Actual source code: toy.c

petsc-3.7.0 2016-04-25
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  1: /* Program usage: mpiexec -n 1 toy[-help] [all TAO options] */

  3: /* ----------------------------------------------------------------------
  4: min f=(x1-x2)^2 + (x2-2)^2 -2*x1-2*x2
  5: s.t.     x1^2 + x2 = 2
  6:       0 <= x1^2 - x2 <= 1
  7:       -1 <= x1,x2 <= 2
  8: ---------------------------------------------------------------------- */

 10: #include <petsctao.h>

 12: static  char help[]="";

 14: /*
 15:    User-defined application context - contains data needed by the
 16:    application-provided call-back routines, FormFunction(),
 17:    FormGradient(), and FormHessian().
 18: */

 20: /*
 21:    x,d in R^n
 22:    f in R
 23:    bin in R^mi
 24:    beq in R^me
 25:    Aeq in R^(me x n)
 26:    Ain in R^(mi x n)
 27:    H in R^(n x n)
 28:    min f=(1/2)*x'*H*x + d'*x
 29:    s.t.  Aeq*x == beq
 30:          Ain*x >= bin
 31: */
 32: typedef struct {
 33:   PetscInt n; /* Length x */
 34:   PetscInt ne; /* number of equality constraints */
 35:   PetscInt ni; /* number of inequality constraints */
 36:   Vec      x,xl,xu;
 37:   Vec      ce,ci,bl,bu;
 38:   Mat      Ae,Ai,H;
 39: } AppCtx;

 41: /* -------- User-defined Routines --------- */

 43: PetscErrorCode InitializeProblem(AppCtx *);
 44: PetscErrorCode DestroyProblem(AppCtx *);
 45: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal *,Vec,void *);
 46: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat, void*);
 47: PetscErrorCode FormInequalityConstraints(Tao,Vec,Vec,void*);
 48: PetscErrorCode FormEqualityConstraints(Tao,Vec,Vec,void*);
 49: PetscErrorCode FormInequalityJacobian(Tao,Vec,Mat,Mat, void*);
 50: PetscErrorCode FormEqualityJacobian(Tao,Vec,Mat,Mat, void*);



 56: PetscErrorCode main(int argc,char **argv)
 57: {
 58:   PetscErrorCode     ierr;                /* used to check for functions returning nonzeros */
 59:   Tao                tao;
 60:   KSP                ksp;
 61:   PC                 pc;
 62:   AppCtx             user;                /* application context */

 64:   PetscInitialize(&argc,&argv,(char *)0,help);
 65:   PetscPrintf(PETSC_COMM_WORLD,"\n---- TOY Problem -----\n");
 66:   PetscPrintf(PETSC_COMM_WORLD,"Solution should be f(1,1)=-2\n");
 67:   InitializeProblem(&user);
 68:   TaoCreate(PETSC_COMM_WORLD,&tao);
 69:   TaoSetType(tao,TAOIPM);
 70:   TaoSetInitialVector(tao,user.x);
 71:   TaoSetVariableBounds(tao,user.xl,user.xu);
 72:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void*)&user);

 74:   TaoSetEqualityConstraintsRoutine(tao,user.ce,FormEqualityConstraints,(void*)&user);
 75:   TaoSetInequalityConstraintsRoutine(tao,user.ci,FormInequalityConstraints,(void*)&user);

 77:   TaoSetJacobianEqualityRoutine(tao,user.Ae,user.Ae,FormEqualityJacobian,(void*)&user);
 78:   TaoSetJacobianInequalityRoutine(tao,user.Ai,user.Ai,FormInequalityJacobian,(void*)&user);
 79:   TaoSetHessianRoutine(tao,user.H,user.H,FormHessian,(void*)&user);
 80:   TaoSetTolerances(tao,0,0,0);

 82:   TaoSetFromOptions(tao);

 84:   TaoGetKSP(tao,&ksp);
 85:   KSPGetPC(ksp,&pc);
 86:   PCSetType(pc,PCLU);
 87:   /*
 88:       This algorithm produces matrices with zeros along the diagonal therefore we need to use
 89:     SuperLU which does partial pivoting
 90:   */
 91:   PCFactorSetMatSolverPackage(pc,MATSOLVERSUPERLU);
 92:   KSPSetType(ksp,KSPPREONLY);
 93:   KSPSetFromOptions(ksp);

 95:   TaoSetTolerances(tao,0,0,0);
 96:   TaoSolve(tao);

 98:   DestroyProblem(&user);
 99:   TaoDestroy(&tao);
100:   PetscFinalize();
101:   return 0;
102: }

106: PetscErrorCode InitializeProblem(AppCtx *user)
107: {

111:   user->n = 2;
112:   VecCreateSeq(PETSC_COMM_SELF,user->n,&user->x);
113:   VecDuplicate(user->x,&user->xl);
114:   VecDuplicate(user->x,&user->xu);
115:   VecSet(user->x,0.0);
116:   VecSet(user->xl,-1.0);
117:   VecSet(user->xu,2.0);

119:   user->ne = 1;
120:   VecCreateSeq(PETSC_COMM_SELF,user->ne,&user->ce);

122:   user->ni = 2;
123:   VecCreateSeq(PETSC_COMM_SELF,user->ni,&user->ci);

125:   MatCreateSeqAIJ(PETSC_COMM_SELF,user->ne,user->n,user->n,NULL,&user->Ae);
126:   MatCreateSeqAIJ(PETSC_COMM_SELF,user->ni,user->n,user->n,NULL,&user->Ai);
127:   MatSetFromOptions(user->Ae);
128:   MatSetFromOptions(user->Ai);


131:   MatCreateSeqAIJ(PETSC_COMM_SELF,user->n,user->n,1,NULL,&user->H);
132:   MatSetFromOptions(user->H);

134:   return(0);
135: }

139: PetscErrorCode DestroyProblem(AppCtx *user)
140: {

144:   MatDestroy(&user->Ae);
145:   MatDestroy(&user->Ai);
146:   MatDestroy(&user->H);

148:   VecDestroy(&user->x);
149:   VecDestroy(&user->ce);
150:   VecDestroy(&user->ci);
151:   VecDestroy(&user->xl);
152:   VecDestroy(&user->xu);
153:   return(0);
154: }

158: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ctx)
159: {
160:   PetscScalar       *g;
161:   const PetscScalar *x;
162:   PetscErrorCode    ierr;

165:   VecGetArrayRead(X,&x);
166:   VecGetArray(G,&g);
167:   *f = (x[0]-2.0)*(x[0]-2.0) + (x[1]-2.0)*(x[1]-2.0) - 2.0*(x[0]+x[1]);
168:   g[0] = 2.0*(x[0]-2.0) - 2.0;
169:   g[1] = 2.0*(x[1]-2.0) - 2.0;
170:   VecRestoreArrayRead(X,&x);
171:   VecRestoreArray(G,&g);
172:   return(0);
173: }

177: PetscErrorCode FormHessian(Tao tao, Vec x, Mat H, Mat Hpre, void *ctx)
178: {
179:   Vec               DE,DI;
180:   const PetscScalar *de, *di;
181:   PetscInt          zero=0,one=1;
182:   PetscScalar       two=2.0;
183:   PetscScalar       val;
184:   PetscErrorCode    ierr;

187:   TaoGetDualVariables(tao,&DE,&DI);

189:   VecGetArrayRead(DE,&de);
190:   VecGetArrayRead(DI,&di);
191:   val=2.0 * (1 + de[0] + di[0] - di[1]);
192:   VecRestoreArrayRead(DE,&de);
193:   VecRestoreArrayRead(DI,&di);

195:   MatSetValues(H,1,&zero,1,&zero,&val,INSERT_VALUES);
196:   MatSetValues(H,1,&one,1,&one,&two,INSERT_VALUES);

198:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
199:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
200:   return(0);
201: }

205: PetscErrorCode FormInequalityConstraints(Tao tao, Vec X, Vec CI, void *ctx)
206: {
207:   const PetscScalar *x;
208:   PetscScalar       *c;
209:   PetscErrorCode    ierr;

212:   VecGetArrayRead(X,&x);
213:   VecGetArray(CI,&c);
214:   c[0] = x[0]*x[0] - x[1];
215:   c[1] = -x[0]*x[0] + x[1] + 1.0;
216:   VecRestoreArrayRead(X,&x);
217:   VecRestoreArray(CI,&c);
218:   return(0);
219: }

223: PetscErrorCode FormEqualityConstraints(Tao tao, Vec X, Vec CE,void *ctx)
224: {
225:   PetscScalar    *x,*c;

229:   VecGetArray(X,&x);
230:   VecGetArray(CE,&c);
231:   c[0] = x[0]*x[0] + x[1] - 2.0;
232:   VecRestoreArray(X,&x);
233:   VecRestoreArray(CE,&c);
234:   return(0);
235: }

239: PetscErrorCode FormInequalityJacobian(Tao tao, Vec X, Mat JI, Mat JIpre,  void *ctx)
240: {
241:   PetscInt          rows[2];
242:   PetscInt          cols[2];
243:   PetscScalar       vals[4];
244:   const PetscScalar *x;
245:   PetscErrorCode    ierr;

248:   VecGetArrayRead(X,&x);
249:   rows[0] = 0;       rows[1] = 1;
250:   cols[0] = 0;       cols[1] = 1;
251:   vals[0] = +2*x[0]; vals[1] = -1.0;
252:   vals[2] = -2*x[0]; vals[3] = +1.0;
253:   VecRestoreArrayRead(X,&x);
254:   MatSetValues(JI,2,rows,2,cols,vals,INSERT_VALUES);
255:   MatAssemblyBegin(JI,MAT_FINAL_ASSEMBLY);
256:   MatAssemblyEnd(JI,MAT_FINAL_ASSEMBLY);

258:   return(0);
259: }

263: PetscErrorCode FormEqualityJacobian(Tao tao, Vec X, Mat JE, Mat JEpre, void *ctx)
264: {
265:   PetscInt          rows[2];
266:   PetscScalar       vals[2];
267:   const PetscScalar *x;
268:   PetscErrorCode    ierr;

271:   VecGetArrayRead(X,&x);
272:   rows[0] = 0;       rows[1] = 1;
273:   vals[0] = 2*x[0];  vals[1] = 1.0;
274:   VecRestoreArrayRead(X,&x);
275:   MatSetValues(JE,1,rows,2,rows,vals,INSERT_VALUES);
276:   MatAssemblyBegin(JE,MAT_FINAL_ASSEMBLY);
277:   MatAssemblyEnd(JE,MAT_FINAL_ASSEMBLY);
278:   return(0);
279: }