Actual source code: ex20opt_p.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: #define rescale 10
7: static char help[] = "Solves the van der Pol equation.\n\
8: Input parameters include:\n";
10: /*
11: Concepts: TS^time-dependent nonlinear problems
12: Concepts: TS^van der Pol equation DAE equivalent
13: Concepts: Optimization using adjoint sensitivity analysis
14: Processors: 1
15: */
16: /* ------------------------------------------------------------------------
18: Notes:
19: This code demonstrates how to solve a DAE-constrained optimization problem with TAO, TSAdjoint and TS.
20: The nonlinear problem is written in a DAE equivalent form.
21: The objective is to minimize the difference between observation and model prediction by finding an optimal value for parameter \mu.
22: The gradient is computed with the discrete adjoint of an implicit theta method, see ex20adj.c for details.
23: ------------------------------------------------------------------------- */
24: #include <petsctao.h>
25: #include <petscts.h>
27: typedef struct _n_User *User;
28: struct _n_User {
29: PetscReal mu;
30: PetscReal next_output;
32: /* Sensitivity analysis support */
33: PetscReal ftime,x_ob[2];
34: Mat A; /* Jacobian matrix */
35: Mat Jacp; /* JacobianP matrix */
36: Vec x,lambda[2],mup[2]; /* adjoint variables */
37: };
39: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
41: /*
42: * User-defined routines
43: */
46: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
47: {
48: PetscErrorCode ierr;
49: User user = (User)ctx;
50: PetscScalar *f;
51: const PetscScalar *x,*xdot;
54: VecGetArrayRead(X,&x);
55: VecGetArrayRead(Xdot,&xdot);
56: VecGetArray(F,&f);
57: f[0] = xdot[0] - x[1];
58: f[1] = c21*(xdot[0]-x[1]) + xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]) ;
59: VecRestoreArrayRead(X,&x);
60: VecRestoreArrayRead(Xdot,&xdot);
61: VecRestoreArray(F,&f);
62: return(0);
63: }
67: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
68: {
69: PetscErrorCode ierr;
70: User user = (User)ctx;
71: PetscInt rowcol[] = {0,1};
72: PetscScalar J[2][2];
73: const PetscScalar *x;
75: VecGetArrayRead(X,&x);
77: J[0][0] = a; J[0][1] = -1.0;
78: 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]);
80: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
81: VecRestoreArrayRead(X,&x);
83: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
84: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
85: if (A != B) {
86: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
87: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
88: }
89: return(0);
90: }
94: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
95: {
96: PetscErrorCode ierr;
97: PetscInt row[] = {0,1},col[]={0};
98: PetscScalar J[2][1];
99: const PetscScalar *x;
101: VecGetArrayRead(X,&x);
103: J[0][0] = 0;
104: J[1][0] = (1.-x[0]*x[0])*x[1]-x[0];
105: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
106: VecRestoreArrayRead(X,&x);
108: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
109: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
110: return(0);
111: }
115: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
116: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
117: {
118: PetscErrorCode ierr;
119: const PetscScalar *x;
120: PetscReal tfinal, dt;
121: User user = (User)ctx;
122: Vec interpolatedX;
125: TSGetTimeStep(ts,&dt);
126: TSGetDuration(ts,NULL,&tfinal);
128: while (user->next_output <= t && user->next_output <= tfinal) {
129: VecDuplicate(X,&interpolatedX);
130: TSInterpolate(ts,user->next_output,interpolatedX);
131: VecGetArrayRead(interpolatedX,&x);
132: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
133: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
134: (double)PetscRealPart(x[1]));
135: VecRestoreArrayRead(interpolatedX,&x);
136: VecDestroy(&interpolatedX);
137: user->next_output += 0.1;
138: }
139: return(0);
140: }
144: int main(int argc,char **argv)
145: {
146: TS ts; /* nonlinear solver */
147: Vec p;
148: PetscBool monitor = PETSC_FALSE;
149: PetscScalar *x_ptr;
150: const PetscScalar *y_ptr;
151: PetscMPIInt size;
152: struct _n_User user;
153: PetscErrorCode ierr;
154: Tao tao;
155: KSP ksp;
156: PC pc;
158: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
159: Initialize program
160: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
161: PetscInitialize(&argc,&argv,NULL,help);
163: MPI_Comm_size(PETSC_COMM_WORLD,&size);
164: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
166: /* Create TAO solver and set desired solution method */
167: TaoCreate(PETSC_COMM_WORLD,&tao);
168: TaoSetType(tao,TAOCG);
170: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171: Set runtime options
172: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
173: user.next_output = 0.0;
174: user.mu = 1.0;
175: user.ftime = 0.5;
176: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
177: PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
179: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
180: Create necessary matrix and vectors, solve same ODE on every process
181: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
182: MatCreate(PETSC_COMM_WORLD,&user.A);
183: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
184: MatSetFromOptions(user.A);
185: MatSetUp(user.A);
186: MatCreateVecs(user.A,&user.x,NULL);
188: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
189: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
190: MatSetFromOptions(user.Jacp);
191: MatSetUp(user.Jacp);
193: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: Create timestepping solver context
195: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196: TSCreate(PETSC_COMM_WORLD,&ts);
197: TSSetType(ts,TSCN);
198: TSSetIFunction(ts,NULL,IFunction,&user);
199: TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
200: TSSetDuration(ts,PETSC_DEFAULT,user.ftime);
201: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
202: if (monitor) {
203: TSMonitorSet(ts,Monitor,&user,NULL);
204: }
206: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
207: Set initial conditions
208: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
209: VecGetArray(user.x,&x_ptr);
210: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
211: VecRestoreArray(user.x,&x_ptr);
212: TSSetInitialTimeStep(ts,0.0,.0001);
214: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
215: Set runtime options
216: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
217: TSSetFromOptions(ts);
219: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
220: Solve nonlinear system
221: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
222: TSSolve(ts,user.x);
224: VecGetArrayRead(user.x,&y_ptr);
225: user.x_ob[0] = y_ptr[0];
226: user.x_ob[1] = y_ptr[1];
227: VecRestoreArrayRead(user.x,&y_ptr);
229: /* Create sensitivity variable */
230: MatCreateVecs(user.A,&user.lambda[0],NULL);
231: MatCreateVecs(user.Jacp,&user.mup[0],NULL);
233: /*
234: Optimization starts
235: */
236: /* Set initial solution guess */
237: MatCreateVecs(user.Jacp,&p,NULL);
238: VecGetArray(p,&x_ptr);
239: x_ptr[0] = 1.2;
240: VecRestoreArray(p,&x_ptr);
241: TaoSetInitialVector(tao,p);
243: /* Set routine for function and gradient evaluation */
244: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
246: /* Check for any TAO command line options */
247: TaoSetFromOptions(tao);
248: TaoGetKSP(tao,&ksp);
249: if (ksp) {
250: KSPGetPC(ksp,&pc);
251: PCSetType(pc,PCNONE);
252: }
254: TaoSetTolerances(tao,1e-7,1e-7,1e-7);
256: TaoSolve(tao);
258: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
259: /* Free TAO data structures */
260: TaoDestroy(&tao);
262: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
263: Free work space. All PETSc objects should be destroyed when they
264: are no longer needed.
265: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
266: MatDestroy(&user.A);
267: MatDestroy(&user.Jacp);
268: VecDestroy(&user.x);
269: VecDestroy(&user.lambda[0]);
270: VecDestroy(&user.mup[0]);
271: TSDestroy(&ts);
272: VecDestroy(&p);
273: PetscFinalize();
274: return(0);
275: }
278: /* ------------------------------------------------------------------ */
281: /*
282: FormFunctionGradient - Evaluates the function and corresponding gradient.
284: Input Parameters:
285: tao - the Tao context
286: X - the input vector
287: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
289: Output Parameters:
290: f - the newly evaluated function
291: G - the newly evaluated gradient
292: */
293: PetscErrorCode FormFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx)
294: {
295: User user_ptr = (User)ctx;
296: TS ts;
297: PetscScalar *x_ptr;
298: const PetscScalar *y_ptr;
299: PetscErrorCode ierr;
301: VecGetArrayRead(P,&y_ptr);
302: user_ptr->mu = y_ptr[0];
303: VecRestoreArrayRead(P,&y_ptr);
305: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
306: Create timestepping solver context
307: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
308: TSCreate(PETSC_COMM_WORLD,&ts);
309: TSSetType(ts,TSCN);
310: TSSetIFunction(ts,NULL,IFunction,user_ptr);
311: TSSetIJacobian(ts,user_ptr->A,user_ptr->A,IJacobian,user_ptr);
312: TSAdjointSetRHSJacobian(ts,user_ptr->Jacp,RHSJacobianP,user_ptr);
314: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
315: Set time
316: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
317: TSSetTime(ts,0.0);
318: TSSetDuration(ts,PETSC_DEFAULT,0.5);
319: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
321: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
322: Save trajectory of solution so that TSAdjointSolve() may be used
323: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
324: TSSetSaveTrajectory(ts);
326: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
327: Set initial conditions
328: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
329: VecGetArray(user_ptr->x,&x_ptr);
330: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
331: VecRestoreArray(user_ptr->x,&x_ptr);
333: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
334: Set runtime options
335: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
336: TSSetFromOptions(ts);
338: TSSolve(ts,user_ptr->x);
339: VecGetArrayRead(user_ptr->x,&y_ptr);
340: *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]);
341: 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)y_ptr[0],(double)y_ptr[1],(double)(*f));
342: /* Redet initial conditions for the adjoint integration */
343: VecGetArray(user_ptr->lambda[0],&x_ptr);
344: x_ptr[0] = rescale*2.*(y_ptr[0]-user_ptr->x_ob[0]);
345: x_ptr[1] = rescale*2.*(y_ptr[1]-user_ptr->x_ob[1]);
346: VecRestoreArrayRead(user_ptr->x,&y_ptr);
347: VecRestoreArray(user_ptr->lambda[0],&x_ptr);
349: VecGetArray(user_ptr->mup[0],&x_ptr);
350: x_ptr[0] = 0.0;
351: VecRestoreArray(user_ptr->mup[0],&x_ptr);
352: TSSetCostGradients(ts,1,user_ptr->lambda,user_ptr->mup);
354: TSAdjointSolve(ts);
355: VecCopy(user_ptr->mup[0],G);
356: TSDestroy(&ts);
357: return(0);
358: }