[37] | 1 | function [F_struc,K,KCut] = lmi2sedumistruct(F) |
---|
| 2 | %lmi2sedumistruct Internal function: Converts LMI to format needed in SeDuMi |
---|
| 3 | % |
---|
| 4 | % % Author Johan Löfberg |
---|
| 5 | % % $Id: lmi2sedumistruct.m,v 1.21 2006/09/22 08:18:37 joloef Exp $ |
---|
| 6 | |
---|
| 7 | nvars = yalmip('nvars'); %Needed lot'sa times... |
---|
| 8 | |
---|
| 9 | % We first browse to see what we have got and the |
---|
| 10 | % dimension of F_struc (massive speed improvement) |
---|
| 11 | %top = 0; |
---|
| 12 | type_of_constraint = zeros(size(F.clauses,2),1); |
---|
| 13 | for i = 1:size(F.clauses,2) |
---|
| 14 | type_of_constraint(i) = F.clauses{i}.type; |
---|
| 15 | % [n,m] = size(F.clauses{i}.data); |
---|
| 16 | % [n,m] = size(getbasematrixwithoutcheck(F.clauses{i}.data,0)); |
---|
| 17 | % top = top+n*m; |
---|
| 18 | % Is it a complex linear cone |
---|
| 19 | % if (type_of_constraint(i)==2) & (~isreal(F.clauses{i}.data)) |
---|
| 20 | % top = top+n*m; % We will have constraints on Re and Im |
---|
| 21 | % end |
---|
| 22 | end |
---|
| 23 | |
---|
| 24 | F_struc = []; |
---|
| 25 | |
---|
| 26 | sdp_con = find(type_of_constraint == 1 | type_of_constraint == 9); |
---|
| 27 | lin_con = find(type_of_constraint == 2 | type_of_constraint == 12); |
---|
| 28 | equ_con = find(type_of_constraint == 3); |
---|
| 29 | qdr_con = find(type_of_constraint == 4); |
---|
| 30 | rlo_con = find(type_of_constraint == 5); |
---|
| 31 | |
---|
| 32 | % SeDuMi struct |
---|
| 33 | K.f = 0; |
---|
| 34 | K.l = 0; |
---|
| 35 | K.q = 0; |
---|
| 36 | K.r = 0; |
---|
| 37 | K.s = 0; |
---|
| 38 | K.rank = []; |
---|
| 39 | K.dualrank = []; |
---|
| 40 | K.scomplex = []; |
---|
| 41 | K.xcomplex = []; |
---|
| 42 | |
---|
| 43 | KCut.f = []; |
---|
| 44 | KCut.l = []; |
---|
| 45 | KCut.q = []; |
---|
| 46 | KCut.r = []; |
---|
| 47 | KCut.s = []; |
---|
| 48 | |
---|
| 49 | top = 1; |
---|
| 50 | localtop = 1; |
---|
| 51 | % Linear equality constraints |
---|
| 52 | for i = 1:length(equ_con) |
---|
| 53 | constraints = equ_con(i); |
---|
| 54 | data = getbase(F.clauses{constraints}.data); |
---|
| 55 | [n,m] = size(F.clauses{constraints}.data); |
---|
| 56 | % Which variables are needed in this constraint |
---|
| 57 | lmi_variables = getvariables(F.clauses{constraints}.data); |
---|
| 58 | if isreal(data) |
---|
| 59 | ntimesm = n*m; %Just as well pre-calc |
---|
| 60 | else |
---|
| 61 | % Complex constraint, Expand to real and Imag |
---|
| 62 | ntimesm = 2*n*m; %Just as well pre-calc |
---|
| 63 | data = [real(data);imag(data)]; |
---|
| 64 | end |
---|
| 65 | mapX = [1 1+lmi_variables]; |
---|
| 66 | [ix,jx,sx] = find(data); |
---|
| 67 | F_structemp = sparse(ix,mapX(jx),sx,ntimesm,1+nvars); |
---|
| 68 | %F_structemp = spalloc(ntimesm,1+nvars,0); |
---|
| 69 | %F_structemp(:,[1 1+lmi_variables(:)'])= data; |
---|
| 70 | |
---|
| 71 | % ...and add them together (efficient for large structures) |
---|
| 72 | % F_struc(top:top+ntimesm-1,:) = F_structemp; |
---|
| 73 | F_struc = [F_struc;F_structemp]; |
---|
| 74 | |
---|
| 75 | if F.clauses{constraints}.cut |
---|
| 76 | KCut.f = [KCut.f localtop:localtop+ntimesm-1]; |
---|
| 77 | end |
---|
| 78 | |
---|
| 79 | localtop = localtop+ntimesm; |
---|
| 80 | top = top+ntimesm; |
---|
| 81 | K.f = K.f+ntimesm; |
---|
| 82 | end |
---|
| 83 | |
---|
| 84 | % Linear inequality constraints |
---|
| 85 | localtop = 1; |
---|
| 86 | F_struc = F_struc'; |
---|
| 87 | % [F_struc,K,KCut] = recursive_lp_fix(F,F_struc,K,KCut,lin_con,nvars,8,1); |
---|
| 88 | % F_struc = F_struc'; |
---|
| 89 | |
---|
| 90 | % |
---|
| 91 | for i = 1:length(lin_con) |
---|
| 92 | constraints = lin_con(i); |
---|
| 93 | data = getbase(F.clauses{constraints}.data); |
---|
| 94 | [n,m] = size(F.clauses{constraints}.data); |
---|
| 95 | |
---|
| 96 | % Which variables are needed in this constraint |
---|
| 97 | lmi_variables = getvariables(F.clauses{constraints}.data); |
---|
| 98 | |
---|
| 99 | % Convert to real problem |
---|
| 100 | if isreal(data) |
---|
| 101 | ntimesm = n*m; %Just as well pre-calc |
---|
| 102 | else |
---|
| 103 | % Complex constraint, Expand to real and Imag |
---|
| 104 | ntimesm = 2*n*m; %Just as well pre-calc |
---|
| 105 | data = [real(data);imag(data)]; |
---|
| 106 | end |
---|
| 107 | |
---|
| 108 | % Add numerical data to complete problem setup |
---|
| 109 | mapX = [1 1+lmi_variables]; |
---|
| 110 | [ix,jx,sx] = find(data); |
---|
| 111 | F_structemp = sparse(mapX(jx),ix,sx,1+nvars,ntimesm); |
---|
| 112 | F_struc = [F_struc F_structemp]; |
---|
| 113 | |
---|
| 114 | if F.clauses{constraints}.cut |
---|
| 115 | KCut.l = [KCut.l localtop:localtop+ntimesm-1]; |
---|
| 116 | end |
---|
| 117 | |
---|
| 118 | localtop = localtop+ntimesm; |
---|
| 119 | top = top+ntimesm; |
---|
| 120 | K.l = K.l+ntimesm; |
---|
| 121 | end |
---|
| 122 | F_struc = F_struc'; |
---|
| 123 | |
---|
| 124 | [F_struc,K,KCut] = recursive_socp_fix(F,F_struc',K,KCut,qdr_con,nvars,8,1); |
---|
| 125 | F_struc = F_struc'; |
---|
| 126 | |
---|
| 127 | |
---|
| 128 | % Rotated Lorentz cone constraints |
---|
| 129 | for i = 1:length(rlo_con) |
---|
| 130 | constraints = rlo_con(i); |
---|
| 131 | |
---|
| 132 | [n,m] = size(F.clauses{constraints}.data); |
---|
| 133 | ntimesm = n*m; %Just as well pre-calc |
---|
| 134 | |
---|
| 135 | % Which variables are needed in this constraint |
---|
| 136 | lmi_variables = getvariables(F.clauses{constraints}.data); |
---|
| 137 | |
---|
| 138 | % We allocate the structure blockwise... |
---|
| 139 | F_structemp = spalloc(ntimesm,1+nvars,0); |
---|
| 140 | % Add these rows only |
---|
| 141 | F_structemp(:,[1 1+lmi_variables(:)'])= getbase(F.clauses{constraints}.data); |
---|
| 142 | % ...and add them together (efficient for large structures) |
---|
| 143 | % F_struc(top:top+ntimesm-1,:) = F_structemp; |
---|
| 144 | F_struc = [F_struc;F_structemp]; |
---|
| 145 | |
---|
| 146 | top = top+ntimesm; |
---|
| 147 | K.r(i) = n; |
---|
| 148 | end |
---|
| 149 | |
---|
| 150 | % Semidefinite constraints |
---|
| 151 | % We append the recursively in order to speed up construction |
---|
| 152 | % of problems with a lot of medium size SDPs |
---|
| 153 | [F_struc,K,KCut] = recursive_sdp_fix(F,F_struc.',K,KCut,sdp_con,nvars,8,1); |
---|
| 154 | F_struc = F_struc.'; |
---|
| 155 | |
---|
| 156 | % Now fix things for the rank constraint |
---|
| 157 | % This is currently a hack... |
---|
| 158 | % Should not be in this file |
---|
| 159 | [rank_variables,dual_rank_variables] = yalmip('rankvariables'); |
---|
| 160 | if ~isempty(rank_variables) |
---|
| 161 | used_in = find(sum(abs(F_struc(:,1+rank_variables)),2)); |
---|
| 162 | if ~isempty(used_in) |
---|
| 163 | if used_in >=1+K.f & used_in < 1+K.l+K.f |
---|
| 164 | for i = 1:length(used_in) |
---|
| 165 | [ii,jj,kk] = find(F_struc(used_in(i),:)); |
---|
| 166 | if length(ii)==2 & kk(2)<1 |
---|
| 167 | r = floor(kk(1)); |
---|
| 168 | var = jj(2)-1; |
---|
| 169 | extstruct = yalmip('extstruct',var); |
---|
| 170 | X = extstruct.arg{1}; |
---|
| 171 | if issymmetric(X) |
---|
| 172 | F_structemp = sedumize(X,nvars); |
---|
| 173 | else |
---|
| 174 | error('Only symmetric matrices can be rank constrained.') |
---|
| 175 | end |
---|
| 176 | F_struc = [F_struc;F_structemp]; |
---|
| 177 | if isequal(K.s,0) |
---|
| 178 | K.s(1,1) = size(extstruct.arg{1},1); |
---|
| 179 | else |
---|
| 180 | K.s(1,end+1) = size(extstruct.arg{1},1); |
---|
| 181 | end |
---|
| 182 | K.rank(1,end+1) = min(r,K.s(end)); |
---|
| 183 | else |
---|
| 184 | error('This rank constraint is not supported (only supports rank(X) < r)') |
---|
| 185 | end |
---|
| 186 | end |
---|
| 187 | % Remove the nonlinear operator constraints |
---|
| 188 | |
---|
| 189 | F_struc(used_in,:) = []; |
---|
| 190 | K.l = K.l - length(used_in); |
---|
| 191 | else |
---|
| 192 | error('You have added a rank constraint on an equality constraint, or a scalar expression?!') |
---|
| 193 | end |
---|
| 194 | end |
---|
| 195 | end |
---|
| 196 | if ~isempty(dual_rank_variables) |
---|
| 197 | used_in = find(sum(abs(F_struc(:,1+dual_rank_variables)),2)); |
---|
| 198 | if ~isempty(used_in) |
---|
| 199 | if used_in >=1+K.f & used_in < 1+K.l+K.f |
---|
| 200 | for i = 1:length(used_in) |
---|
| 201 | [ii,jj,kk] = find(F_struc(used_in(i),:)); |
---|
| 202 | if length(ii)==2 & kk(2)<1 |
---|
| 203 | r = floor(kk(1)); |
---|
| 204 | var = jj(2)-1; |
---|
| 205 | extstruct = yalmip('extstruct',var); |
---|
| 206 | X = extstruct.arg{1}; |
---|
| 207 | id = getlmiid(X); |
---|
| 208 | inlist=getlmiid(F); |
---|
| 209 | index=find(id==inlist); |
---|
| 210 | if ~isempty(index) |
---|
| 211 | K.rank(1,index) = min(r,K.s(index)); |
---|
| 212 | end |
---|
| 213 | else |
---|
| 214 | error('This rank constraint is not supported (only supports rank(X) < r)') |
---|
| 215 | end |
---|
| 216 | end |
---|
| 217 | % Remove the nonlinear operator constraints |
---|
| 218 | F_struc(used_in,:) = []; |
---|
| 219 | K.l = K.l - length(used_in); |
---|
| 220 | else |
---|
| 221 | error('You have added a rank constraint on an equality constraint, or a scalar expression?!') |
---|
| 222 | end |
---|
| 223 | end |
---|
| 224 | end |
---|
| 225 | |
---|
| 226 | function F_structemp = sedumize(Fi,nvars) |
---|
| 227 | Fibase = getbase(Fi); |
---|
| 228 | [n,m] = size(Fi); |
---|
| 229 | ntimesm = n*m; |
---|
| 230 | lmi_variables = getvariables(Fi); |
---|
| 231 | [ix,jx,sx] = find(Fibase); |
---|
| 232 | mapX = [1 1+lmi_variables]; |
---|
| 233 | F_structemp = sparse(ix,mapX(jx),sx,ntimesm,1+nvars); |
---|
| 234 | |
---|
| 235 | function [F_struc,K,KCut] = recursive_lp_fix(F,F_struc,K,KCut,lp_con,nvars,maxnlp,startindex) |
---|
| 236 | |
---|
| 237 | % Check if we should recurse |
---|
| 238 | if length(lp_con)>2*maxnlp |
---|
| 239 | % recursing costs, so do 4 in one step |
---|
| 240 | ind = 1+ceil(length(lp_con)*(0:0.25:1)); |
---|
| 241 | [F_struc1,K,KCut] = recursive_lp_fix(F,[],K,KCut,lp_con(ind(1):ind(2)-1),nvars,maxnlp,startindex+ind(1)-1); |
---|
| 242 | [F_struc2,K,KCut] = recursive_lp_fix(F,[],K,KCut,lp_con(ind(2):ind(3)-1),nvars,maxnlp,startindex+ind(2)-1); |
---|
| 243 | [F_struc3,K,KCut] = recursive_lp_fix(F,[],K,KCut,lp_con(ind(3):ind(4)-1),nvars,maxnlp,startindex+ind(3)-1); |
---|
| 244 | [F_struc4,K,KCut] = recursive_lp_fix(F,[],K,KCut,lp_con(ind(4):ind(5)-1),nvars,maxnlp,startindex+ind(4)-1); |
---|
| 245 | F_struc = [F_struc F_struc1 F_struc2 F_struc3 F_struc4]; |
---|
| 246 | return |
---|
| 247 | elseif length(lp_con)>maxnlp |
---|
| 248 | mid = ceil(length(lp_con)/2); |
---|
| 249 | [F_struc1,K,KCut] = recursive_lp_fix(F,[],K,KCut,lp_con(1:mid),nvars,maxnlp,startindex); |
---|
| 250 | [F_struc2,K,KCut] = recursive_lp_fix(F,[],K,KCut,lp_con(mid+1:end),nvars,maxnlp,startindex+mid); |
---|
| 251 | F_struc = [F_struc F_struc1 F_struc2]; |
---|
| 252 | return |
---|
| 253 | end |
---|
| 254 | |
---|
| 255 | oldF_struc = F_struc; |
---|
| 256 | F_struc = []; |
---|
| 257 | for i = 1:length(lp_con) |
---|
| 258 | constraints = lp_con(i); |
---|
| 259 | Fi = F.clauses{constraints}.data; |
---|
| 260 | Fibase = getbase(Fi); |
---|
| 261 | [n,m] = size(Fi); |
---|
| 262 | |
---|
| 263 | %ntimesm = n*m; %Just as well pre-calc |
---|
| 264 | |
---|
| 265 | |
---|
| 266 | % Convert to real problem |
---|
| 267 | if isreal(Fibase) |
---|
| 268 | ntimesm = n*m; %Just as well pre-calc |
---|
| 269 | else |
---|
| 270 | % Complex constraint, Expand to real and Imag |
---|
| 271 | ntimesm = 2*n*m; %Just as well pre-calc |
---|
| 272 | Fibase = [real(Fibase);imag(Fibase)]; |
---|
| 273 | end |
---|
| 274 | |
---|
| 275 | % Which variables are needed in this constraint |
---|
| 276 | lmi_variables = getvariables(Fi); |
---|
| 277 | mapX = [1 1+lmi_variables]; |
---|
| 278 | |
---|
| 279 | [ix,jx,sx] = find(Fibase); |
---|
| 280 | |
---|
| 281 | F_structemp = sparse(mapX(jx),ix,sx,1+nvars,ntimesm); |
---|
| 282 | F_struc = [F_struc F_structemp]; |
---|
| 283 | |
---|
| 284 | if F.clauses{constraints}.cut |
---|
| 285 | KCut.l = [KCut.l i+startindex-1]; |
---|
| 286 | end |
---|
| 287 | |
---|
| 288 | K.l(i+startindex-1) = n; |
---|
| 289 | end |
---|
| 290 | K.l = sum(K.l); |
---|
| 291 | F_struc = [oldF_struc F_struc]; |
---|
| 292 | |
---|
| 293 | |
---|
| 294 | function [F_struc,K,KCut] = recursive_sdp_fix(F,F_struc,K,KCut,sdp_con,nvars,maxnsdp,startindex) |
---|
| 295 | |
---|
| 296 | % Check if we should recurse |
---|
| 297 | if length(sdp_con)>2*maxnsdp |
---|
| 298 | % recursing costs, so do 4 in one step |
---|
| 299 | ind = 1+ceil(length(sdp_con)*(0:0.25:1)); |
---|
| 300 | [F_struc1,K,KCut] = recursive_sdp_fix(F,[],K,KCut,sdp_con(ind(1):ind(2)-1),nvars,maxnsdp,startindex+ind(1)-1); |
---|
| 301 | [F_struc2,K,KCut] = recursive_sdp_fix(F,[],K,KCut,sdp_con(ind(2):ind(3)-1),nvars,maxnsdp,startindex+ind(2)-1); |
---|
| 302 | [F_struc3,K,KCut] = recursive_sdp_fix(F,[],K,KCut,sdp_con(ind(3):ind(4)-1),nvars,maxnsdp,startindex+ind(3)-1); |
---|
| 303 | [F_struc4,K,KCut] = recursive_sdp_fix(F,[],K,KCut,sdp_con(ind(4):ind(5)-1),nvars,maxnsdp,startindex+ind(4)-1); |
---|
| 304 | F_struc = [F_struc F_struc1 F_struc2 F_struc3 F_struc4]; |
---|
| 305 | return |
---|
| 306 | elseif length(sdp_con)>maxnsdp |
---|
| 307 | mid = ceil(length(sdp_con)/2); |
---|
| 308 | [F_struc1,K,KCut] = recursive_sdp_fix(F,[],K,KCut,sdp_con(1:mid),nvars,maxnsdp,startindex); |
---|
| 309 | [F_struc2,K,KCut] = recursive_sdp_fix(F,[],K,KCut,sdp_con(mid+1:end),nvars,maxnsdp,startindex+mid); |
---|
| 310 | F_struc = [F_struc F_struc1 F_struc2]; |
---|
| 311 | return |
---|
| 312 | end |
---|
| 313 | |
---|
| 314 | oldF_struc = F_struc; |
---|
| 315 | F_struc = []; |
---|
| 316 | for i = 1:length(sdp_con) |
---|
| 317 | constraints = sdp_con(i); |
---|
| 318 | Fi = F.clauses{constraints}.data; |
---|
| 319 | Fibase = getbase(Fi); |
---|
| 320 | [n,m] = size(Fi); |
---|
| 321 | ntimesm = n*m; %Just as well pre-calc |
---|
| 322 | |
---|
| 323 | % Which variables are needed in this constraint |
---|
| 324 | lmi_variables = getvariables(Fi); |
---|
| 325 | mapX = [1 1+lmi_variables]; |
---|
| 326 | |
---|
| 327 | [ix,jx,sx] = find(Fibase); |
---|
| 328 | |
---|
| 329 | F_structemp = sparse(mapX(jx),ix,sx,1+nvars,ntimesm); |
---|
| 330 | F_struc = [F_struc F_structemp]; |
---|
| 331 | |
---|
| 332 | if F.clauses{constraints}.cut |
---|
| 333 | KCut.s = [KCut.s i+startindex-1]; |
---|
| 334 | end |
---|
| 335 | K.s(i+startindex-1) = n; |
---|
| 336 | K.rank(i+startindex-1) = n; |
---|
| 337 | K.dualrank(i+startindex-1) = n; |
---|
| 338 | % Check for a complex structure |
---|
| 339 | if ~isreal(F_structemp) |
---|
| 340 | K.scomplex = [K.scomplex i+startindex-1]; |
---|
| 341 | end |
---|
| 342 | end |
---|
| 343 | F_struc = [oldF_struc F_struc]; |
---|
| 344 | |
---|
| 345 | |
---|
| 346 | |
---|
| 347 | |
---|
| 348 | |
---|
| 349 | function [F_struc,K,KCut] = recursive_socp_fix(F,F_struc,K,KCut,qdr_con,nvars,maxnsocp,startindex); |
---|
| 350 | |
---|
| 351 | % Check if we should recurse |
---|
| 352 | if length(qdr_con)>2*maxnsocp |
---|
| 353 | % recursing costs, so do 4 in one step |
---|
| 354 | ind = 1+ceil(length(qdr_con)*(0:0.25:1)); |
---|
| 355 | [F_struc1,K,KCut] = recursive_socp_fix(F,[],K,KCut,qdr_con(ind(1):ind(2)-1),nvars,maxnsocp,startindex+ind(1)-1); |
---|
| 356 | [F_struc2,K,KCut] = recursive_socp_fix(F,[],K,KCut,qdr_con(ind(2):ind(3)-1),nvars,maxnsocp,startindex+ind(2)-1); |
---|
| 357 | [F_struc3,K,KCut] = recursive_socp_fix(F,[],K,KCut,qdr_con(ind(3):ind(4)-1),nvars,maxnsocp,startindex+ind(3)-1); |
---|
| 358 | [F_struc4,K,KCut] = recursive_socp_fix(F,[],K,KCut,qdr_con(ind(4):ind(5)-1),nvars,maxnsocp,startindex+ind(4)-1); |
---|
| 359 | F_struc = [F_struc F_struc1 F_struc2 F_struc3 F_struc4]; |
---|
| 360 | return |
---|
| 361 | elseif length(qdr_con)>maxnsocp |
---|
| 362 | mid = ceil(length(qdr_con)/2); |
---|
| 363 | [F_struc1,K,KCut] = recursive_socp_fix(F,[],K,KCut,qdr_con(1:mid),nvars,maxnsocp,startindex); |
---|
| 364 | [F_struc2,K,KCut] = recursive_socp_fix(F,[],K,KCut,qdr_con(mid+1:end),nvars,maxnsocp,startindex+mid); |
---|
| 365 | F_struc = [F_struc F_struc1 F_struc2]; |
---|
| 366 | return |
---|
| 367 | end |
---|
| 368 | |
---|
| 369 | % second order cone constraints |
---|
| 370 | for i = 1:length(qdr_con) |
---|
| 371 | constraints = qdr_con(i); |
---|
| 372 | |
---|
| 373 | [n,m] = size(F.clauses{constraints}.data); |
---|
| 374 | ntimesm = n*m; %Just as well pre-calc |
---|
| 375 | |
---|
| 376 | % Which variables are needed in this constraint |
---|
| 377 | lmi_variables = getvariables(F.clauses{constraints}.data); |
---|
| 378 | |
---|
| 379 | data = getbase(F.clauses{constraints}.data); |
---|
| 380 | if isreal(data) |
---|
| 381 | mapX = [1 1+lmi_variables]; |
---|
| 382 | [ix,jx,sx] = find(data); |
---|
| 383 | F_structemp = sparse(mapX(jx),ix,sx,1+nvars,ntimesm); |
---|
| 384 | else |
---|
| 385 | n = n+(n-1); |
---|
| 386 | ntimesm = n*m; |
---|
| 387 | F_structemp = spalloc(ntimesm,1+nvars,0); |
---|
| 388 | data = [data(1,:);real(data(2:end,:));imag(data(2:end,:))]; |
---|
| 389 | F_structemp(:,[1 1+lmi_variables(:)'])= data; |
---|
| 390 | F_structemp = F_structemp'; |
---|
| 391 | end |
---|
| 392 | % ...and add them together (efficient for large structures) |
---|
| 393 | F_struc = [F_struc F_structemp]; |
---|
| 394 | K.q(i+startindex-1) = n; |
---|
| 395 | end |
---|
| 396 | |
---|
| 397 | |
---|
| 398 | |
---|
| 399 | |
---|
| 400 | |
---|
| 401 | |
---|