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