Actual source code: ex20opt_p.c
petsc-3.6.4 2016-04-12
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: This program solves the van der Pol DAE ODE equivalent
19: y' = z (1)
20: z' = mu[(1-y^2)z-y]
21: on the domain 0 <= x <= 1, with the boundary conditions
22: y(0) = 2, y'(0) = -6.666665432100101e-01,
23: and
24: mu = 10^6.
25: This is a nonlinear equation.
27: Notes:
28: This code demonstrates the TS solver interface to a variant of
29: linear problems, u_t = f(u,t), namely turning (1) into a system of
30: first order differential equations,
32: [ y' ] = [ z ]
33: [ z' ] [ mu[(1-y^2)z-y] ]
35: which then we can write as a vector equation
37: [ u_1' ] = [ u_2 ] (2)
38: [ u_2' ] [ mu[(1-u_1^2)u_2-u_1] ]
40: which is now in the desired form of u_t = f(u,t).
41: ------------------------------------------------------------------------- */
42: #include <petsctao.h>
43: #include <petscts.h>
45: typedef struct _n_User *User;
46: struct _n_User {
47: PetscReal mu;
48: PetscReal next_output;
49:
50: /* Sensitivity analysis support */
51: PetscReal ftime,x_ob[2];
52: Mat A; /* Jacobian matrix */
53: Mat Jacp; /* JacobianP matrix */
54: Vec x,lambda[2],mup[2]; /* adjoint variables */
55: };
57: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
59: /*
60: * User-defined routines
61: */
64: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
65: {
66: PetscErrorCode ierr;
67: User user = (User)ctx;
68: PetscScalar *f;
69: const PetscScalar *x,*xdot;
72: VecGetArrayRead(X,&x);
73: VecGetArrayRead(Xdot,&xdot);
74: VecGetArray(F,&f);
75: f[0] = xdot[0] - x[1];
76: f[1] = c21*(xdot[0]-x[1]) + xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]) ;
77: VecRestoreArrayRead(X,&x);
78: VecRestoreArrayRead(Xdot,&xdot);
79: VecRestoreArray(F,&f);
80: return(0);
81: }
85: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
86: {
87: PetscErrorCode ierr;
88: User user = (User)ctx;
89: PetscInt rowcol[] = {0,1};
90: PetscScalar J[2][2];
91: const PetscScalar *x;
93: VecGetArrayRead(X,&x);
95: J[0][0] = a; J[0][1] = -1.0;
96: 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]);
97:
98: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
99: VecRestoreArrayRead(X,&x);
101: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
102: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
103: if (A != B) {
104: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
105: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
106: }
107: return(0);
108: }
112: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
113: {
114: PetscErrorCode ierr;
115: PetscInt row[] = {0,1},col[]={0};
116: PetscScalar J[2][1];
117: const PetscScalar *x;
119: VecGetArrayRead(X,&x);
121: J[0][0] = 0;
122: J[1][0] = (1.-x[0]*x[0])*x[1]-x[0];
123: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
124: VecRestoreArrayRead(X,&x);
126: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
127: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
128: return(0);
129: }
133: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
134: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
135: {
136: PetscErrorCode ierr;
137: const PetscScalar *x;
138: PetscReal tfinal, dt;
139: User user = (User)ctx;
140: Vec interpolatedX;
143: TSGetTimeStep(ts,&dt);
144: TSGetDuration(ts,NULL,&tfinal);
146: while (user->next_output <= t && user->next_output <= tfinal) {
147: VecDuplicate(X,&interpolatedX);
148: TSInterpolate(ts,user->next_output,interpolatedX);
149: VecGetArrayRead(interpolatedX,&x);
150: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
151: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
152: (double)PetscRealPart(x[1]));
153: VecRestoreArrayRead(interpolatedX,&x);
154: VecDestroy(&interpolatedX);
155: user->next_output += 0.1;
156: }
157: return(0);
158: }
162: int main(int argc,char **argv)
163: {
164: TS ts; /* nonlinear solver */
165: Vec p;
166: PetscBool monitor = PETSC_FALSE;
167: PetscScalar *x_ptr;
168: const PetscScalar *y_ptr;
169: PetscMPIInt size;
170: struct _n_User user;
171: PetscErrorCode ierr;
172: Tao tao;
173: TaoConvergedReason reason;
174: KSP ksp;
175: PC pc;
177: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: Initialize program
179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
180: PetscInitialize(&argc,&argv,NULL,help);
181:
182: MPI_Comm_size(PETSC_COMM_WORLD,&size);
183: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
185: /* Create TAO solver and set desired solution method */
186: TaoCreate(PETSC_COMM_WORLD,&tao);
187: TaoSetType(tao,TAOCG);
189: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: Set runtime options
191: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
192: user.next_output = 0.0;
193: user.mu = 1.0;
194: user.ftime = 0.5;
195: PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);
196: PetscOptionsGetReal(NULL,"-mu",&user.mu,NULL);
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Create necessary matrix and vectors, solve same ODE on every process
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: MatCreate(PETSC_COMM_WORLD,&user.A);
202: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
203: MatSetFromOptions(user.A);
204: MatSetUp(user.A);
205: MatCreateVecs(user.A,&user.x,NULL);
207: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
208: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
209: MatSetFromOptions(user.Jacp);
210: MatSetUp(user.Jacp);
212: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
213: Create timestepping solver context
214: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
215: TSCreate(PETSC_COMM_WORLD,&ts);
216: TSSetType(ts,TSCN);
217: TSSetIFunction(ts,NULL,IFunction,&user);
218: TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
219: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
220: TSSetDuration(ts,PETSC_DEFAULT,user.ftime);
221: if (monitor) {
222: TSMonitorSet(ts,Monitor,&user,NULL);
223: }
225: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: Set initial conditions
227: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
228: VecGetArray(user.x,&x_ptr);
229: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
230: VecRestoreArray(user.x,&x_ptr);
231: TSSetInitialTimeStep(ts,0.0,.0001);
233: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
234: Set runtime options
235: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
236: TSSetFromOptions(ts);
238: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
239: Solve nonlinear system
240: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
241: TSSolve(ts,user.x);
243: VecGetArrayRead(user.x,&y_ptr);
244: user.x_ob[0] = y_ptr[0];
245: user.x_ob[1] = y_ptr[1];
246: VecRestoreArrayRead(user.x,&y_ptr);
248: /* Create sensitivity variable */
249: MatCreateVecs(user.A,&user.lambda[0],NULL);
250: MatCreateVecs(user.Jacp,&user.mup[0],NULL);
252: /*
253: Optimization starts
254: */
255: /* Set initial solution guess */
256: MatCreateVecs(user.Jacp,&p,NULL);
257: VecGetArray(p,&x_ptr);
258: x_ptr[0] = 1.2;
259: VecRestoreArray(p,&x_ptr);
260: TaoSetInitialVector(tao,p);
262: /* Set routine for function and gradient evaluation */
263: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
265: /* Check for any TAO command line options */
266: TaoSetFromOptions(tao);
267: TaoGetKSP(tao,&ksp);
268: if (ksp) {
269: KSPGetPC(ksp,&pc);
270: PCSetType(pc,PCNONE);
271: }
273: TaoSetTolerances(tao,1e-7,1e-7,1e-7,1e-7,1e-7);
275: TaoSolve(tao);
276: /* Get information on termination */
277: TaoGetConvergedReason(tao,&reason);
278: if (reason <= 0){
279: ierr=PetscPrintf(MPI_COMM_WORLD, "Try another method! \n");
280: }
281: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
282: /* Free TAO data structures */
283: TaoDestroy(&tao);
285: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
286: Free work space. All PETSc objects should be destroyed when they
287: are no longer needed.
288: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
289: MatDestroy(&user.A);
290: MatDestroy(&user.Jacp);
291: VecDestroy(&user.x);
292: VecDestroy(&user.lambda[0]);
293: VecDestroy(&user.mup[0]);
294: TSDestroy(&ts);
295: VecDestroy(&p);
296: PetscFinalize();
297: return(0);
298: }
301: /* ------------------------------------------------------------------ */
304: /*
305: FormFunctionGradient - Evaluates the function and corresponding gradient.
307: Input Parameters:
308: tao - the Tao context
309: X - the input vector
310: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
312: Output Parameters:
313: f - the newly evaluated function
314: G - the newly evaluated gradient
315: */
316: PetscErrorCode FormFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx)
317: {
318: User user_ptr = (User)ctx;
319: TS ts;
320: PetscScalar *x_ptr;
321: const PetscScalar *y_ptr;
322: PetscErrorCode ierr;
324: VecGetArrayRead(P,&y_ptr);
325: user_ptr->mu = y_ptr[0];
326: VecRestoreArrayRead(P,&y_ptr);
328: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
329: Create timestepping solver context
330: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
331: TSCreate(PETSC_COMM_WORLD,&ts);
332: TSSetType(ts,TSCN);
333: TSSetIFunction(ts,NULL,IFunction,user_ptr);
334: TSSetIJacobian(ts,user_ptr->A,user_ptr->A,IJacobian,user_ptr);
335: TSAdjointSetRHSJacobian(ts,user_ptr->Jacp,RHSJacobianP,user_ptr);
336: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
338: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
339: Set time
340: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
341: TSSetTime(ts,0.0);
342: TSSetDuration(ts,PETSC_DEFAULT,0.5);
344: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
345: Save trajectory of solution so that TSAdjointSolve() may be used
346: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
347: TSSetSaveTrajectory(ts);
349: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
350: Set initial conditions
351: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
352: VecGetArray(user_ptr->x,&x_ptr);
353: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
354: VecRestoreArray(user_ptr->x,&x_ptr);
355:
356: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
357: Set runtime options
358: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
359: TSSetFromOptions(ts);
361: TSSolve(ts,user_ptr->x);
362: VecGetArrayRead(user_ptr->x,&y_ptr);
363: *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]);
364: 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));
365: /* Redet initial conditions for the adjoint integration */
366: VecGetArray(user_ptr->lambda[0],&x_ptr);
367: x_ptr[0] = rescale*2.*(y_ptr[0]-user_ptr->x_ob[0]);
368: x_ptr[1] = rescale*2.*(y_ptr[1]-user_ptr->x_ob[1]);
369: VecRestoreArrayRead(user_ptr->x,&y_ptr);
370: VecRestoreArray(user_ptr->lambda[0],&x_ptr);
372: VecGetArray(user_ptr->mup[0],&x_ptr);
373: x_ptr[0] = 0.0;
374: VecRestoreArray(user_ptr->mup[0],&x_ptr);
375: TSSetCostGradients(ts,1,user_ptr->lambda,user_ptr->mup);
377: TSAdjointSolve(ts);
378: VecCopy(user_ptr->mup[0],G);
379: TSDestroy(&ts);
380: return(0);
381: }