Actual source code: ex20opt_ic.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: static char help[] = "Solves the van der Pol equation.\n\
6: Input parameters include:\n";
8: /*
9: Concepts: TS^time-dependent nonlinear problems
10: Concepts: TS^van der Pol equation DAE equivalent
11: Concepts: Optimization using adjoint sensitivity analysis
12: Processors: 1
13: */
14: /* ------------------------------------------------------------------------
16: This program solves the van der Pol DAE ODE equivalent
17: y' = z (1)
18: z' = mu[(1-y^2)z-y]
19: on the domain 0 <= x <= 1, with the boundary conditions
20: y(0) = 2, y'(0) = -6.666665432100101e-01,
21: and
22: mu = 10^6.
23: This is a nonlinear equation.
25: Notes:
26: This code demonstrates the TS solver interface to a variant of
27: linear problems, u_t = f(u,t), namely turning (1) into a system of
28: first order differential equations,
30: [ y' ] = [ z ]
31: [ z' ] [ mu[(1-y^2)z-y] ]
33: which then we can write as a vector equation
35: [ u_1' ] = [ u_2 ] (2)
36: [ u_2' ] [ mu[(1-u_1^2)u_2-u_1] ]
38: which is now in the desired form of u_t = f(u,t).
40: ------------------------------------------------------------------------- */
41: #include <petsctao.h>
42: #include <petscts.h>
44: typedef struct _n_User *User;
45: struct _n_User {
46: PetscReal mu;
47: PetscReal next_output;
48:
49: /* Sensitivity analysis support */
50: PetscReal ftime,x_ob[2];
51: Mat A; /* Jacobian matrix */
52: Vec x,lambda[2]; /* adjoint variables */
53: };
55: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
57: /*
58: * User-defined routines
59: */
62: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
63: {
64: PetscErrorCode ierr;
65: User user = (User)ctx;
66: PetscScalar *f;
67: const PetscScalar *x,*xdot;
70: VecGetArrayRead(X,&x);
71: VecGetArrayRead(Xdot,&xdot);
72: VecGetArray(F,&f);
73: f[0] = xdot[0] - x[1];
74: f[1] = c21*(xdot[0]-x[1]) + xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]) ;
75: VecRestoreArrayRead(X,&x);
76: VecRestoreArrayRead(Xdot,&xdot);
77: VecRestoreArray(F,&f);
78: return(0);
79: }
83: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
84: {
85: PetscErrorCode ierr;
86: User user = (User)ctx;
87: PetscInt rowcol[] = {0,1};
88: PetscScalar J[2][2];
89: const PetscScalar *x;
92: VecGetArrayRead(X,&x);
94: J[0][0] = a; J[0][1] = -1.0;
95: 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]);
96:
97: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
98: VecRestoreArrayRead(X,&x);
100: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
101: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
102: if (A != B) {
103: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
104: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
105: }
106: return(0);
107: }
111: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
112: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
113: {
114: PetscErrorCode ierr;
115: const PetscScalar *x;
116: PetscReal tfinal, dt;
117: User user = (User)ctx;
118: Vec interpolatedX;
121: TSGetTimeStep(ts,&dt);
122: TSGetDuration(ts,NULL,&tfinal);
124: while (user->next_output <= t && user->next_output <= tfinal) {
125: VecDuplicate(X,&interpolatedX);
126: TSInterpolate(ts,user->next_output,interpolatedX);
127: VecGetArrayRead(interpolatedX,&x);
128: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
129: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
130: (double)PetscRealPart(x[1]));
131: VecRestoreArrayRead(interpolatedX,&x);
132: VecDestroy(&interpolatedX);
133: user->next_output += 0.1;
134: }
135: return(0);
136: }
140: int main(int argc,char **argv)
141: {
142: TS ts; /* nonlinear solver */
143: Vec ic;
144: PetscBool monitor = PETSC_FALSE;
145: PetscScalar *x_ptr;
146: PetscMPIInt size;
147: struct _n_User user;
148: PetscErrorCode ierr;
149: Tao tao;
150: TaoConvergedReason reason;
151: KSP ksp;
152: PC pc;
154: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155: Initialize program
156: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
157: PetscInitialize(&argc,&argv,NULL,help);
158:
159: MPI_Comm_size(PETSC_COMM_WORLD,&size);
160: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
162: /* Create TAO solver and set desired solution method */
163: TaoCreate(PETSC_COMM_WORLD,&tao);
164: TaoSetType(tao,TAOCG);
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Set runtime options
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: user.next_output = 0.0;
170: user.mu = 1.0e6;
171: user.ftime = 0.5;
172: PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);
173: PetscOptionsGetReal(NULL,"-mu",&user.mu,NULL);
175: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176: Create necessary matrix and vectors, solve same ODE on every process
177: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
178: MatCreate(PETSC_COMM_WORLD,&user.A);
179: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
180: MatSetFromOptions(user.A);
181: MatSetUp(user.A);
182: MatCreateVecs(user.A,&user.x,NULL);
184: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Create timestepping solver context
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
187: TSCreate(PETSC_COMM_WORLD,&ts);
188: TSSetType(ts,TSCN);
189: TSSetIFunction(ts,NULL,IFunction,&user);
190: TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
191: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
192: TSSetDuration(ts,PETSC_DEFAULT,user.ftime);
193:
194: if (monitor) {
195: TSMonitorSet(ts,Monitor,&user,NULL);
196: }
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Set initial conditions
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: VecGetArray(user.x,&x_ptr);
202: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
203: VecRestoreArray(user.x,&x_ptr);
204: TSSetInitialTimeStep(ts,0.0,.0001);
206: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
207: Save trajectory of solution so that TSAdjointSolve() may be used
208: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
209: TSSetSaveTrajectory(ts);
211: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
212: Set runtime options
213: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
214: TSSetFromOptions(ts);
216: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
217: Solve nonlinear system
218: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
219: TSSolve(ts,user.x);
221: VecGetArray(user.x,&x_ptr);
222: user.x_ob[0] = x_ptr[0];
223: user.x_ob[1] = x_ptr[1];
225: /* Create sensitivity variable */
226: MatCreateVecs(user.A,&user.lambda[0],NULL);
227: MatCreateVecs(user.A,&user.lambda[1],NULL);
229: /* Set initial solution guess */
230: MatCreateVecs(user.A,&ic,NULL);
231: VecGetArray(ic,&x_ptr);
232: x_ptr[0] = 2.1;
233: x_ptr[1] = -0.66666654321;
234: VecRestoreArray(ic,&x_ptr);
236: TaoSetInitialVector(tao,ic);
238: /* Set routine for function and gradient evaluation */
239: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
241: /* Check for any TAO command line options */
242: TaoSetFromOptions(tao);
243: TaoGetKSP(tao,&ksp);
244: if (ksp) {
245: KSPGetPC(ksp,&pc);
246: PCSetType(pc,PCNONE);
247: }
249: TaoSetTolerances(tao,1e-10,1e-10,1e-10,PETSC_DEFAULT,PETSC_DEFAULT);
251: /* SOLVE THE APPLICATION */
252: TaoSolve(tao);
254: /* Get information on termination */
255: TaoGetConvergedReason(tao,&reason);
256: if (reason <= 0){
257: ierr=PetscPrintf(MPI_COMM_WORLD, "Try another method! \n");
258: }
260: VecView(ic,PETSC_VIEWER_STDOUT_WORLD);
261: /* Free TAO data structures */
262: TaoDestroy(&tao);
264: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
265: Free work space. All PETSc objects should be destroyed when they
266: are no longer needed.
267: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
268: MatDestroy(&user.A);
269: VecDestroy(&user.x);
270: VecDestroy(&user.lambda[0]);
271: VecDestroy(&user.lambda[1]);
272: TSDestroy(&ts);
274: VecDestroy(&ic);
275: PetscFinalize();
276: return(0);
277: }
280: /* ------------------------------------------------------------------ */
283: /*
284: FormFunctionGradient - Evaluates the function and corresponding gradient.
286: Input Parameters:
287: tao - the Tao context
288: X - the input vector
289: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
291: Output Parameters:
292: f - the newly evaluated function
293: G - the newly evaluated gradient
294: */
295: PetscErrorCode FormFunctionGradient(Tao tao,Vec IC,PetscReal *f,Vec G,void *ctx)
296: {
297: User user_ptr = (User)ctx;
298: TS ts;
299: PetscScalar *x_ptr,*y_ptr;
302: VecCopy(IC,user_ptr->x);
304: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
305: Create timestepping solver context
306: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
307: TSCreate(PETSC_COMM_WORLD,&ts);
308: TSSetType(ts,TSCN);
309: TSSetIFunction(ts,NULL,IFunction,user_ptr);
310: TSSetIJacobian(ts,user_ptr->A,user_ptr->A,IJacobian,user_ptr);
311: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
313: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
314: Set time
315: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
316: TSSetTime(ts,0.0);
317: TSSetDuration(ts,PETSC_DEFAULT,0.5);
319: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
320: Save trajectory of solution so that TSAdjointSolve() may be used
321: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
322: TSSetSaveTrajectory(ts);
323:
324: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
325: Set runtime options
326: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
327: TSSetFromOptions(ts);
329: TSSolve(ts,user_ptr->x);
330: VecGetArray(user_ptr->x,&x_ptr);
331: *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]);
332: 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));
334: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
335: Adjoint model starts here
336: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
337: /* Redet initial conditions for the adjoint integration */
338: VecGetArray(user_ptr->lambda[0],&y_ptr);
339: y_ptr[0] = 2.*(x_ptr[0]-user_ptr->x_ob[0]);
340: y_ptr[1] = 2.*(x_ptr[1]-user_ptr->x_ob[1]);
341: VecRestoreArray(user_ptr->lambda[0],&y_ptr);
342: TSSetCostGradients(ts,1,user_ptr->lambda,NULL);
344: TSAdjointSolve(ts);
345: VecCopy(user_ptr->lambda[0],G);
346: TSDestroy(&ts);
347: return(0);
348: }