Actual source code: ex20opt_ic.c
petsc-3.9.4 2018-09-11
1: #define c11 1.0
2: #define c12 0
3: #define c21 2.0
4: #define c22 1.0
5: static char help[] = "Solves a DAE-constrained optimization problem -- finding the optimal initial conditions for the van der Pol equation.\n";
7: /*
8: Concepts: TS^time-dependent nonlinear problems
9: Concepts: TS^van der Pol equation DAE equivalent
10: Concepts: Optimization using adjoint sensitivities
11: Processors: 1
12: */
13: /* ------------------------------------------------------------------------
14: Notes:
15: This code demonstrates how to solve a DAE-constrained optimization problem with TAO, TSAdjoint and TS.
16: The nonlinear problem is written in a DAE equivalent form.
17: The objective is to minimize the difference between observation and model prediction by finding optimal values for initial conditions.
18: The gradient is computed with the discrete adjoint of an implicit theta method, see ex20adj.c for details.
19: ------------------------------------------------------------------------- */
20: #include <petsctao.h>
21: #include <petscts.h>
23: typedef struct _n_User *User;
24: struct _n_User {
25: PetscReal mu;
26: PetscReal next_output;
28: /* Sensitivity analysis support */
29: PetscReal ftime,x_ob[2];
30: Mat A; /* Jacobian matrix */
31: Vec x,lambda[2]; /* adjoint variables */
32: };
34: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
36: /*
37: * User-defined routines
38: */
39: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
40: {
41: PetscErrorCode ierr;
42: User user = (User)ctx;
43: PetscScalar *f;
44: const PetscScalar *x,*xdot;
47: VecGetArrayRead(X,&x);
48: VecGetArrayRead(Xdot,&xdot);
49: VecGetArray(F,&f);
50: f[0] = xdot[0] - x[1];
51: f[1] = c21*(xdot[0]-x[1]) + xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]) ;
52: VecRestoreArrayRead(X,&x);
53: VecRestoreArrayRead(Xdot,&xdot);
54: VecRestoreArray(F,&f);
55: return(0);
56: }
58: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
59: {
60: PetscErrorCode ierr;
61: User user = (User)ctx;
62: PetscInt rowcol[] = {0,1};
63: PetscScalar J[2][2];
64: const PetscScalar *x;
67: VecGetArrayRead(X,&x);
69: J[0][0] = a; J[0][1] = -1.0;
70: J[1][0] = c21*a + user->mu*(1.0 + 2.0*x[0]*x[1]); J[1][1] = -c21 + a - user->mu*(1.0-x[0]*x[0]);
72: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
73: VecRestoreArrayRead(X,&x);
75: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
76: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
77: if (A != B) {
78: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
79: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
80: }
81: return(0);
82: }
84: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
85: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
86: {
87: PetscErrorCode ierr;
88: const PetscScalar *x;
89: PetscReal tfinal, dt;
90: User user = (User)ctx;
91: Vec interpolatedX;
94: TSGetTimeStep(ts,&dt);
95: TSGetMaxTime(ts,&tfinal);
97: while (user->next_output <= t && user->next_output <= tfinal) {
98: VecDuplicate(X,&interpolatedX);
99: TSInterpolate(ts,user->next_output,interpolatedX);
100: VecGetArrayRead(interpolatedX,&x);
101: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
102: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
103: (double)PetscRealPart(x[1]));
104: VecRestoreArrayRead(interpolatedX,&x);
105: VecDestroy(&interpolatedX);
106: user->next_output += 0.1;
107: }
108: return(0);
109: }
111: int main(int argc,char **argv)
112: {
113: TS ts; /* nonlinear solver */
114: Vec ic;
115: PetscBool monitor = PETSC_FALSE;
116: PetscScalar *x_ptr;
117: PetscMPIInt size;
118: struct _n_User user;
119: PetscErrorCode ierr;
120: Tao tao;
121: KSP ksp;
122: PC pc;
124: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Initialize program
126: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127: PetscInitialize(&argc,&argv,NULL,help);
128: MPI_Comm_size(PETSC_COMM_WORLD,&size);
129: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
131: /* Create TAO solver and set desired solution method */
132: TaoCreate(PETSC_COMM_WORLD,&tao);
133: TaoSetType(tao,TAOBLMVM);
135: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: Set runtime options
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138: user.next_output = 0.0;
139: user.mu = 1.0;
140: user.ftime = 1.0;
141: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
142: PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
144: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: Create necessary matrix and vectors, solve same ODE on every process
146: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147: MatCreate(PETSC_COMM_WORLD,&user.A);
148: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
149: MatSetFromOptions(user.A);
150: MatSetUp(user.A);
151: MatCreateVecs(user.A,&user.x,NULL);
153: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
154: Create timestepping solver context
155: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
156: TSCreate(PETSC_COMM_WORLD,&ts);
157: TSSetType(ts,TSCN);
158: TSSetIFunction(ts,NULL,IFunction,&user);
159: TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
160: TSSetMaxTime(ts,user.ftime);
161: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
163: if (monitor) {
164: TSMonitorSet(ts,Monitor,&user,NULL);
165: }
167: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168: Set initial conditions
169: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
170: VecGetArray(user.x,&x_ptr);
171: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
172: VecRestoreArray(user.x,&x_ptr);
173: TSSetTimeStep(ts,0.03125);
175: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176: Save trajectory of solution so that TSAdjointSolve() may be used
177: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
178: TSSetSaveTrajectory(ts);
180: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181: Set runtime options
182: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183: TSSetFromOptions(ts);
185: TSSolve(ts,user.x);
187: VecGetArray(user.x,&x_ptr);
188: user.x_ob[0] = x_ptr[0];
189: user.x_ob[1] = x_ptr[1];
191: /* Create sensitivity variable */
192: MatCreateVecs(user.A,&user.lambda[0],NULL);
193: MatCreateVecs(user.A,&user.lambda[1],NULL);
195: /* Set initial solution guess */
196: MatCreateVecs(user.A,&ic,NULL);
197: VecGetArray(ic,&x_ptr);
198: x_ptr[0] = 2.2;
199: x_ptr[1] = -0.7;
200: VecRestoreArray(ic,&x_ptr);
202: TaoSetInitialVector(tao,ic);
204: /* Set routine for function and gradient evaluation */
205: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
207: /* Check for any TAO command line options */
208: TaoSetFromOptions(tao);
209: TaoGetKSP(tao,&ksp);
210: if (ksp) {
211: KSPGetPC(ksp,&pc);
212: PCSetType(pc,PCNONE);
213: }
215: /* SOLVE THE APPLICATION */
216: TaoSolve(tao);
218: VecView(ic,PETSC_VIEWER_STDOUT_WORLD);
219: /* Free TAO data structures */
220: TaoDestroy(&tao);
222: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
223: Free work space. All PETSc objects should be destroyed when they
224: are no longer needed.
225: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
226: MatDestroy(&user.A);
227: VecDestroy(&user.x);
228: VecDestroy(&user.lambda[0]);
229: VecDestroy(&user.lambda[1]);
230: TSDestroy(&ts);
231: VecDestroy(&ic);
232: PetscFinalize();
233: return ierr;
234: }
237: /* ------------------------------------------------------------------ */
238: /*
239: FormFunctionGradient - Evaluates the function and corresponding gradient.
241: Input Parameters:
242: tao - the Tao context
243: X - the input vector
244: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
246: Output Parameters:
247: f - the newly evaluated function
248: G - the newly evaluated gradient
249: */
250: PetscErrorCode FormFunctionGradient(Tao tao,Vec IC,PetscReal *f,Vec G,void *ctx)
251: {
252: User user_ptr = (User)ctx;
253: TS ts;
254: PetscScalar *x_ptr,*y_ptr;
258: VecCopy(IC,user_ptr->x);
260: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
261: Create timestepping solver context
262: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
263: TSCreate(PETSC_COMM_WORLD,&ts);
264: TSSetType(ts,TSCN);
265: TSSetIFunction(ts,NULL,IFunction,user_ptr);
266: TSSetIJacobian(ts,user_ptr->A,user_ptr->A,IJacobian,user_ptr);
268: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269: Set time
270: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
271: TSSetTime(ts,0.0);
272: TSSetMaxTime(ts,user_ptr->ftime);
273: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
274: TSSetTimeStep(ts,0.03125);
276: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
277: Save trajectory of solution so that TSAdjointSolve() may be used
278: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
279: TSSetSaveTrajectory(ts);
281: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
282: Set runtime options
283: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
284: TSSetFromOptions(ts);
286: TSSolve(ts,user_ptr->x);
287: VecGetArray(user_ptr->x,&x_ptr);
288: *f = (x_ptr[0]-user_ptr->x_ob[0])*(x_ptr[0]-user_ptr->x_ob[0])+(x_ptr[1]-user_ptr->x_ob[1])*(x_ptr[1]-user_ptr->x_ob[1]);
289: 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)x_ptr[0],(double)x_ptr[1],(double)(*f));
291: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
292: Adjoint model starts here
293: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
294: /* Redet initial conditions for the adjoint integration */
295: VecGetArray(user_ptr->lambda[0],&y_ptr);
296: y_ptr[0] = 2.*(x_ptr[0]-user_ptr->x_ob[0]);
297: y_ptr[1] = 2.*(x_ptr[1]-user_ptr->x_ob[1]);
298: VecRestoreArray(user_ptr->lambda[0],&y_ptr);
299: TSSetCostGradients(ts,1,user_ptr->lambda,NULL);
301: TSAdjointSolve(ts);
302: VecCopy(user_ptr->lambda[0],G);
303: TSDestroy(&ts);
304: return(0);
305: }
307: /*TEST
308: build:
309: requires: !complex !single
310: test:
311: args: -monitor 0 -ts_type theta -ts_theta_endpoint -ts_theta_theta 0.5 -viewer_binary_skip_info -tao_view -mu 1.0 -ts_trajectory_dirname ex20opt_icdir
312: output_file: output/ex20opt_ic_1.out
314: TEST*/