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1 ## Copyright (C) 2006, 2007 David Bateman |
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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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6126
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19 function sparseimages (nm, typ) |
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20 if (strcmp (typ, "png")) |
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21 set (0, "defaulttextfontname", "*"); |
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22 endif |
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23 if (! isempty (findstr (octave_config_info ("DEFS"), "HAVE_COLAMD")) |
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24 && ! isempty (findstr (octave_config_info ("DEFS"), "HAVE_CHOLMOD")) |
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25 && ! isempty (findstr (octave_config_info ("DEFS"), "HAVE_UMFPACK"))) |
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6126
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26 if (strcmp(typ,"txt")) |
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27 txtimages (nm, 15, typ); |
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28 else |
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29 if (strcmp (nm, "gplot")) |
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30 gplotimages ("gplot", typ); |
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31 elseif (strcmp (nm, "grid")) |
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32 femimages ("grid", typ); |
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33 else |
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34 otherimages (nm, 200, typ); |
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35 endif |
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36 endif |
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37 else ## There is no sparse matrix implementation available because |
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38 ## of missing libraries, plot sombreros instead |
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39 sombreroimage (nm, typ); |
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40 endif |
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41 endfunction |
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42 |
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43 function bury_output () |
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44 f = figure (1); |
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45 set (f, "visible", "off"); |
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46 endfunction |
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47 |
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6040
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48 function gplotimages (nm, typ) |
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49 bury_output (); |
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50 A = sparse ([2,6,1,3,2,4,3,5,4,6,1,5], |
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51 [1,1,2,2,3,3,4,4,5,5,6,6], 1, 6, 6); |
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52 xy = [0,4,8,6,4,2;5,0,5,7,5,7]'; |
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53 gplot (A, xy) |
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54 print (strcat (nm, ".", typ), strcat ("-d", typ)) |
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55 bury_output (); |
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56 endfunction |
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57 |
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58 function txtimages(nm,n,typ) |
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59 a = 10*speye(n) + sparse(1:n,ceil([1:n]/2),1,n,n) + ... |
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60 sparse(ceil([1:n]/2),1:n,1,n,n); |
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61 if (strcmp (nm, "gplot") || strcmp (nm, "grid")) |
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62 fid = fopen (sprintf ("%s.txt", nm), "wt"); |
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63 fputs (fid, "\n"); |
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64 fputs (fid, "+---------------------------------+\n"); |
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65 fputs (fid, "| Image unavailable in text mode. |\n"); |
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66 fputs (fid, "+---------------------------------+\n"); |
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67 fclose (fid); |
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68 elseif (strcmp (nm, "spmatrix")) |
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69 printsparse(a,strcat("spmatrix.",typ)); |
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70 else |
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71 if (!isempty(findstr(octave_config_info ("DEFS"),"HAVE_COLAMD")) && |
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72 !isempty(findstr(octave_config_info ("DEFS"),"HAVE_CHOLMOD"))) |
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73 if (strcmp (nm, "spchol")) |
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74 r1 = chol(a); |
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75 printsparse(r1,strcat("spchol.",typ)); |
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76 elseif (strcmp (nm, "spcholperm")) |
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77 [r2,p2,q2]=chol(a); |
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78 printsparse(r2,strcat("spcholperm.",typ)); |
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79 endif |
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80 ## printf("Text NNZ: Matrix %d, Chol %d, PermChol %d\n",nnz(a),nnz(r1),nnz(r2)); |
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81 endif |
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82 endif |
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83 endfunction |
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84 |
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85 function otherimages(nm,n,typ) |
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86 bury_output (); |
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87 a = 10*speye(n) + sparse(1:n,ceil([1:n]/2),1,n,n) + ... |
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88 sparse(ceil([1:n]/2),1:n,1,n,n); |
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89 if (strcmp (nm, "spmatrix")) |
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90 spy(a); |
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91 axis("ij") |
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92 print(strcat("spmatrix.",typ),strcat("-d",typ)) |
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93 bury_output (); |
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94 else |
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95 if (!isempty(findstr(octave_config_info ("DEFS"),"HAVE_COLAMD")) && |
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96 !isempty(findstr(octave_config_info ("DEFS"),"HAVE_CHOLMOD"))) |
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97 if (strcmp (nm, "spchol")) |
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98 r1 = chol(a); |
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99 spy(r1); |
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100 axis("ij") |
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101 print(strcat("spchol.",typ),strcat("-d",typ)) |
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102 bury_output (); |
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103 elseif (strcmp (nm, "spcholperm")) |
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104 [r2,p2,q2]=chol(a); |
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105 spy(r2); |
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106 axis("ij") |
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107 print(strcat("spcholperm.",typ),strcat("-d",typ)) |
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108 bury_output (); |
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109 endif |
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110 ## printf("Image NNZ: Matrix %d, Chol %d, PermChol %d\n",nnz(a),nnz(r1),nnz(r2)); |
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111 endif |
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112 endif |
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113 endfunction |
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114 |
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115 function printsparse(a,nm) |
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116 fid = fopen (nm,"wt"); |
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117 fputs (fid, "\n"); |
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118 for i = 1:size(a,1) |
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119 if (rem(i,5) == 0) |
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120 fprintf (fid," %2d - ", i); |
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121 else |
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122 fprintf (fid," | "); |
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123 endif |
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124 for j = 1:size(a,2) |
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125 if (a(i,j) == 0) |
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126 fprintf(fid," ") |
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127 else |
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128 fprintf(fid," *") |
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129 endif |
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130 endfor |
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131 fprintf(fid,"\n") |
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132 endfor |
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133 fprintf(fid," |-"); |
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134 for j=1:size(a,2) |
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135 if (rem(j,5)==0) |
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136 fprintf(fid,"-|"); |
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137 else |
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138 fprintf(fid,"--"); |
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139 endif |
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140 endfor |
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141 fprintf(fid,"\n") |
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142 fprintf(fid," "); |
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143 for j=1:size(a,2) |
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144 if (rem(j,5)==0) |
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145 fprintf(fid,"%2d",j); |
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146 else |
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147 fprintf(fid," "); |
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148 endif |
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149 endfor |
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150 fclose(fid); |
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151 endfunction |
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152 |
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153 function femimages (nm,typ) |
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154 bury_output (); |
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155 if (!isempty(findstr(octave_config_info ("DEFS"),"HAVE_COLAMD")) && |
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156 !isempty(findstr(octave_config_info ("DEFS"),"HAVE_CHOLMOD")) && |
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157 !isempty(findstr(octave_config_info ("DEFS"),"HAVE_UMFPACK"))) |
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158 ## build a rectangle |
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159 node_y = [1;1.2;1.5;1.8;2]*ones(1,11); |
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160 node_x = ones(5,1)*[1,1.05,1.1,1.2,1.3,1.5,1.7,1.8,1.9,1.95,2]; |
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161 nodes = [node_x(:), node_y(:)]; |
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162 |
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163 [h,w] = size(node_x); |
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164 elems = []; |
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165 for idx = 1:w-1 |
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166 widx = (idx-1)*h; |
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167 elems = [elems; widx+[(1:h-1);(2:h);h+(1:h-1)]']; |
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168 elems = [elems; widx+[(2:h);h+(2:h);h+(1:h-1)]']; |
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169 endfor |
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170 |
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171 E = size(elems,1); #No. of elements |
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172 N = size(nodes,1); #No. of elements |
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173 D = size(elems,2); #dimentions+1 |
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174 |
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175 ## Plot FEM Geometry |
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176 elemx = elems(:,[1,2,3,1])'; |
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177 xelems = reshape( nodes(elemx, 1), 4, E); |
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178 yelems = reshape( nodes(elemx, 2), 4, E); |
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179 |
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180 ## Set element conductivity |
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181 conductivity = [1*ones(1,16),2*ones(1,48),1*ones(1,16)]; |
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182 |
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183 ## Dirichlet boundary conditions |
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184 D_nodes = [1:5, 51:55]; |
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185 D_value = [10*ones(1,5), 20*ones(1,5)]; |
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186 |
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187 ## Neumann boundary conditions |
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188 ## Note that N_value must be normalized by the boundary |
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189 ## length and element conductivity |
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190 N_nodes = []; |
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191 N_value = []; |
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192 |
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193 ## Calculate connectivity matrix |
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194 C = sparse((1:D*E), reshape(elems',D*E,1),1, D*E, N); |
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195 |
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196 ## Calculate stiffness matrix |
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197 Siidx = floor([0:D*E-1]'/D)*D*ones(1,D) + ones(D*E,1)*(1:D) ; |
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198 Sjidx = [1:D*E]'*ones(1,D); |
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199 Sdata = zeros(D*E,D); |
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200 dfact = prod(2:(D-1)); |
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201 for j = 1:E |
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202 a = inv([ ones(D,1), nodes( elems(j,:), : ) ]); |
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203 const = conductivity(j)*2/dfact/abs(det(a)); |
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204 Sdata(D*(j-1)+(1:D),:)= const * a(2:D,:)'*a(2:D,:); |
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205 endfor |
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206 |
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207 ## Element-wise system matrix |
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208 SE = sparse(Siidx,Sjidx,Sdata); |
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209 ## Global system matrix |
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210 S = C'* SE *C; |
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211 |
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212 ## Set Dirichlet boundary |
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213 V = zeros(N,1); |
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214 V(D_nodes) = D_value; |
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215 idx = 1:N; |
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216 idx(D_nodes) = []; |
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217 |
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218 ## Set Neumann boundary |
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219 Q = zeros(N,1); |
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220 Q(N_nodes) = N_value; # FIXME |
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221 |
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222 V(idx) = S(idx,idx)\( Q(idx) - S(idx,D_nodes)*V(D_nodes) ); |
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223 |
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224 velems = reshape( V(elemx), 4, E); |
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225 |
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226 sz = size(xelems,2); |
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227 |
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228 plot3 (xelems, yelems, velems); |
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229 view (10, 10); |
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230 print(strcat(nm,".",typ),strcat("-d",typ)) |
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231 bury_output (); |
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232 endif |
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233 endfunction |
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234 |
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235 ## There is no sparse matrix implementation available because of missing |
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236 ## libraries, plot sombreros instead. Also plot a nice title that we are |
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237 ## sorry about that. |
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238 function sombreroimage (nm, typ) |
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239 if (strcmp (typ, "txt")) |
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240 fid = fopen (sprintf ("%s.txt", nm), "wt"); |
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241 fputs (fid, "\n"); |
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242 fputs (fid, "+---------------------------------------+\n"); |
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243 fputs (fid, "| Image unavailable because of a |\n"); |
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244 fputs (fid, "| missing sparse matrix implementation. |\n"); |
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245 fputs (fid, "+---------------------------------------+\n"); |
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246 fclose (fid); |
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247 return; |
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248 else ## if (!strcmp (typ, "txt")) |
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249 |
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250 bury_output (); |
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251 |
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252 x = y = linspace (-8, 8, 41)'; |
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253 [xx, yy] = meshgrid (x, y); |
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254 r = sqrt (xx .^ 2 + yy .^ 2) + eps; |
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255 z = sin (r) ./ r; |
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256 unwind_protect |
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257 mesh (x, y, z); |
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258 title ("Sorry, graphics not available because octave was\\ncompiled without the sparse matrix implementation."); |
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259 unwind_protect_cleanup |
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260 print (strcat (nm, ".", typ), strcat ("-d", typ)); |
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261 bury_output (); |
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262 end_unwind_protect |
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263 endif |
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264 endfunction |
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265 |
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266 ## generate something for the texinfo @image command to process |
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267 function image_as_txt(nm) |
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268 fid = fopen (sprintf ("%s.txt", nm), "wt"); |
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269 fputs (fid, "\n"); |
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270 fputs (fid, "+---------------------------------+\n"); |
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271 fputs (fid, "| Image unavailable in text mode. |\n"); |
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272 fputs (fid, "+---------------------------------+\n"); |
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273 fclose (fid); |
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274 endfunction |
