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annotate scripts/deprecated/bicubic.m @ 20815:a260a6acb70f

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fix test failures introduced by a22d8a2eb0e5 * scripts/ode/private/integrate_adaptive.m: fix stepping backwards, fix invocation of OutputFcn, fix text of some error messages * scripts/ode/private/integrate_const.m: remove use of option OutputSave * scripts/ode/private/integrate_n_steps.m: remove use of option OutputSave
author Carlo de Falco <carlo.defalco@polimi.it>
date Sun, 11 Oct 2015 23:09:01 +0200
parents 4197fc428c7d
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
19898
4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 2005-2015 Hoxide Ma
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{zi} =} bicubic (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{extrapval})
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21 ##
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22 ## @code{bicubic} is deprecated and will be removed in Octave version 4.4.
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23 ## Use @code{interp2 (@dots{}, "spline")} for the equivalent functionality.
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24 ##
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25 ## Return a matrix @var{zi} corresponding to the bicubic
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26 ## interpolations at @var{xi} and @var{yi} of the data supplied
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27 ## as @var{x}, @var{y} and @var{z}. Points outside the grid are set
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28 ## to @var{extrapval}.
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29 ##
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30 ## See @url{http://wiki.woodpecker.org.cn/moin/Octave/Bicubic}
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31 ## for further information.
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32 ## @seealso{interp2}
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33 ## @end deftypefn
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34
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35 ## Bicubic interpolation method.
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36 ## Author: Hoxide Ma <hoxide_dirac@yahoo.com.cn>
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37
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38 ## Deprecated in version 4.0
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39
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40 function zi = bicubic (x, y, z, xi, yi, extrapval, spline_alpha)
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41
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42 persistent warned = false;
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43 if (! warned)
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44 warned = true;
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45 warning ("Octave:deprecated-function",
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46 "bicubic is obsolete and will be removed from a future version of Octave, please use interp2 instead");
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47 endif
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48
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49 if (nargin < 1 || nargin > 7)
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50 print_usage ();
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51 endif
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52
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53 if (nargin == 7 && isscalar (spline_alpha))
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54 a = spline_alpha;
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55 else
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56 a = 0.5;
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57 endif
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58
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59 if (nargin < 6)
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60 extrapval = NaN;
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61 endif
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62
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63 if (isa (x, "single") || isa (y, "single") || isa (z, "single")
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64 || isa (xi, "single") || isa (yi, "single"))
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65 myeps = eps ("single");
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66 else
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67 myeps = eps ();
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68 endif
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69
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70 if (nargin <= 2)
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71 ## bicubic (z) or bicubic (z, 2)
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72 if (nargin == 1)
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73 n = 1;
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74 else
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75 n = y;
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76 endif
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77 z = x;
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78 x = [];
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79 [rz, cz] = size (z);
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80 s = linspace (1, cz, (cz-1) * pow2 (n) + 1);
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81 t = linspace (1, rz, (rz-1) * pow2 (n) + 1);
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82 elseif (nargin == 3)
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83 if (! isvector (x) || ! isvector (y))
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84 error ("bicubic: XI and YI must be vector");
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85 endif
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86 s = y;
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87 t = z;
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88 z = x;
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89 [rz, cz] = size (z);
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90 elseif (nargin == 5 || nargin == 6)
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91 [rz, cz] = size (z) ;
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92 if (isvector (x) && isvector (y))
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93 if (rz != length (y) || cz != length (x))
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94 error ("bicubic: length of X and Y must match the size of Z");
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95 endif
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96 elseif (size_equal (x, y) && size_equal (x, z))
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97 x = x(1,:);
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98 y = y(:,1);
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99 else
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100 error ("bicubic: X, Y and Z must be equal size matrices of same size");
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101 endif
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102
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103 if (all (diff (x) < 0))
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104 flipx = true;
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105 x = fliplr (x);
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106 elseif (all (diff (x) > 0))
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107 flipx = false;
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108 else
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109 error ("bicubic:nonmonotonic", "bicubic: X values must be monotonic");
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110 endif
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111 if (all (diff (y) < 0))
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112 flipy = true;
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113 y = flipud (y);
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114 elseif (all (diff (y) > 0))
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115 flipy = false;
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116 else
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117 error ("bicubic:nonmonotonic", "bicubic: Y values must be monotonic");
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118 endif
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119
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120 ## Mark values outside the lookup table.
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121 xfirst_ind = find (xi < x(1));
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122 xlast_ind = find (xi > x(cz));
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123 yfirst_ind = find (yi < y(1));
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124 ylast_ind = find (yi > y(rz));
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125 ## Set value outside the table preliminary to min max index.
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126 xi(xfirst_ind) = x(1);
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127 xi(xlast_ind) = x(cz);
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128 yi(yfirst_ind) = y(1);
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129 yi(ylast_ind) = y(rz);
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130
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131 x = reshape (x, 1, cz);
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132 x(cz) *= 1 + sign (x(cz)) * myeps;
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133 if (x(cz) == 0)
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134 x(cz) = myeps;
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135 endif;
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136 xi = reshape (xi, 1, length (xi));
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137 [m, i] = sort ([x, xi]);
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138 o = cumsum (i <= cz);
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139 xidx = o(find (i > cz));
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140
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141 y = reshape (y, rz, 1);
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142 y(rz) *= 1 + sign (y(rz)) * myeps;
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143 if (y(rz) == 0)
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144 y(rz) = myeps;
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145 endif;
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146 yi = reshape (yi, length (yi), 1);
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147 [m, i] = sort ([y; yi]);
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148 o = cumsum (i <= rz);
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149 yidx = o([find(i > rz)]);
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150
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151 ## Set s and t used follow codes.
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152 s = xidx + ((xi .- x(xidx)) ./ (x(xidx+1) .- x(xidx)));
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153 t = yidx + ((yi - y(yidx)) ./ (y(yidx+1) - y(yidx)));
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154
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155 if (flipx)
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156 s = fliplr (s);
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157 endif
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158 if (flipy)
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159 t = flipud (t);
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160 endif
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161 else
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162 print_usage ();
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163 endif
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164
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165 if (rz < 3 || cz < 3)
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166 error ("bicubic: Z at least a 3 by 3 matrices");
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167 endif
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168
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169 inds = floor (s);
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170 d = find (s == cz);
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171 s = s - floor (s);
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172 inds(d) = cz-1;
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173 s(d) = 1.0;
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174
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175 d = [];
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176 indt = floor (t);
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177 d = find (t == rz);
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178 t = t - floor (t);
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179 indt(d) = rz-1;
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180 t(d) = 1.0;
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181 d = [];
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182
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183 p = zeros (size (z) + 2);
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184 p(2:rz+1,2:cz+1) = z;
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185 p(1,:) = (6*(1-a))*p(2,:) - 3*p(3,:) + (6*a-2)*p(4,:);
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186 p(rz+2,:) = (6*(1-a))*p(rz+1,:) - 3*p(rz,:) + (6*a-2)*p(rz-1,:);
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187 p(:,1) = (6*(1-a))*p(:,2) - 3*p(:,3) + (6*a-2)*p(:,4);
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188 p(:,cz+2) = (6*(1-a))*p(:,cz+1) - 3*p(:,cz) + (6*a-2)*p(:,cz-1);
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189
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190 ## Calculte the C1(t) C2(t) C3(t) C4(t) and C1(s) C2(s) C3(s) C4(s).
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191 t2 = t.*t;
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192 t3 = t2.*t;
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193
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194 ct0 = -a .* t3 + (2 * a) .* t2 - a .* t ; # -a G0
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195 ct1 = (2-a) .* t3 + (-3+a) .* t2 + 1 ; # F0 - a G1
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196 ct2 = (a-2) .* t3 + (-2 *a + 3) .* t2 + a .* t ; # F1 + a G0
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197 ct3 = a .* t3 - a .* t2; # a G1
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198 t = []; t2 = []; t3 = [];
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199
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200 s2 = s.*s;
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201 s3 = s2.*s;
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202
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203 cs0 = -a .* s3 + (2 * a) .* s2 - a .*s ; # -a G0
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204 cs1 = (2-a) .* s3 + (-3 + a) .* s2 + 1 ; # F0 - a G1
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205 cs2 = (a-2) .* s3 + (-2 *a + 3) .* s2 + a .*s ; # F1 + a G0
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206 cs3 = a .* s3 - a .* s2; # a G1
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207 s = []; s2 = []; s3 = [];
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208
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209 cs0 = cs0([1,1,1,1],:);
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210 cs1 = cs1([1,1,1,1],:);
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211 cs2 = cs2([1,1,1,1],:);
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212 cs3 = cs3([1,1,1,1],:);
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diff changeset
213
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diff changeset
214 lent = length (ct0);
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diff changeset
215 lens = columns (cs0);
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diff changeset
216 zi = zeros (lent, lens);
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diff changeset
217
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diff changeset
218 for i = 1:lent
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diff changeset
219 it = indt(i);
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diff changeset
220 int = [it, it+1, it+2, it+3];
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diff changeset
221 zi(i,:) = ([ct0(i),ct1(i),ct2(i),ct3(i)]
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diff changeset
222 * (p(int,inds) .* cs0 + p(int,inds+1) .* cs1
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diff changeset
223 + p(int,inds+2) .* cs2 + p(int,inds+3) .* cs3));
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224 endfor
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225
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226 ## Set points outside the table to extrapval.
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227 if (! (isempty (xfirst_ind) && isempty (xlast_ind)))
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228 zi(:, [xfirst_ind, xlast_ind]) = extrapval;
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diff changeset
229 endif
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230 if (! (isempty (yfirst_ind) && isempty (ylast_ind)))
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diff changeset
231 zi([yfirst_ind; ylast_ind], :) = extrapval;
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232 endif
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233
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe]
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diff changeset
234 endfunction
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diff changeset
235
17338
1c89599167a6 maint: End m-files with 1 blank line.
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diff changeset
236
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diff changeset
237 %!demo
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diff changeset
238 %! clf;
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239 %! colormap ("default");
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240 %! A = [13,-1,12;5,4,3;1,6,2];
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241 %! x = [0,1,4]+10;
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diff changeset
242 %! y = [-10,-9,-8];
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243 %! xi = linspace (min (x), max (x), 17);
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244 %! yi = linspace (min (y), max (y), 26)';
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245 %! mesh (xi, yi, bicubic (x,y,A,xi,yi));
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246 %! [x,y] = meshgrid (x,y);
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247 %! hold on; plot3 (x(:),y(:),A(:),"b*"); hold off;
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248
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249 %!test
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diff changeset
250 %! x = linspace (1, -1, 10);
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diff changeset
251 %! [xx, yy] = meshgrid (x);
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diff changeset
252 %! z = cos (6 * xx) + sin (6 * yy);
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253 %! x = linspace (1, -1, 30);
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diff changeset
254 %! [xx2, yy2] = meshgrid (x);
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diff changeset
255 %! z1 = interp2 (xx, yy, z, xx2, yy2, "spline");
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diff changeset
256 %! z2 = interp2 (fliplr (xx), flipud (yy), fliplr (flipud(z)),
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257 %! fliplr (xx2), flipud (yy2), "spline");
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258 %! z2 = fliplr (flipud (z2));
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diff changeset
259 %! assert (z1, z2, 100 * eps ())
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diff changeset
260