Actual source code: ex16fwd.c
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 tangent linear model.
19: Notes:
20: This code demonstrates the TSForward 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; 0; 0 ]
47: --- = [ ]
48: d\mu [ 0; 0; (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: */
65: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx)
66: {
67: PetscErrorCode ierr;
68: User user = (User)ctx;
69: PetscScalar *f;
70: const PetscScalar *x;
73: VecGetArrayRead(X,&x);
74: VecGetArray(F,&f);
75: f[0] = x[1];
76: f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0];
77: VecRestoreArrayRead(X,&x);
78: VecRestoreArray(F,&f);
79: return(0);
80: }
82: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx)
83: {
84: PetscErrorCode ierr;
85: User user = (User)ctx;
86: PetscReal mu = user->mu;
87: PetscInt rowcol[] = {0,1};
88: PetscScalar J[2][2];
89: const PetscScalar *x;
92: VecGetArrayRead(X,&x);
93: J[0][0] = 0;
94: J[1][0] = -2.*mu*x[1]*x[0]-1.;
95: J[0][1] = 1.0;
96: J[1][1] = mu*(1.0-x[0]*x[0]);
97: MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
98: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
99: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
100: if (A != B) {
101: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
102: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
103: }
104: VecRestoreArrayRead(X,&x);
105: return(0);
106: }
108: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
109: {
110: PetscErrorCode ierr;
111: PetscInt row[] = {0,1},col[]={2};
112: PetscScalar J[2][1];
113: const PetscScalar *x;
116: VecGetArrayRead(X,&x);
117: J[0][0] = 0;
118: J[1][0] = (1.-x[0]*x[0])*x[1];
119: VecRestoreArrayRead(X,&x);
120: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
122: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
123: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
124: return(0);
125: }
127: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
128: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
129: {
130: PetscErrorCode ierr;
131: const PetscScalar *x;
132: PetscReal tfinal, dt, tprev;
133: User user = (User)ctx;
136: TSGetTimeStep(ts,&dt);
137: TSGetMaxTime(ts,&tfinal);
138: TSGetPrevTime(ts,&tprev);
139: VecGetArrayRead(X,&x);
140: 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]));
141: PetscPrintf(PETSC_COMM_WORLD,"t %.6f (tprev = %.6f) \n",(double)t,(double)tprev);
142: VecRestoreArrayRead(X,&x);
143: return(0);
144: }
146: int main(int argc,char **argv)
147: {
148: TS ts; /* nonlinear solver */
149: Vec x; /* solution, residual vectors */
150: Mat A; /* Jacobian matrix */
151: Mat Jacp; /* JacobianP matrix */
152: PetscInt steps;
153: PetscReal ftime =0.5;
154: PetscBool monitor = PETSC_FALSE;
155: PetscScalar *x_ptr;
156: PetscMPIInt size;
157: struct _n_User user;
159: Mat sp;
161: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: Initialize program
163: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
164: PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
165: MPI_Comm_size(PETSC_COMM_WORLD,&size);
166: if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");
168: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
169: Set runtime options
170: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
171: user.mu = 1;
172: user.next_output = 0.0;
175: PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
176: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
178: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: Create necessary matrix and vectors, solve same ODE on every process
180: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181: MatCreate(PETSC_COMM_WORLD,&A);
182: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
183: MatSetFromOptions(A);
184: MatSetUp(A);
185: MatCreateVecs(A,&x,NULL);
187: MatCreate(PETSC_COMM_WORLD,&Jacp);
188: MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,3);
189: MatSetFromOptions(Jacp);
190: MatSetUp(Jacp);
192: MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,2,3,NULL,&sp);
193: MatZeroEntries(sp);
194: MatShift(sp,1.0);
196: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
197: Create timestepping solver context
198: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
199: TSCreate(PETSC_COMM_WORLD,&ts);
200: TSSetType(ts,TSRK);
201: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
202: /* Set RHS Jacobian for the adjoint integration */
203: TSSetRHSJacobian(ts,A,A,RHSJacobian,&user);
204: TSSetMaxTime(ts,ftime);
205: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
206: if (monitor) {
207: TSMonitorSet(ts,Monitor,&user,NULL);
208: }
209: TSForwardSetSensitivities(ts,3,sp);
210: TSSetRHSJacobianP(ts,Jacp,RHSJacobianP,&user);
212: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
213: Set initial conditions
214: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
215: VecGetArray(x,&x_ptr);
217: x_ptr[0] = 2; x_ptr[1] = 0.66666654321;
218: VecRestoreArray(x,&x_ptr);
219: TSSetTimeStep(ts,.001);
222: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
223: Set runtime options
224: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
225: TSSetFromOptions(ts);
227: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
228: Solve nonlinear system
229: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
230: TSSolve(ts,x);
231: TSGetSolveTime(ts,&ftime);
232: TSGetStepNumber(ts,&steps);
233: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,steps,(double)ftime);
234: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
236: PetscPrintf(PETSC_COMM_WORLD,"\n forward sensitivity: d[y(tf) z(tf)]/d[y0 z0 mu]\n");
237: MatView(sp,PETSC_VIEWER_STDOUT_WORLD);
239: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
240: Free work space. All PETSc objects should be destroyed when they
241: are no longer needed.
242: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
243: MatDestroy(&A);
244: MatDestroy(&Jacp);
245: VecDestroy(&x);
246: MatDestroy(&sp);
247: TSDestroy(&ts);
248: PetscFinalize();
249: return ierr;
250: }
252: /*TEST
254: test:
255: args: -monitor 0 -ts_adapt_type none
257: TEST*/