Actual source code: ex20opt_p.c
petsc-3.8.4 2018-03-24
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: */
44: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
45: {
46: PetscErrorCode ierr;
47: User user = (User)ctx;
48: PetscScalar *f;
49: const PetscScalar *x,*xdot;
52: VecGetArrayRead(X,&x);
53: VecGetArrayRead(Xdot,&xdot);
54: VecGetArray(F,&f);
55: f[0] = xdot[0] - x[1];
56: f[1] = c21*(xdot[0]-x[1]) + xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]) ;
57: VecRestoreArrayRead(X,&x);
58: VecRestoreArrayRead(Xdot,&xdot);
59: VecRestoreArray(F,&f);
60: return(0);
61: }
63: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
64: {
65: PetscErrorCode ierr;
66: User user = (User)ctx;
67: PetscInt rowcol[] = {0,1};
68: PetscScalar J[2][2];
69: 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: }
88: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
89: {
90: PetscErrorCode ierr;
91: PetscInt row[] = {0,1},col[]={0};
92: PetscScalar J[2][1];
93: const PetscScalar *x;
95: VecGetArrayRead(X,&x);
97: J[0][0] = 0;
98: J[1][0] = (1.-x[0]*x[0])*x[1]-x[0];
99: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
100: VecRestoreArrayRead(X,&x);
102: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
103: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
104: return(0);
105: }
107: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
108: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
109: {
110: PetscErrorCode ierr;
111: const PetscScalar *x;
112: PetscReal tfinal, dt;
113: User user = (User)ctx;
114: Vec interpolatedX;
117: TSGetTimeStep(ts,&dt);
118: TSGetMaxTime(ts,&tfinal);
120: while (user->next_output <= t && user->next_output <= tfinal) {
121: VecDuplicate(X,&interpolatedX);
122: TSInterpolate(ts,user->next_output,interpolatedX);
123: VecGetArrayRead(interpolatedX,&x);
124: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
125: user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(x[0]),
126: (double)PetscRealPart(x[1]));
127: VecRestoreArrayRead(interpolatedX,&x);
128: VecDestroy(&interpolatedX);
129: user->next_output += 0.1;
130: }
131: return(0);
132: }
134: int main(int argc,char **argv)
135: {
136: TS ts; /* nonlinear solver */
137: Vec p;
138: PetscBool monitor = PETSC_FALSE;
139: PetscScalar *x_ptr;
140: const PetscScalar *y_ptr;
141: PetscMPIInt size;
142: struct _n_User user;
143: PetscErrorCode ierr;
144: Tao tao;
145: KSP ksp;
146: PC pc;
148: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: Initialize program
150: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
151: PetscInitialize(&argc,&argv,NULL,help);
152: MPI_Comm_size(PETSC_COMM_WORLD,&size);
153: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
155: /* Create TAO solver and set desired solution method */
156: TaoCreate(PETSC_COMM_WORLD,&tao);
157: TaoSetType(tao,TAOBLMVM);
159: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: Set runtime options
161: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
162: user.next_output = 0.0;
163: user.mu = 1.0;
164: user.ftime = 1.0;
165: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
166: PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
168: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
169: Create necessary matrix and vectors, solve same ODE on every process
170: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
171: MatCreate(PETSC_COMM_WORLD,&user.A);
172: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
173: MatSetFromOptions(user.A);
174: MatSetUp(user.A);
175: MatCreateVecs(user.A,&user.x,NULL);
177: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
178: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
179: MatSetFromOptions(user.Jacp);
180: MatSetUp(user.Jacp);
182: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
183: Create timestepping solver context
184: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
185: TSCreate(PETSC_COMM_WORLD,&ts);
186: TSSetType(ts,TSCN);
187: TSSetIFunction(ts,NULL,IFunction,&user);
188: TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
189: TSSetMaxTime(ts,user.ftime);
190: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
191: if (monitor) {
192: TSMonitorSet(ts,Monitor,&user,NULL);
193: }
195: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: Set initial conditions
197: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198: VecGetArray(user.x,&x_ptr);
199: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
200: VecRestoreArray(user.x,&x_ptr);
201: TSSetTimeStep(ts,0.03125);
203: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204: Set runtime options
205: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
206: TSSetFromOptions(ts);
208: TSSolve(ts,user.x);
210: VecGetArrayRead(user.x,&y_ptr);
211: user.x_ob[0] = y_ptr[0];
212: user.x_ob[1] = y_ptr[1];
213: VecRestoreArrayRead(user.x,&y_ptr);
215: /* Create sensitivity variable */
216: MatCreateVecs(user.A,&user.lambda[0],NULL);
217: MatCreateVecs(user.Jacp,&user.mup[0],NULL);
219: /*
220: Optimization starts
221: */
222: /* Set initial solution guess */
223: MatCreateVecs(user.Jacp,&p,NULL);
224: VecGetArray(p,&x_ptr);
225: x_ptr[0] = 1.2;
226: VecRestoreArray(p,&x_ptr);
227: TaoSetInitialVector(tao,p);
229: /* Set routine for function and gradient evaluation */
230: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
232: /* Check for any TAO command line options */
233: TaoSetFromOptions(tao);
234: TaoGetKSP(tao,&ksp);
235: if (ksp) {
236: KSPGetPC(ksp,&pc);
237: PCSetType(pc,PCNONE);
238: }
240: TaoSolve(tao);
242: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
243: /* Free TAO data structures */
244: TaoDestroy(&tao);
246: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
247: Free work space. All PETSc objects should be destroyed when they
248: are no longer needed.
249: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
250: MatDestroy(&user.A);
251: MatDestroy(&user.Jacp);
252: VecDestroy(&user.x);
253: VecDestroy(&user.lambda[0]);
254: VecDestroy(&user.mup[0]);
255: TSDestroy(&ts);
256: VecDestroy(&p);
257: PetscFinalize();
258: return ierr;
259: }
262: /* ------------------------------------------------------------------ */
263: /*
264: FormFunctionGradient - Evaluates the function and corresponding gradient.
266: Input Parameters:
267: tao - the Tao context
268: X - the input vector
269: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
271: Output Parameters:
272: f - the newly evaluated function
273: G - the newly evaluated gradient
274: */
275: PetscErrorCode FormFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx)
276: {
277: User user_ptr = (User)ctx;
278: TS ts;
279: PetscScalar *x_ptr;
280: const PetscScalar *y_ptr;
281: PetscErrorCode ierr;
283: VecGetArrayRead(P,&y_ptr);
284: user_ptr->mu = y_ptr[0];
285: VecRestoreArrayRead(P,&y_ptr);
287: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
288: Create timestepping solver context
289: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
290: TSCreate(PETSC_COMM_WORLD,&ts);
291: TSSetType(ts,TSCN);
292: TSSetIFunction(ts,NULL,IFunction,user_ptr);
293: TSSetIJacobian(ts,user_ptr->A,user_ptr->A,IJacobian,user_ptr);
294: TSAdjointSetRHSJacobian(ts,user_ptr->Jacp,RHSJacobianP,user_ptr);
296: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
297: Set time
298: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
299: TSSetTime(ts,0.0);
300: TSSetMaxTime(ts,user_ptr->ftime);
301: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
303: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
304: Save trajectory of solution so that TSAdjointSolve() may be used
305: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
306: TSSetSaveTrajectory(ts);
308: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
309: Set initial conditions
310: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
311: VecGetArray(user_ptr->x,&x_ptr);
312: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
313: VecRestoreArray(user_ptr->x,&x_ptr);
315: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
316: Set runtime options
317: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
318: TSSetFromOptions(ts);
320: TSSolve(ts,user_ptr->x);
321: VecGetArrayRead(user_ptr->x,&y_ptr);
322: *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]);
323: 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));
324: /* Redet initial conditions for the adjoint integration */
325: VecGetArray(user_ptr->lambda[0],&x_ptr);
326: x_ptr[0] = rescale*2.*(y_ptr[0]-user_ptr->x_ob[0]);
327: x_ptr[1] = rescale*2.*(y_ptr[1]-user_ptr->x_ob[1]);
328: VecRestoreArrayRead(user_ptr->x,&y_ptr);
329: VecRestoreArray(user_ptr->lambda[0],&x_ptr);
331: VecGetArray(user_ptr->mup[0],&x_ptr);
332: x_ptr[0] = 0.0;
333: VecRestoreArray(user_ptr->mup[0],&x_ptr);
334: TSSetCostGradients(ts,1,user_ptr->lambda,user_ptr->mup);
336: TSAdjointSolve(ts);
337: VecCopy(user_ptr->mup[0],G);
338: TSDestroy(&ts);
339: return(0);
340: }