Actual source code: ex20opt_p.c

petsc-3.11.2 2019-05-18
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  1: #define c21 2.0
  2: #define rescale 10

  4: static char help[] = "Solves the van der Pol equation.\n\
  5: Input parameters include:\n";

  7: /*
  8:    Concepts: TS^time-dependent nonlinear problems
  9:    Concepts: TS^van der Pol equation DAE equivalent
 10:    Concepts: Optimization using adjoint sensitivity analysis
 11:    Processors: 1
 12: */
 13: /* ------------------------------------------------------------------------

 15:   Notes:
 16:   This code demonstrates how to solve a DAE-constrained optimization problem with TAO, TSAdjoint and TS.
 17:   The nonlinear problem is written in a DAE equivalent form.
 18:   The objective is to minimize the difference between observation and model prediction by finding an optimal value for parameter \mu.
 19:   The gradient is computed with the discrete adjoint of an implicit theta method, see ex20adj.c for details.
 20:   ------------------------------------------------------------------------- */
 21:  #include <petsctao.h>
 22:  #include <petscts.h>

 24: typedef struct _n_User *User;
 25: struct _n_User {
 26:   PetscReal mu;
 27:   PetscReal next_output;

 29:   /* Sensitivity analysis support */
 30:   PetscReal ftime,x_ob[2];
 31:   Mat       A;                       /* Jacobian matrix */
 32:   Mat       Jacp;                    /* JacobianP matrix */
 33:   Vec       x,lambda[2],mup[2];  /* adjoint variables */
 34: };

 36: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);

 38: /*
 39: *  User-defined routines
 40: */
 41: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
 42: {
 43:   PetscErrorCode    ierr;
 44:   User              user = (User)ctx;
 45:   PetscScalar       *f;
 46:   const PetscScalar *x,*xdot;

 49:   VecGetArrayRead(X,&x);
 50:   VecGetArrayRead(Xdot,&xdot);
 51:   VecGetArray(F,&f);
 52:   f[0] = xdot[0] - x[1];
 53:   f[1] = c21*(xdot[0]-x[1]) + xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]) ;
 54:   VecRestoreArrayRead(X,&x);
 55:   VecRestoreArrayRead(Xdot,&xdot);
 56:   VecRestoreArray(F,&f);
 57:   return(0);
 58: }

 60: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
 61: {
 62:   PetscErrorCode    ierr;
 63:   User              user     = (User)ctx;
 64:   PetscInt          rowcol[] = {0,1};
 65:   PetscScalar       J[2][2];
 66:   const PetscScalar *x;

 69:   VecGetArrayRead(X,&x);
 70:   J[0][0] = a;
 71:   J[0][1] = -1.0;
 72:   J[1][0] = c21*a + user->mu*(1.0 + 2.0*x[0]*x[1]);
 73:   J[1][1] = -c21 + a - user->mu*(1.0-x[0]*x[0]);
 74:   MatZeroEntries(A);
 75:   MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
 76:   VecRestoreArrayRead(X,&x);
 77:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 78:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 79:   if (B && A != B) {
 80:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 81:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 82:   }
 83:   return(0);
 84: }

 86: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
 87: {
 88:   PetscErrorCode    ierr;
 89:   PetscInt          row[] = {0,1},col[]={0};
 90:   PetscScalar       J[2][1];
 91:   const PetscScalar *x;

 94:   MatZeroEntries(A);
 95:   VecGetArrayRead(X,&x);
 96:   J[0][0] = 0;
 97:   J[1][0] = (1.-x[0]*x[0])*x[1]-x[0];
 98:   MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
 99:   VecRestoreArrayRead(X,&x);
100:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
101:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
102:   return(0);
103: }

105: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
106: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
107: {
108:   PetscErrorCode    ierr;
109:   const PetscScalar *x;
110:   PetscReal         tfinal, dt;
111:   User              user = (User)ctx;
112:   Vec               interpolatedX;

115:   TSGetTimeStep(ts,&dt);
116:   TSGetMaxTime(ts,&tfinal);

118:   while (user->next_output <= t && user->next_output <= tfinal) {
119:     VecDuplicate(X,&interpolatedX);
120:     TSInterpolate(ts,user->next_output,interpolatedX);
121:     VecGetArrayRead(interpolatedX,&x);
122:     PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
123:                        user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(x[0]),
124:                        (double)PetscRealPart(x[1]));
125:     VecRestoreArrayRead(interpolatedX,&x);
126:     VecDestroy(&interpolatedX);
127:     user->next_output += 0.1;
128:   }
129:   return(0);
130: }

132: int main(int argc,char **argv)
133: {
134:   TS                 ts;            /* nonlinear solver */
135:   Vec                p;
136:   PetscBool          monitor = PETSC_FALSE;
137:   PetscScalar        *x_ptr;
138:   const PetscScalar  *y_ptr;
139:   PetscMPIInt        size;
140:   struct _n_User     user;
141:   PetscErrorCode     ierr;
142:   Tao                tao;
143:   KSP                ksp;
144:   PC                 pc;

146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147:      Initialize program
148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149:   PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
150:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
151:   if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");

153:   /* Create TAO solver and set desired solution method */
154:   TaoCreate(PETSC_COMM_WORLD,&tao);
155:   TaoSetType(tao,TAOBLMVM);

157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158:     Set runtime options
159:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160:   user.next_output = 0.0;
161:   user.mu          = 1.0;
162:   user.ftime       = 1.0;
163:   PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
164:   PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);

166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167:     Create necessary matrix and vectors, solve same ODE on every process
168:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169:   MatCreate(PETSC_COMM_WORLD,&user.A);
170:   MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
171:   MatSetFromOptions(user.A);
172:   MatSetUp(user.A);
173:   MatCreateVecs(user.A,&user.x,NULL);

175:   MatCreate(PETSC_COMM_WORLD,&user.Jacp);
176:   MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
177:   MatSetFromOptions(user.Jacp);
178:   MatSetUp(user.Jacp);

180:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181:      Create timestepping solver context
182:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183:   TSCreate(PETSC_COMM_WORLD,&ts);
184:   TSSetType(ts,TSCN);
185:   TSSetIFunction(ts,NULL,IFunction,&user);
186:   TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
187:   TSSetMaxTime(ts,user.ftime);
188:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
189:   if (monitor) {
190:     TSMonitorSet(ts,Monitor,&user,NULL);
191:   }

193:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194:      Set initial conditions
195:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196:   VecGetArray(user.x,&x_ptr);
197:   x_ptr[0] = 2.0;   x_ptr[1] = -0.66666654321;
198:   VecRestoreArray(user.x,&x_ptr);
199:   TSSetTimeStep(ts,0.03125);

201:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202:      Set runtime options
203:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
204:   TSSetFromOptions(ts);

206:   TSSolve(ts,user.x);

208:   VecGetArrayRead(user.x,&y_ptr);
209:   user.x_ob[0] = y_ptr[0];
210:   user.x_ob[1] = y_ptr[1];
211:   VecRestoreArrayRead(user.x,&y_ptr);

213:   /* Create sensitivity variable */
214:   MatCreateVecs(user.A,&user.lambda[0],NULL);
215:   MatCreateVecs(user.Jacp,&user.mup[0],NULL);

217:   /*
218:      Optimization starts
219:   */
220:   /* Set initial solution guess */
221:   MatCreateVecs(user.Jacp,&p,NULL);
222:   VecGetArray(p,&x_ptr);
223:   x_ptr[0] = 1.2;
224:   VecRestoreArray(p,&x_ptr);
225:   TaoSetInitialVector(tao,p);

227:   /* Set routine for function and gradient evaluation */
228:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);

230:   /* Check for any TAO command line options */
231:   TaoSetFromOptions(tao);
232:   TaoGetKSP(tao,&ksp);
233:   if (ksp) {
234:     KSPGetPC(ksp,&pc);
235:     PCSetType(pc,PCNONE);
236:   }

238:   TaoSolve(tao);

240:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);
241:   /* Free TAO data structures */
242:   TaoDestroy(&tao);

244:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
245:      Free work space.  All PETSc objects should be destroyed when they
246:      are no longer needed.
247:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
248:   MatDestroy(&user.A);
249:   MatDestroy(&user.Jacp);
250:   VecDestroy(&user.x);
251:   VecDestroy(&user.lambda[0]);
252:   VecDestroy(&user.mup[0]);
253:   TSDestroy(&ts);
254:   VecDestroy(&p);
255:   PetscFinalize();
256:   return ierr;
257: }


260: /* ------------------------------------------------------------------ */
261: /*
262:    FormFunctionGradient - Evaluates the function and corresponding gradient.

264:    Input Parameters:
265:    tao - the Tao context
266:    X   - the input vector
267:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()

269:    Output Parameters:
270:    f   - the newly evaluated function
271:    G   - the newly evaluated gradient
272: */
273: PetscErrorCode FormFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx)
274: {
275:   User              user_ptr = (User)ctx;
276:   TS                ts;
277:   PetscScalar       *x_ptr;
278:   const PetscScalar *y_ptr;
279:   PetscErrorCode    ierr;

282:   VecGetArrayRead(P,&y_ptr);
283:   user_ptr->mu = y_ptr[0];
284:   VecRestoreArrayRead(P,&y_ptr);

286:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
287:      Create timestepping solver context
288:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
289:   TSCreate(PETSC_COMM_WORLD,&ts);
290:   TSSetType(ts,TSCN);
291:   TSSetIFunction(ts,NULL,IFunction,user_ptr);
292:   TSSetIJacobian(ts,user_ptr->A,user_ptr->A,IJacobian,user_ptr);
293:   TSSetRHSJacobianP(ts,user_ptr->Jacp,RHSJacobianP,user_ptr);

295:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
296:      Set time
297:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
298:   TSSetTime(ts,0.0);
299:   TSSetMaxTime(ts,user_ptr->ftime);
300:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);

302:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
303:     Save trajectory of solution so that TSAdjointSolve() may be used
304:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
305:   TSSetSaveTrajectory(ts);

307:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
308:      Set initial conditions
309:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
310:   VecGetArray(user_ptr->x,&x_ptr);
311:   x_ptr[0] = 2.0;   x_ptr[1] = -0.66666654321;
312:   VecRestoreArray(user_ptr->x,&x_ptr);

314:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
315:      Set runtime options
316:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
317:   TSSetFromOptions(ts);

319:   TSSolve(ts,user_ptr->x);
320:   VecGetArrayRead(user_ptr->x,&y_ptr);
321:   *f   = rescale*(y_ptr[0]-user_ptr->x_ob[0])*(y_ptr[0]-user_ptr->x_ob[0])+rescale*(y_ptr[1]-user_ptr->x_ob[1])*(y_ptr[1]-user_ptr->x_ob[1]);
322:   PetscPrintf(PETSC_COMM_WORLD,"Observed value y_ob=[%g; %g], ODE solution y=[%g;%g], Cost function f=%g\n",(double)user_ptr->x_ob[0],(double)user_ptr->x_ob[1],(double)y_ptr[0],(double)y_ptr[1],(double)(*f));
323:   /*   Redet initial conditions for the adjoint integration */
324:   VecGetArray(user_ptr->lambda[0],&x_ptr);
325:   x_ptr[0] = rescale*2.*(y_ptr[0]-user_ptr->x_ob[0]);
326:   x_ptr[1] = rescale*2.*(y_ptr[1]-user_ptr->x_ob[1]);
327:   VecRestoreArrayRead(user_ptr->x,&y_ptr);
328:   VecRestoreArray(user_ptr->lambda[0],&x_ptr);

330:   VecGetArray(user_ptr->mup[0],&x_ptr);
331:   x_ptr[0] = 0.0;
332:   VecRestoreArray(user_ptr->mup[0],&x_ptr);
333:   TSSetCostGradients(ts,1,user_ptr->lambda,user_ptr->mup);

335:   TSAdjointSolve(ts);
336:   VecCopy(user_ptr->mup[0],G);
337:   TSDestroy(&ts);
338:   return(0);
339: }

341: /*TEST
342:     build:
343:       requires: !complex !single
344:     test:
345:       args:  -monitor 0 -ts_type theta -ts_theta_endpoint -ts_theta_theta 0.5 -viewer_binary_skip_info -tao_view  -ts_trajectory_dirname ex20opt_pdir -tao_blmvm_mat_lmvm_scale_type none
346:       output_file: output/ex20opt_p_1.out

348: TEST*/