Actual source code: ex16adj.c
petsc-3.7.5 2017-01-01
1: static char help[] = "Performs adjoint sensitivity analysis for the van der Pol equation.\n\
2: Input parameters include:\n\
3: -mu : stiffness parameter\n\n";
5: /*
6: Concepts: TS^time-dependent nonlinear problems
7: Concepts: TS^van der Pol equation
8: Concepts: TS^adjoint sensitivity analysis
9: Processors: 1
10: */
11: /* ------------------------------------------------------------------------
13: This program solves the van der Pol equation
14: y'' - \mu (1-y^2)*y' + y = 0 (1)
15: on the domain 0 <= x <= 1, with the boundary conditions
16: y(0) = 2, y'(0) = 0,
17: and computes the sensitivities of the final solution w.r.t. initial conditions and parameter \mu with an explicit Runge-Kutta method and its discrete adjoint.
19: Notes:
20: This code demonstrates the TSAdjoint interface to a system of ordinary differential equations (ODEs) in the form of u_t = F(u,t).
22: (1) can be turned into a system of first order ODEs
23: [ y' ] = [ z ]
24: [ z' ] [ \mu (1 - y^2) z - y ]
26: which then we can write as a vector equation
28: [ u_1' ] = [ u_2 ] (2)
29: [ u_2' ] [ \mu (1 - u_1^2) u_2 - u_1 ]
31: which is now in the form of u_t = F(u,t).
33: The user provides the right-hand-side function
35: [ F(u,t) ] = [ u_2 ]
36: [ \mu (1 - u_1^2) u_2 - u_1 ]
38: the Jacobian function
40: dF [ 0 ; 1 ]
41: -- = [ ]
42: du [ -2 \mu u_1*u_2 - 1; \mu (1 - u_1^2) ]
44: and the JacobainP (the Jacobian w.r.t. parameter) function
46: dF [ 0 ]
47: --- = [ ]
48: d\mu [ (1 - u_1^2) u_2 ]
51: ------------------------------------------------------------------------- */
53: #include <petscts.h>
54: #include <petscmat.h>
55: typedef struct _n_User *User;
56: struct _n_User {
57: PetscReal mu;
58: PetscReal next_output;
59: PetscReal tprev;
60: };
62: /*
63: * User-defined routines
64: */
67: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx)
68: {
69: PetscErrorCode ierr;
70: User user = (User)ctx;
71: PetscScalar *f;
72: const PetscScalar *x;
75: VecGetArrayRead(X,&x);
76: VecGetArray(F,&f);
77: f[0] = x[1];
78: f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0];
79: VecRestoreArrayRead(X,&x);
80: VecRestoreArray(F,&f);
81: return(0);
82: }
86: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx)
87: {
88: PetscErrorCode ierr;
89: User user = (User)ctx;
90: PetscReal mu = user->mu;
91: PetscInt rowcol[] = {0,1};
92: PetscScalar J[2][2];
93: const PetscScalar *x;
96: VecGetArrayRead(X,&x);
97: J[0][0] = 0;
98: J[1][0] = -2.*mu*x[1]*x[0]-1.;
99: J[0][1] = 1.0;
100: J[1][1] = mu*(1.0-x[0]*x[0]);
101: MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
102: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
103: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
104: if (A != B) {
105: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
106: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
107: }
108: VecRestoreArrayRead(X,&x);
109: return(0);
110: }
114: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
115: {
116: PetscErrorCode ierr;
117: PetscInt row[] = {0,1},col[]={0};
118: PetscScalar J[2][1];
119: const PetscScalar *x;
122: VecGetArrayRead(X,&x);
123: J[0][0] = 0;
124: J[1][0] = (1.-x[0]*x[0])*x[1];
125: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
126: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
127: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
128: VecRestoreArrayRead(X,&x);
129: return(0);
130: }
134: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
135: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
136: {
137: PetscErrorCode ierr;
138: const PetscScalar *x;
139: PetscReal tfinal, dt, tprev;
140: User user = (User)ctx;
143: TSGetTimeStep(ts,&dt);
144: TSGetDuration(ts,NULL,&tfinal);
145: TSGetPrevTime(ts,&tprev);
146: VecGetArrayRead(X,&x);
147: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",(double)user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(x[0]),(double)PetscRealPart(x[1]));
148: PetscPrintf(PETSC_COMM_WORLD,"t %.6f (tprev = %.6f) \n",(double)t,(double)tprev);
149: VecRestoreArrayRead(X,&x);
150: return(0);
151: }
155: int main(int argc,char **argv)
156: {
157: TS ts; /* nonlinear solver */
158: Vec x; /* solution, residual vectors */
159: Mat A; /* Jacobian matrix */
160: Mat Jacp; /* JacobianP matrix */
161: PetscInt steps;
162: PetscReal ftime =0.5;
163: PetscBool monitor = PETSC_FALSE;
164: PetscScalar *x_ptr;
165: PetscMPIInt size;
166: struct _n_User user;
168: Vec lambda[2],mu[2];
170: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171: Initialize program
172: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
173: PetscInitialize(&argc,&argv,NULL,help);
175: MPI_Comm_size(PETSC_COMM_WORLD,&size);
176: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
178: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: Set runtime options
180: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181: user.mu = 1;
182: user.next_output = 0.0;
185: PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
186: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
188: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189: Create necessary matrix and vectors, solve same ODE on every process
190: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
191: MatCreate(PETSC_COMM_WORLD,&A);
192: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
193: MatSetFromOptions(A);
194: MatSetUp(A);
195: MatCreateVecs(A,&x,NULL);
197: MatCreate(PETSC_COMM_WORLD,&Jacp);
198: MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
199: MatSetFromOptions(Jacp);
200: MatSetUp(Jacp);
202: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203: Create timestepping solver context
204: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
205: TSCreate(PETSC_COMM_WORLD,&ts);
206: TSSetType(ts,TSRK);
207: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
208: TSSetDuration(ts,PETSC_DEFAULT,ftime);
209: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
210: if (monitor) {
211: TSMonitorSet(ts,Monitor,&user,NULL);
212: }
214: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
215: Set initial conditions
216: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
217: VecGetArray(x,&x_ptr);
219: x_ptr[0] = 2; x_ptr[1] = 0.66666654321;
220: VecRestoreArray(x,&x_ptr);
221: TSSetInitialTimeStep(ts,0.0,.001);
223: /*
224: Have the TS save its trajectory so that TSAdjointSolve() may be used
225: */
226: TSSetSaveTrajectory(ts);
228: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
229: Set runtime options
230: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
231: TSSetFromOptions(ts);
233: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
234: Solve nonlinear system
235: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
236: TSSolve(ts,x);
237: TSGetSolveTime(ts,&ftime);
238: TSGetTimeStepNumber(ts,&steps);
239: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,steps,(double)ftime);
240: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
242: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
243: Start the Adjoint model
244: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
245: MatCreateVecs(A,&lambda[0],NULL);
246: MatCreateVecs(A,&lambda[1],NULL);
247: /* Reset initial conditions for the adjoint integration */
248: VecGetArray(lambda[0],&x_ptr);
249: x_ptr[0] = 1.0; x_ptr[1] = 0.0;
250: VecRestoreArray(lambda[0],&x_ptr);
251: VecGetArray(lambda[1],&x_ptr);
252: x_ptr[0] = 0.0; x_ptr[1] = 1.0;
253: VecRestoreArray(lambda[1],&x_ptr);
255: MatCreateVecs(Jacp,&mu[0],NULL);
256: MatCreateVecs(Jacp,&mu[1],NULL);
257: VecGetArray(mu[0],&x_ptr);
258: x_ptr[0] = 0.0;
259: VecRestoreArray(mu[0],&x_ptr);
260: VecGetArray(mu[1],&x_ptr);
261: x_ptr[0] = 0.0;
262: VecRestoreArray(mu[1],&x_ptr);
263: TSSetCostGradients(ts,2,lambda,mu);
265: /* Set RHS Jacobian for the adjoint integration */
266: TSSetRHSJacobian(ts,A,A,RHSJacobian,&user);
268: /* Set RHS JacobianP */
269: TSAdjointSetRHSJacobian(ts,Jacp,RHSJacobianP,&user);
271: TSAdjointSolve(ts);
273: VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD);
274: VecView(lambda[1],PETSC_VIEWER_STDOUT_WORLD);
275: VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD);
276: VecView(mu[1],PETSC_VIEWER_STDOUT_WORLD);
278: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
279: Free work space. All PETSc objects should be destroyed when they
280: are no longer needed.
281: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
282: MatDestroy(&A);
283: MatDestroy(&Jacp);
284: VecDestroy(&x);
285: VecDestroy(&lambda[0]);
286: VecDestroy(&lambda[1]);
287: VecDestroy(&mu[0]);
288: VecDestroy(&mu[1]);
289: TSDestroy(&ts);
291: PetscFinalize();
292: return(0);
293: }