Actual source code: ex20opt_ic.c
petsc-3.7.5 2017-01-01
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: */
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: }
62: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
63: {
64: PetscErrorCode ierr;
65: User user = (User)ctx;
66: PetscInt rowcol[] = {0,1};
67: PetscScalar J[2][2];
68: const PetscScalar *x;
71: VecGetArrayRead(X,&x);
73: J[0][0] = a; J[0][1] = -1.0;
74: 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]);
76: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
77: VecRestoreArrayRead(X,&x);
79: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
80: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
81: if (A != B) {
82: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
83: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
84: }
85: return(0);
86: }
90: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
91: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
92: {
93: PetscErrorCode ierr;
94: const PetscScalar *x;
95: PetscReal tfinal, dt;
96: User user = (User)ctx;
97: Vec interpolatedX;
100: TSGetTimeStep(ts,&dt);
101: TSGetDuration(ts,NULL,&tfinal);
103: while (user->next_output <= t && user->next_output <= tfinal) {
104: VecDuplicate(X,&interpolatedX);
105: TSInterpolate(ts,user->next_output,interpolatedX);
106: VecGetArrayRead(interpolatedX,&x);
107: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
108: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
109: (double)PetscRealPart(x[1]));
110: VecRestoreArrayRead(interpolatedX,&x);
111: VecDestroy(&interpolatedX);
112: user->next_output += 0.1;
113: }
114: return(0);
115: }
119: int main(int argc,char **argv)
120: {
121: TS ts; /* nonlinear solver */
122: Vec ic;
123: PetscBool monitor = PETSC_FALSE;
124: PetscScalar *x_ptr;
125: PetscMPIInt size;
126: struct _n_User user;
127: PetscErrorCode ierr;
128: Tao tao;
129: KSP ksp;
130: PC pc;
132: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133: Initialize program
134: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135: PetscInitialize(&argc,&argv,NULL,help);
137: MPI_Comm_size(PETSC_COMM_WORLD,&size);
138: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
140: /* Create TAO solver and set desired solution method */
141: TaoCreate(PETSC_COMM_WORLD,&tao);
142: TaoSetType(tao,TAOCG);
144: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: Set runtime options
146: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147: user.next_output = 0.0;
148: user.mu = 1.0e6;
149: user.ftime = 0.5;
150: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
151: PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
153: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
154: Create necessary matrix and vectors, solve same ODE on every process
155: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
156: MatCreate(PETSC_COMM_WORLD,&user.A);
157: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
158: MatSetFromOptions(user.A);
159: MatSetUp(user.A);
160: MatCreateVecs(user.A,&user.x,NULL);
162: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: Create timestepping solver context
164: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
165: TSCreate(PETSC_COMM_WORLD,&ts);
166: TSSetType(ts,TSCN);
167: TSSetIFunction(ts,NULL,IFunction,&user);
168: TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
169: TSSetDuration(ts,PETSC_DEFAULT,user.ftime);
170: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
172: if (monitor) {
173: TSMonitorSet(ts,Monitor,&user,NULL);
174: }
176: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: Set initial conditions
178: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
179: VecGetArray(user.x,&x_ptr);
180: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
181: VecRestoreArray(user.x,&x_ptr);
182: TSSetInitialTimeStep(ts,0.0,.0001);
184: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Save trajectory of solution so that TSAdjointSolve() may be used
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
187: TSSetSaveTrajectory(ts);
189: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: Set runtime options
191: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
192: TSSetFromOptions(ts);
194: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195: Solve nonlinear system
196: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
197: TSSolve(ts,user.x);
199: VecGetArray(user.x,&x_ptr);
200: user.x_ob[0] = x_ptr[0];
201: user.x_ob[1] = x_ptr[1];
203: /* Create sensitivity variable */
204: MatCreateVecs(user.A,&user.lambda[0],NULL);
205: MatCreateVecs(user.A,&user.lambda[1],NULL);
207: /* Set initial solution guess */
208: MatCreateVecs(user.A,&ic,NULL);
209: VecGetArray(ic,&x_ptr);
210: x_ptr[0] = 2.1;
211: x_ptr[1] = -0.66666654321;
212: VecRestoreArray(ic,&x_ptr);
214: TaoSetInitialVector(tao,ic);
216: /* Set routine for function and gradient evaluation */
217: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
219: /* Check for any TAO command line options */
220: TaoSetFromOptions(tao);
221: TaoGetKSP(tao,&ksp);
222: if (ksp) {
223: KSPGetPC(ksp,&pc);
224: PCSetType(pc,PCNONE);
225: }
227: TaoSetTolerances(tao,1e-10,PETSC_DEFAULT,PETSC_DEFAULT);
229: /* SOLVE THE APPLICATION */
230: TaoSolve(tao);
232: VecView(ic,PETSC_VIEWER_STDOUT_WORLD);
233: /* Free TAO data structures */
234: TaoDestroy(&tao);
236: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
237: Free work space. All PETSc objects should be destroyed when they
238: are no longer needed.
239: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
240: MatDestroy(&user.A);
241: VecDestroy(&user.x);
242: VecDestroy(&user.lambda[0]);
243: VecDestroy(&user.lambda[1]);
244: TSDestroy(&ts);
246: VecDestroy(&ic);
247: PetscFinalize();
248: return(0);
249: }
252: /* ------------------------------------------------------------------ */
255: /*
256: FormFunctionGradient - Evaluates the function and corresponding gradient.
258: Input Parameters:
259: tao - the Tao context
260: X - the input vector
261: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
263: Output Parameters:
264: f - the newly evaluated function
265: G - the newly evaluated gradient
266: */
267: PetscErrorCode FormFunctionGradient(Tao tao,Vec IC,PetscReal *f,Vec G,void *ctx)
268: {
269: User user_ptr = (User)ctx;
270: TS ts;
271: PetscScalar *x_ptr,*y_ptr;
274: VecCopy(IC,user_ptr->x);
276: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
277: Create timestepping solver context
278: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
279: TSCreate(PETSC_COMM_WORLD,&ts);
280: TSSetType(ts,TSCN);
281: TSSetIFunction(ts,NULL,IFunction,user_ptr);
282: TSSetIJacobian(ts,user_ptr->A,user_ptr->A,IJacobian,user_ptr);
284: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
285: Set time
286: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
287: TSSetTime(ts,0.0);
288: TSSetDuration(ts,PETSC_DEFAULT,0.5);
289: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
291: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
292: Save trajectory of solution so that TSAdjointSolve() may be used
293: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
294: TSSetSaveTrajectory(ts);
296: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
297: Set runtime options
298: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
299: TSSetFromOptions(ts);
301: TSSolve(ts,user_ptr->x);
302: VecGetArray(user_ptr->x,&x_ptr);
303: *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]);
304: PetscPrintf(PETSC_COMM_WORLD,"Observed value y_ob=[%f; %f], ODE solution y=[%f;%f], Cost function f=%f\n",(double)user_ptr->x_ob[0],(double)user_ptr->x_ob[1],(double)x_ptr[0],(double)x_ptr[1],(double)(*f));
306: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
307: Adjoint model starts here
308: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
309: /* Redet initial conditions for the adjoint integration */
310: VecGetArray(user_ptr->lambda[0],&y_ptr);
311: y_ptr[0] = 2.*(x_ptr[0]-user_ptr->x_ob[0]);
312: y_ptr[1] = 2.*(x_ptr[1]-user_ptr->x_ob[1]);
313: VecRestoreArray(user_ptr->lambda[0],&y_ptr);
314: TSSetCostGradients(ts,1,user_ptr->lambda,NULL);
316: TSAdjointSolve(ts);
317: VecCopy(user_ptr->lambda[0],G);
318: TSDestroy(&ts);
319: return(0);
320: }