1 | function x_opt = plot(varargin) |
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2 | %plot plots feasible set |
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3 | % |
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4 | % p = plot(F,x,c,n,options) |
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5 | % |
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6 | % F: set object |
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7 | % x: projected variables [At most three variables] |
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8 | % c: color [double] ([r g b] format) |
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9 | % n: #vertices [double ] |
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10 | % options: options structure from sdpsettings |
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11 | |
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12 | |
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13 | % Author Johan Löfberg |
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14 | % $Id: plot.m,v 1.13 2006/04/25 11:22:57 joloef Exp $ |
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15 | |
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16 | % Get the onstraints |
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17 | if nargin<1 |
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18 | return |
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19 | end |
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20 | |
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21 | F = varargin{1}; |
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22 | |
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23 | if length(F)==0 |
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24 | return; |
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25 | end |
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26 | |
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27 | if nargin < 5 |
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28 | opts = sdpsettings('verbose',0); |
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29 | else |
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30 | opts = varargin{5}; |
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31 | if isempty(opts) |
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32 | opts = sdpsettings('verbose',0); |
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33 | end |
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34 | end |
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35 | |
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36 | if nargin < 3 |
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37 | color = [1 0.1 0.1]; |
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38 | else |
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39 | color = varargin{3}; |
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40 | if isempty(color) |
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41 | color = [1 0.1 0.1]; |
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42 | end |
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43 | end |
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44 | |
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45 | % Plot onto this projection (at most in 3D) |
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46 | if nargin < 2 |
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47 | x = []; |
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48 | else |
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49 | x = varargin{2}; |
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50 | if ~isempty(x) |
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51 | x = x(:); |
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52 | x = x(1:min(3,length(x))); |
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53 | end |
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54 | end |
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55 | |
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56 | if isempty(F) |
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57 | return |
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58 | end |
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59 | |
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60 | % Create a model in YALMIPs low level format |
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61 | % All we change later is the cost vector |
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62 | %sol = solvesdp(F,sum(x),opts); |
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63 | [model,recoverdata,diagnostic,internalmodel] = export(F,[],opts,[],[],0); |
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64 | if isempty(internalmodel) | (~isempty(diagnostic) & diagnostic.problem) |
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65 | error('Could not create model. Can you actually solve problems with this model?') |
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66 | end |
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67 | internalmodel.options.saveduals = 0; |
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68 | internalmodel.getsolvertime = 0; |
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69 | internalmodel.options.dimacs = 0; |
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70 | |
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71 | % Try to find a suitable set to plot |
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72 | if isempty(x) |
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73 | if isempty(internalmodel.extended_variables) |
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74 | x = depends(F); |
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75 | x = x(1:min(3,length(x))); |
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76 | localindex = 1; |
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77 | localindex = find(ismember(recoverdata.used_variables,x)); |
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78 | else |
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79 | % not extended variables |
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80 | candidates = setdiff(1:length(internalmodel.c),internalmodel.extended_variables); |
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81 | % Not nonlinear variables |
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82 | candidates = candidates(find(internalmodel.variabletype(candidates)==0)); |
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83 | % Settle with this guess |
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84 | localindex = candidates(1:min(3,length(candidates))); |
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85 | x = localindex; |
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86 | end |
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87 | else |
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88 | localindex = []; |
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89 | for i = 1:length(x) |
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90 | localindex = [localindex find(ismember(recoverdata.used_variables,getvariables(x(i))))]; |
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91 | end |
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92 | end |
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93 | |
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94 | if nargin < 4 |
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95 | if length(x)==3 |
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96 | n = 100; |
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97 | else |
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98 | n = 25; |
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99 | end |
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100 | else |
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101 | n = varargin{4}; |
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102 | if isempty(n) |
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103 | if length(x)==3 |
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104 | n = 100; |
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105 | else |
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106 | n = 25; |
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107 | end |
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108 | end |
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109 | if ~isa(n,'double') |
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110 | error('4th argument should be an integer>0'); |
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111 | end |
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112 | end |
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113 | |
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114 | |
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115 | x_opt = []; |
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116 | phi = []; |
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117 | status = 0; |
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118 | try % Try to ensure that we close h |
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119 | if length(x)==2 |
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120 | mu =0.5; |
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121 | else |
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122 | mu=1; |
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123 | end |
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124 | n_ = n; |
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125 | n = ceil(mu*n); |
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126 | h = waitbar(0,['Please wait, solving ' num2str(n_) ' problems using ' internalmodel.solver.tag]); |
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127 | angles = (0:(n))*2*pi/n; |
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128 | if length(x)==2 |
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129 | c = [cos(angles);sin(angles)]; |
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130 | else |
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131 | c = randn(3,n); |
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132 | end |
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133 | i=1; |
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134 | while i<=n & status == 0 |
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135 | xi = solvefordirection(c(:,i),internalmodel,localindex); |
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136 | x_opt = [x_opt xi]; |
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137 | waitbar(i/n_,h) |
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138 | i=i+1; |
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139 | end |
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140 | |
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141 | if status==0 & length(x)==2 |
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142 | % Close the set |
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143 | x_opt = [x_opt x_opt(:,1)]; |
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144 | |
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145 | % Add points adaptively |
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146 | pick = 1; |
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147 | n = floor((1-mu)*n_); |
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148 | for i = 1:1:n |
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149 | for j= 1:(size(x_opt,2)-1) |
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150 | d = x_opt(:,j)-x_opt(:,j+1); |
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151 | distance(j,1) = d'*d; |
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152 | end |
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153 | [dist,pos]=sort(-distance); |
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154 | % Select insertion point |
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155 | phii=(angles(pos(pick))+angles(pos(pick)+1))/2; |
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156 | xi = solvefordirection([cos(phii);sin(phii)],internalmodel,localindex); |
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157 | d1=xi-x_opt(:,pos(pick)); |
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158 | d2=xi-x_opt(:,pos(pick)+1); |
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159 | if d1'*d1<1e-3 | d2'*d2<1e-3 |
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160 | pick = pick+1; |
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161 | else |
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162 | angles = [angles(1:pos(pick)) phii angles((pos(pick))+1:end)]; |
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163 | x_opt = [x_opt(:,1:pos(pick)) xi x_opt(:,(pos(pick))+1:end)]; |
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164 | end |
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165 | waitbar((ceil(n_*mu)+i)/n_,h); |
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166 | end |
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167 | end |
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168 | close(h); |
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169 | catch |
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170 | close(h); |
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171 | end |
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172 | |
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173 | if status |
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174 | if nargout==0 |
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175 | plot(0); |
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176 | end |
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177 | end |
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178 | |
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179 | if nargout == 0 & status==0 |
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180 | if length(x)==2 |
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181 | patch(x_opt(1,:),x_opt(2,:),color); |
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182 | else |
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183 | K = convhulln(x_opt'); |
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184 | p = patch('Vertices', x_opt', 'Faces', K, 'FaceVertexCData', color, 'FaceColor', color);%, 'FaceAlpha', 0.5); |
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185 | set(p,'LineStyle','none') |
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186 | lighting gouraud; |
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187 | view(3); |
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188 | camlight('headlight','local'); |
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189 | camlight('headlight','local'); |
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190 | camlight('right','local'); |
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191 | camlight('left','local'); |
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192 | end |
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193 | end |
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194 | |
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195 | |
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196 | function [xout,status] = solvefordirection(c,internalmodel,uv) |
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197 | internalmodel.c = 0*internalmodel.c; |
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198 | internalmodel.c(uv) = c; |
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199 | sol = feval(internalmodel.solver.call,internalmodel); |
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200 | xout = sol.Primal; |
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201 | xout = xout(uv(:)); |
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202 | status = sol.problem; |
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203 | |
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204 | |
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205 | |
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206 | |
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