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149 coef[2*i+1] = (y[i][m] - x[i][j])/(x[i][j+1] - x[i][j]);
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150 coef[2*i] = 1 - coef[2*i+1];
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151 }
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152 }
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153
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154
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155 if (out)
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156 vi[m] = extrapval;
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157 else
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158 {
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159 vi[m] = 0;
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160
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161 // loop over all corners of hypercube (1<<n = 2^n)
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162 for (int i = 0; i < (1 << n); i++)
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163 {
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164 T c = 1;
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165 octave_idx_type l = 0;
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166
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167 // loop over all dimensions
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168 for (int j = 0; j < n; j++)
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169 {
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170 // test if the jth bit in i is set
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171 bit = i >> j & 1;
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172 l += scale[j] * (index[j] + bit);
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173 c *= coef[2*j+bit];
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174 }
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175
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176 vi[m] += c * v[l];
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177 }
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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 template <class T, class M>
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183 octave_value
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184 lin_interpn (int n, M *X, const M V, M *Y)
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185 {
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186 octave_value retval;
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187
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188 M Vi = M (Y[0].dims ());
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189
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190 OCTAVE_LOCAL_BUFFER (const T *, y, n);
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191 OCTAVE_LOCAL_BUFFER (octave_idx_type, size, n);
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192
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193 for (int i = 0; i < n; i++)
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194 {
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195 y[i] = Y[i].data ();
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196 size[i] = V.dims()(i);
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197 }
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198
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199 OCTAVE_LOCAL_BUFFER (const T *, x, n);
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200 OCTAVE_LOCAL_BUFFER (octave_idx_type, scale, n);
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201
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202 const T *v = V.data ();
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203 T *vi = Vi.fortran_vec ();
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204 octave_idx_type Ni = Vi.numel ();
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205
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206 T extrapval = octave_NA;
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207
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208 // offset in memory of each dimension
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209
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210 scale[0] = 1;
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211
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212 for (int i = 1; i < n; i++)
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213 scale[i] = scale[i-1] * size[i-1];
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214
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215 // tests if X[0] is a vector, if yes, assume that all elements of X are
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216 // in the ndgrid format.
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217
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218 if (! isvector (X[0]))
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219 {
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220 for (int i = 0; i < n; i++)
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221 {
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222 if (X[i].dims () != V.dims ())
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223 {
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224 error ("interpn: incompatible size of argument number %d", i+1);
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225 return retval;
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226 }
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227 else
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228 {
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229 M tmp = M (dim_vector (size[i], 1));
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230
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231 for (octave_idx_type j = 0; j < size[i]; j++)
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232 tmp(j) = X[i](scale[i]*j);
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233
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234 X[i] = tmp;
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235 }
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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 {
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243 error ("interpn: incompatible size of argument number %d", i+1);
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244 return retval;
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245 }
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246 else
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247 x[i] = X[i].data ();
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248 }
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249
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250 lin_interpn (n, size, scale, Ni, extrapval, x, v, y, vi);
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251
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252 retval = Vi;
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253
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254 return retval;
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255 }
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256
6945
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257 // Perform @var{n}-dimensional interpolation. Each element of then
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258 // @var{n}-dimensional array @var{v} represents a value at a location
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259 // given by the parameters @var{x1}, @var{x2},...,@var{xn}. The parameters
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260 // @var{x1}, @var{x2}, @dots{}, @var{xn} are either @var{n}-dimensional
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261 // arrays of the same size as the array @var{v} in the \"ndgrid\" format
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262 // or vectors. The parameters @var{y1}, @var{y2}, @dots{}, @var{yn} are
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263 // all @var{n}-dimensional arrays of the same size and represent the
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264 // points at which the array @var{vi} is interpolated.
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265 //
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266 //This function only performs linear interpolation.
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267
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268 DEFUN_DLD (__lin_interpn__, args, ,
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269 "-*- texinfo -*-\n\
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270 @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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271 Undocumented internal function.\n\
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272 @end deftypefn")
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273 {
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274 octave_value retval;
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275
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276 int nargin = args.length ();
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277
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278 if (nargin < 2 || nargin % 2 == 0)
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279 {
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280 print_usage ();
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281 return retval;
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282 }
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283
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284 // dimension of the problem
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285 int n = (nargin-1)/2;
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286
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287 if (args(n).is_single_type())
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288 {
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289 OCTAVE_LOCAL_BUFFER (FloatNDArray, X, n);
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290 OCTAVE_LOCAL_BUFFER (FloatNDArray, Y, n);
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291
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292 const FloatNDArray V = args(n).float_array_value ();
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293
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294 if (error_state)
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295 {
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296 print_usage ();
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297 return retval;
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298 }
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299
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300 for (int i = 0; i < n; i++)
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301 {
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302 X[i] = args(i).float_array_value ();
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303 Y[i] = args(n+i+1).float_array_value ();
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304
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305 if (error_state)
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306 {
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307 print_usage ();
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308 return retval;
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309 }
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310
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311 if (Y[0].dims () != Y[i].dims ())
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312 {
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313 error ("interpn: incompatible size of argument number %d", n+i+2);
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314 return retval;
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315 }
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316 }
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317
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318 retval = lin_interpn<float, FloatNDArray> (n, X, V, Y);
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319 }
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320 else
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321 {
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322 OCTAVE_LOCAL_BUFFER (NDArray, X, n);
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323 OCTAVE_LOCAL_BUFFER (NDArray, Y, n);
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324
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325 const NDArray V = args(n).array_value ();
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326
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327 if (error_state)
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328 {
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329 print_usage ();
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330 return retval;
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331 }
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332
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333 for (int i = 0; i < n; i++)
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334 {
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335 X[i] = args(i).array_value ();
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336 Y[i] = args(n+i+1).array_value ();
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337
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338 if (error_state)
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339 {
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340 print_usage ();
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341 return retval;
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342 }
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343
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344 if (Y[0].dims () != Y[i].dims ())
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345 {
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346 error ("interpn: incompatible size of argument number %d", n+i+2);
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347 return retval;
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348 }
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349 }
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350
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351 retval = lin_interpn<double, NDArray> (n, X, V, Y);
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352 }
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353
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354 return retval;
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355 }