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5708
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1 function sparseimages(nm,typ) |
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2 if (strcmp(typ,"txt")) |
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3 txtimages(nm,15,typ); |
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4 else |
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5 if (strcmp (nm, "gplot")) |
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6 gplotimages("gplot",typ); |
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5717
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7 elseif (strcmp (nm, "grid")) |
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5708
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8 femimages("grid",typ); |
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5717
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9 else |
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10 otherimages(nm,200,typ); |
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5708
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11 endif |
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12 endif |
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13 ## Kluge to give gnuplot enough time to process last figure before we |
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14 ## exit. Otherwise, Octave will delete the temporary data files when |
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15 ## it exits and gnuplot will fail... |
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16 sleep (1); |
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17 endfunction |
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18 |
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19 ## Use this function before plotting commands and after every call to |
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20 ## print since print() resets output to stdout (unfortunately, gnpulot |
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21 ## can't pop output as it can the terminal type). |
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22 function bury_output () |
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23 automatic_replot = false; |
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5681
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24 __gnuplot_set__ term dumb |
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25 [status, dummy] = fileattrib("/dev/null"); |
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26 if (status) |
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5806
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27 __gnuplot_raw__ ("set output \"/dev/null\"\n"); |
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5681
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28 endif |
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5648
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29 endfunction |
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30 |
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5708
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31 function gplotimages(nm,typ) |
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32 bury_output (); |
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5648
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33 A = sparse([2,6,1,3,2,4,3,5,4,6,1,5], |
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34 [1,1,2,2,3,3,4,4,5,5,6,6],1,6,6); |
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35 xy = [0,4,8,6,4,2;5,0,5,7,5,7]'; |
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36 gplot(A,xy) |
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5708
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37 print(strcat(nm,".",typ),strcat("-d",typ)) |
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38 bury_output (); |
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5648
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39 endfunction |
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40 |
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5708
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41 function txtimages(nm,n,typ) |
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5648
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42 a = 10*speye(n) + sparse(1:n,ceil([1:n]/2),1,n,n) + ... |
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43 sparse(ceil([1:n]/2),1:n,1,n,n); |
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5711
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44 if (strcmp (nm, "gplot") || strcmp (nm, "grid")) |
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45 fid = fopen (sprintf ("%s.txt", nm), "wt"); |
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46 fputs (fid, "+---------------------------------+\n"); |
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47 fputs (fid, "| Image unavailable in text mode. |\n"); |
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48 fputs (fid, "+---------------------------------+\n"); |
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49 fclose (fid); |
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5717
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50 elseif (strcmp (nm, "spmatrix")) |
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5708
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51 printsparse(a,strcat("spmatrix.",typ)); |
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5717
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52 else |
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53 if (!isempty(findstr(octave_config_info ("DEFS"),"HAVE_COLAMD")) && |
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54 !isempty(findstr(octave_config_info ("DEFS"),"HAVE_CHOLMOD"))) |
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55 if (strcmp (nm, "spchol")) |
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56 r1 = chol(a); |
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57 printsparse(r1,strcat("spchol.",typ)); |
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58 elseif (strcmp (nm, "spcholperm")) |
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59 [r2,p2,q2]=chol(a); |
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60 printsparse(r2,strcat("spcholperm.",typ)); |
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61 endif |
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62 ## printf("Text NNZ: Matrix %d, Chol %d, PermChol %d\n",nnz(a),nnz(r1),nnz(r2)); |
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5708
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63 endif |
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5648
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64 endif |
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65 endfunction |
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66 |
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5708
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67 function otherimages(nm,n,typ) |
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68 bury_output (); |
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5648
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69 a = 10*speye(n) + sparse(1:n,ceil([1:n]/2),1,n,n) + ... |
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70 sparse(ceil([1:n]/2),1:n,1,n,n); |
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5708
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71 if (strcmp (nm, "spmatrix")) |
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5717
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72 spy(a); |
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73 axis("ij") |
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5708
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74 print(strcat("spmatrix.",typ),strcat("-d",typ)) |
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75 bury_output (); |
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5717
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76 else |
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77 if (!isempty(findstr(octave_config_info ("DEFS"),"HAVE_COLAMD")) && |
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78 !isempty(findstr(octave_config_info ("DEFS"),"HAVE_CHOLMOD"))) |
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79 if (strcmp (nm, "spchol")) |
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80 r1 = chol(a); |
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81 spy(r1); |
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82 axis("ij") |
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83 print(strcat("spchol.",typ),strcat("-d",typ)) |
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84 bury_output (); |
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85 elseif (strcmp (nm, "spcholperm")) |
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86 [r2,p2,q2]=chol(a); |
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87 spy(r2); |
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88 axis("ij") |
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89 print(strcat("spcholperm.",typ),strcat("-d",typ)) |
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90 bury_output (); |
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91 endif |
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92 ## printf("Image NNZ: Matrix %d, Chol %d, PermChol %d\n",nnz(a),nnz(r1),nnz(r2)); |
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5718
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93 endif |
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5648
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94 endif |
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95 endfunction |
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96 |
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97 function printsparse(a,nm) |
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98 fid = fopen (nm,"wt"); |
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99 for i = 1:size(a,1) |
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100 if (rem(i,5) == 0) |
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101 fprintf (fid," %2d - ", i); |
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102 else |
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103 fprintf (fid," | "); |
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104 endif |
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105 for j = 1:size(a,2) |
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106 if (a(i,j) == 0) |
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107 fprintf(fid," ") |
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108 else |
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109 fprintf(fid," *") |
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110 endif |
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111 endfor |
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112 fprintf(fid,"\n") |
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113 endfor |
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114 fprintf(fid," |-"); |
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115 for j=1:size(a,2) |
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116 if (rem(j,5)==0) |
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117 fprintf(fid,"-|"); |
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118 else |
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119 fprintf(fid,"--"); |
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120 endif |
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121 endfor |
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122 fprintf(fid,"\n") |
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123 fprintf(fid," "); |
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124 for j=1:size(a,2) |
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125 if (rem(j,5)==0) |
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126 fprintf(fid,"%2d",j); |
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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 fclose(fid); |
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132 endfunction |
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133 |
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5708
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134 function femimages (nm,typ) |
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135 bury_output (); |
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5648
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136 if (!isempty(findstr(octave_config_info ("DEFS"),"HAVE_COLAMD")) && |
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137 !isempty(findstr(octave_config_info ("DEFS"),"HAVE_CHOLMOD")) && |
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138 !isempty(findstr(octave_config_info ("DEFS"),"HAVE_UMFPACK"))) |
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139 ## build a rectangle |
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140 node_y = [1;1.2;1.5;1.8;2]*ones(1,11); |
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141 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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142 nodes = [node_x(:), node_y(:)]; |
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143 |
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144 [h,w] = size(node_x); |
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145 elems = []; |
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146 for idx = 1:w-1 |
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147 widx = (idx-1)*h; |
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148 elems = [elems; widx+[(1:h-1);(2:h);h+(1:h-1)]']; |
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149 elems = [elems; widx+[(2:h);h+(2:h);h+(1:h-1)]']; |
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150 endfor |
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151 |
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152 E = size(elems,1); #No. of elements |
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153 N = size(nodes,1); #No. of elements |
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154 D = size(elems,2); #dimentions+1 |
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155 |
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156 ## Plot FEM Geometry |
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157 elemx = elems(:,[1,2,3,1])'; |
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158 xelems = reshape( nodes(elemx, 1), 4, E); |
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159 yelems = reshape( nodes(elemx, 2), 4, E); |
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160 |
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161 ## Set element conductivity |
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162 conductivity = [1*ones(1,16),2*ones(1,48),1*ones(1,16)]; |
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163 |
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164 ## Dirichlet boundary conditions |
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165 D_nodes = [1:5, 51:55]; |
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166 D_value = [10*ones(1,5), 20*ones(1,5)]; |
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167 |
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168 ## Neumann boundary conditions |
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169 ## Note that N_value must be normalized by the boundary |
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170 ## length and element conductivity |
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171 N_nodes = []; |
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172 N_value = []; |
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173 |
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174 ## Calculate connectivity matrix |
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175 C = sparse((1:D*E), reshape(elems',D*E,1),1, D*E, N); |
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176 |
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177 ## Calculate stiffness matrix |
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178 Siidx = floor([0:D*E-1]'/D)*D*ones(1,D) + ones(D*E,1)*(1:D) ; |
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179 Sjidx = [1:D*E]'*ones(1,D); |
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180 Sdata = zeros(D*E,D); |
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181 dfact = prod(2:(D-1)); |
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182 for j = 1:E |
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183 a = inv([ ones(D,1), nodes( elems(j,:), : ) ]); |
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184 const = conductivity(j)*2/dfact/abs(det(a)); |
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185 Sdata(D*(j-1)+(1:D),:)= const * a(2:D,:)'*a(2:D,:); |
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186 endfor |
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187 |
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188 ## Element-wise system matrix |
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189 SE = sparse(Siidx,Sjidx,Sdata); |
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190 ## Global system matrix |
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191 S = C'* SE *C; |
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192 |
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193 ## Set Dirichlet boundary |
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194 V = zeros(N,1); |
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195 V(D_nodes) = D_value; |
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196 idx = 1:N; |
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197 idx(D_nodes) = []; |
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198 |
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199 ## Set Neumann boundary |
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200 Q = zeros(N,1); |
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201 Q(N_nodes) = N_value; # FIXME |
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202 |
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203 V(idx) = S(idx,idx)\( Q(idx) - S(idx,D_nodes)*V(D_nodes) ); |
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204 |
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205 velems = reshape( V(elemx), 4, E); |
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206 |
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207 sz = size(xelems,2); |
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208 ## FIXME How can I do this without a gnuplot specific commands? plot3 anyone? |
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209 unwind_protect |
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210 __gnuplot_set__ parametric; |
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211 __gnuplot_raw__ ("set nohidden3d;\n"); |
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212 tmp = [([xelems; NaN*ones(1,sz)])(:), ([yelems; NaN*ones(1,sz)])(:), ([velems; NaN*ones(1,sz)])(:)]; |
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213 __gnuplot_splot__(tmp); |
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214 __gnuplot_raw__ ("set view 80,10;\n") |
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5708
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215 print(strcat(nm,".",typ),strcat("-d",typ)) |
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216 bury_output (); |
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5648
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217 unwind_protect_cleanup |
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218 __gnuplot_set__ noparametric; |
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219 end_unwind_protect |
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220 endif |
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221 endfunction |
