Actual source code: ex16opt_ic.c
petsc-3.6.1 2015-08-06
2: static char help[] = "Solves the van der Pol equation.\n\
3: Input parameters include:\n\
4: -mu : stiffness parameter\n\n";
6: /*
7: Concepts: TS^time-dependent nonlinear problems
8: Concepts: TS^van der Pol equation
9: Concepts: Optimization using adjoint sensitivity analysis
10: Processors: 1
11: */
12: /* ------------------------------------------------------------------------
14: This program solves the van der Pol equation
15: y'' - \mu (1-y^2)*y' + y = 0 (1)
16: on the domain 0 <= x <= 1, with the boundary conditions
17: y(0) = 2, y'(0) = 0,
18: This is a nonlinear equation.
20: Notes:
21: This code demonstrates the TS solver interface to two variants of
22: linear problems, u_t = f(u,t), namely turning (1) into a system of
23: first order differential equations,
25: [ y' ] = [ z ]
26: [ z' ] [ \mu (1 - y^2) z - y ]
28: which then we can write as a vector equation
30: [ u_1' ] = [ u_2 ] (2)
31: [ u_2' ] [ \mu (1 - u_1^2) u_2 - u_1 ]
33: which is now in the desired form of u_t = f(u,t).
34: ------------------------------------------------------------------------- */
35: #include <petsctao.h>
36: #include <petscts.h>
37: #include <petscmat.h>
38: typedef struct _n_User *User;
39: struct _n_User {
40: PetscReal mu;
41: PetscReal next_output;
43: PetscInt steps;
44: PetscReal ftime,x_ob[2];
45: Mat A; /* Jacobian matrix */
46: Vec x,lambda[2]; /* adjoint variables */
47: };
49: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
51: /*
52: * User-defined routines
53: */
56: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx)
57: {
58: PetscErrorCode ierr;
59: User user = (User)ctx;
60: PetscScalar *f;
61: const PetscScalar *x;
64: VecGetArrayRead(X,&x);
65: VecGetArray(F,&f);
66: f[0] = x[1];
67: f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0];
68: VecRestoreArrayRead(X,&x);
69: VecRestoreArray(F,&f);
70: return(0);
71: }
75: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx)
76: {
77: PetscErrorCode ierr;
78: User user = (User)ctx;
79: PetscReal mu = user->mu;
80: PetscInt rowcol[] = {0,1};
81: PetscScalar J[2][2];
82: const PetscScalar *x;
85: VecGetArrayRead(X,&x);
86: J[0][0] = 0;
87: J[1][0] = -2.*mu*x[1]*x[0]-1;
88: J[0][1] = 1.0;
89: J[1][1] = mu*(1.0-x[0]*x[0]);
90: MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
91: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
92: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
93: if (A != B) {
94: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
95: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
96: }
97: VecRestoreArrayRead(X,&x);
98: return(0);
99: }
103: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
104: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
105: {
106: PetscErrorCode ierr;
107: const PetscScalar *x;
108: PetscReal tfinal, dt, tprev;
109: User user = (User)ctx;
112: TSGetTimeStep(ts,&dt);
113: TSGetDuration(ts,NULL,&tfinal);
114: TSGetPrevTime(ts,&tprev);
115: VecGetArrayRead(X,&x);
116: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",(double)user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(x[0]),(double)PetscRealPart(x[1]));
117: PetscPrintf(PETSC_COMM_WORLD,"t %.6f (tprev = %.6f) \n",(double)t,(double)tprev);
118: VecGetArrayRead(X,&x);
119: return(0);
120: }
124: int main(int argc,char **argv)
125: {
126: TS ts; /* nonlinear solver */
127: Vec ic;
128: PetscBool monitor = PETSC_FALSE;
129: PetscScalar *x_ptr;
130: PetscMPIInt size;
131: struct _n_User user;
132: PetscErrorCode ierr;
133: Tao tao;
134: TaoConvergedReason reason;
135: KSP ksp;
136: PC pc;
138: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139: Initialize program
140: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
141: PetscInitialize(&argc,&argv,NULL,help);
143: MPI_Comm_size(PETSC_COMM_WORLD,&size);
144: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
146: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: Set runtime options
148: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149: user.mu = 1.0;
150: user.next_output = 0.0;
151: user.steps = 0;
152: user.ftime = 0.5;
154: PetscOptionsGetReal(NULL,"-mu",&user.mu,NULL);
155: PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);
157: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158: Create necessary matrix and vectors, solve same ODE on every process
159: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160: MatCreate(PETSC_COMM_WORLD,&user.A);
161: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
162: MatSetFromOptions(user.A);
163: MatSetUp(user.A);
164: MatCreateVecs(user.A,&user.x,NULL);
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Create timestepping solver context
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: TSCreate(PETSC_COMM_WORLD,&ts);
170: TSSetType(ts,TSRK);
171: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
172: TSSetDuration(ts,PETSC_DEFAULT,user.ftime);
173: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
174: if (monitor) {
175: TSMonitorSet(ts,Monitor,&user,NULL);
176: }
178: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: Set initial conditions
180: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181: VecGetArray(user.x,&x_ptr);
182: x_ptr[0] = 2.0; x_ptr[1] = 0.66666654321;
183: VecRestoreArray(user.x,&x_ptr);
184: TSSetTime(ts,0.0);
185: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)(user.ftime));
187: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: Save trajectory of solution so that TSAdjointSolve() may be used
189: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
190: TSSetSaveTrajectory(ts);
192: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: Set runtime options
194: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195: TSSetFromOptions(ts);
197: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198: Solve nonlinear system
199: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200: TSSolve(ts,user.x);
201: TSGetSolveTime(ts,&(user.ftime));
202: TSGetTimeStepNumber(ts,&user.steps);
203: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)user.ftime);
205: VecGetArray(user.x,&x_ptr);
206: user.x_ob[0] = x_ptr[0];
207: user.x_ob[1] = x_ptr[1];
209: MatCreateVecs(user.A,&user.lambda[0],NULL);
211: /* Create TAO solver and set desired solution method */
212: TaoCreate(PETSC_COMM_WORLD,&tao);
213: TaoSetType(tao,TAOCG);
215: /* Set initial solution guess */
216: MatCreateVecs(user.A,&ic,NULL);
217: VecGetArray(ic,&x_ptr);
218: x_ptr[0] = 2.1;
219: x_ptr[1] = 0.7;
220: VecRestoreArray(ic,&x_ptr);
221:
222: TaoSetInitialVector(tao,ic);
224: /* Set routine for function and gradient evaluation */
225: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
226:
227: /* Check for any TAO command line options */
228: TaoSetFromOptions(tao);
229: TaoGetKSP(tao,&ksp);
230: if (ksp) {
231: KSPGetPC(ksp,&pc);
232: PCSetType(pc,PCNONE);
233: }
234:
235: TaoSetTolerances(tao,1e-10,1e-10,1e-10,PETSC_DEFAULT,PETSC_DEFAULT);
237: /* SOLVE THE APPLICATION */
238: TaoSolve(tao);
240: /* Get information on termination */
241: TaoGetConvergedReason(tao,&reason);
242: if (reason <= 0){
243: ierr=PetscPrintf(MPI_COMM_WORLD, "Try another method! \n");
244: }
245:
246: /* Free TAO data structures */
247: TaoDestroy(&tao);
249: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
250: Free work space. All PETSc objects should be destroyed when they
251: are no longer needed.
252: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
253: MatDestroy(&user.A);
254: VecDestroy(&user.x);
255: VecDestroy(&user.lambda[0]);
256: TSDestroy(&ts);
258: VecDestroy(&ic);
259: PetscFinalize();
260: return(0);
261: }
263: /* ------------------------------------------------------------------ */
266: /*
267: FormFunctionGradient - Evaluates the function and corresponding gradient.
269: Input Parameters:
270: tao - the Tao context
271: X - the input vector
272: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
274: Output Parameters:
275: f - the newly evaluated function
276: G - the newly evaluated gradient
277: */
278: PetscErrorCode FormFunctionGradient(Tao tao,Vec IC,PetscReal *f,Vec G,void *ctx)
279: {
280: User user = (User)ctx;
281: TS ts;
282: PetscScalar *x_ptr,*y_ptr;
283: PetscErrorCode ierr;
284: PetscScalar *ic_ptr;
286: VecCopy(IC,user->x);
288: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
289: Create timestepping solver context
290: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
291: TSCreate(PETSC_COMM_WORLD,&ts);
292: TSSetType(ts,TSRK);
293: TSSetRHSFunction(ts,NULL,RHSFunction,user);
294: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
295:
296: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
297: Set time
298: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
299: TSSetTime(ts,0.0);
300: TSSetInitialTimeStep(ts,0.0,.001);
301: TSSetDuration(ts,2000,0.5);
303: TSSetTolerances(ts,1e-7,NULL,1e-7,NULL);
305: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
306: Save trajectory of solution so that TSAdjointSolve() may be used
307: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
308: TSSetSaveTrajectory(ts);
309:
310: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
311: Set runtime options
312: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
313: TSSetFromOptions(ts);
315: TSSolve(ts,user->x);
316: TSGetSolveTime(ts,&user->ftime);
317: TSGetTimeStepNumber(ts,&user->steps);
318: PetscPrintf(PETSC_COMM_WORLD,"mu %.6f, steps %D, ftime %g\n",(double)user->mu,user->steps,(double)user->ftime);
320: VecGetArray(IC,&ic_ptr);
321: VecGetArray(user->x,&x_ptr);
322: *f = (x_ptr[0]-user->x_ob[0])*(x_ptr[0]-user->x_ob[0])+(x_ptr[1]-user->x_ob[1])*(x_ptr[1]-user->x_ob[1]);
323: PetscPrintf(PETSC_COMM_WORLD,"Observed value y_ob=[%f; %f], ODE solution y=[%f;%f], Cost function f=%f\n",(double)user->x_ob[0],(double)user->x_ob[1],(double)x_ptr[0],(double)x_ptr[1],(double)(*f));
325: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
326: Adjoint model starts here
327: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
328: /* Redet initial conditions for the adjoint integration */
329: VecGetArray(user->lambda[0],&y_ptr);
330: y_ptr[0] = 2.*(x_ptr[0]-user->x_ob[0]);
331: y_ptr[1] = 2.*(x_ptr[1]-user->x_ob[1]);
332: VecRestoreArray(user->lambda[0],&y_ptr);
333: TSSetCostGradients(ts,1,user->lambda,NULL);
335: /* Set RHS Jacobian for the adjoint integration */
336: TSSetRHSJacobian(ts,user->A,user->A,RHSJacobian,user);
338: TSAdjointSolve(ts);
340: VecCopy(user->lambda[0],G);
342: TSDestroy(&ts);
343: return(0);
344: }