Actual source code: ex20adj.c
petsc-3.7.5 2017-01-01
1: #define c11 1.0
2: #define c12 0
3: #define c21 2.0
4: #define c22 1.0
5: static char help[] = "Performs adjoint sensitivity analysis for the van der Pol equation.\n";
7: /*
8: Concepts: TS^time-dependent nonlinear problems
9: Concepts: TS^van der Pol equation DAE equivalent
10: Concepts: TS^adjoint sensitivity analysis
11: Processors: 1
12: */
13: /* ------------------------------------------------------------------------
15: This program solves the van der Pol DAE ODE equivalent
16: [ u_1' ] = [ u_2 ] (2)
17: [ u_2' ] [ mu[(1-u_1^2)u_2-u_1] ]
18: on the domain 0 <= x <= 1, with the boundary conditions
19: u_1(0) = 2, u_2(0) = -6.666665432100101e-01,
20: and
21: mu = 10^6,
22: and computes the sensitivities of the final solution w.r.t. initial conditions and parameter \mu with the implicit theta method and its discrete adjoint.
24: Notes:
25: This code demonstrates the TSAdjoint interface to a DAE system.
27: The user provides the implicit right-hand-side function
28: [ G(u',u,t) ] = [u' - f(u,t)] = [ u_1'] - [ u_2 ]
29: [ u_2'] [ mu[(1-u_1^2)u_2-u_1] ]
31: and the Jacobian of G (from the PETSc user manual)
33: dG dG
34: J(G) = a * -- + --
35: du' du
37: and the JacobianP of the explicit right-hand side of (2) f(u,t) ( which is equivalent to -G(0,u,t) ).
38: df [ 0 ]
39: -- = [ ]
40: dp [ (1 - u_1^2) u_2 ].
42: See ex20.c for more details on the Jacobian.
44: Many DAEs can be represented in a general form M u_t = f(u,t).
45: Thus both sides of (1) are multiplied by an artificial matrix
46: M = [ c11 c12 ]
47: [ c21 c22 ]
48: to turn (1) into the general form. This operation does not change the solution and it is intended for illustration only.
50: ------------------------------------------------------------------------- */
51: #include <petscts.h>
52: #include <petsctao.h>
54: typedef struct _n_User *User;
55: struct _n_User {
56: PetscReal mu;
57: PetscReal next_output;
59: /* Sensitivity analysis support */
60: PetscInt steps;
61: PetscReal ftime;
62: Mat A; /* Jacobian matrix */
63: Mat Jacp; /* JacobianP matrix */
64: Vec x,lambda[2],mup[2]; /* adjoint variables */
65: };
67: /*
68: * User-defined routines
69: */
72: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
73: {
74: PetscErrorCode ierr;
75: User user = (User)ctx;
76: const PetscScalar *x,*xdot;
77: PetscScalar *f;
80: VecGetArrayRead(X,&x);
81: VecGetArrayRead(Xdot,&xdot);
82: VecGetArray(F,&f);
83: f[0] = xdot[0] - x[1];
84: f[1] = c21*(xdot[0]-x[1]) + xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]) ;
85: VecRestoreArrayRead(X,&x);
86: VecRestoreArrayRead(Xdot,&xdot);
87: VecRestoreArray(F,&f);
88: return(0);
89: }
93: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
94: {
95: PetscErrorCode ierr;
96: User user = (User)ctx;
97: PetscInt rowcol[] = {0,1};
98: PetscScalar J[2][2];
99: const PetscScalar *x;
102: VecGetArrayRead(X,&x);
104: J[0][0] = a; J[0][1] = -1.0;
105: 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]);
107: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
108: VecRestoreArrayRead(X,&x);
110: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
111: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
112: if (A != B) {
113: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
114: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
115: }
116: return(0);
117: }
121: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
122: {
123: PetscErrorCode ierr;
124: PetscInt row[] = {0,1},col[]={0};
125: PetscScalar J[2][1];
126: const PetscScalar *x;
129: VecGetArrayRead(X,&x);
131: J[0][0] = 0;
132: J[1][0] = (1.-x[0]*x[0])*x[1]-x[0];
133: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
135: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
136: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
137: return(0);
138: }
142: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
143: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
144: {
145: PetscErrorCode ierr;
146: const PetscScalar *x;
147: PetscReal tfinal, dt;
148: User user = (User)ctx;
149: Vec interpolatedX;
152: TSGetTimeStep(ts,&dt);
153: TSGetDuration(ts,NULL,&tfinal);
155: while (user->next_output <= t && user->next_output <= tfinal) {
156: VecDuplicate(X,&interpolatedX);
157: TSInterpolate(ts,user->next_output,interpolatedX);
158: VecGetArrayRead(interpolatedX,&x);
159: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
160: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
161: (double)PetscRealPart(x[1]));
162: VecRestoreArrayRead(interpolatedX,&x);
163: VecDestroy(&interpolatedX);
164: user->next_output += 0.1;
165: }
166: return(0);
167: }
171: int main(int argc,char **argv)
172: {
173: TS ts; /* nonlinear solver */
174: PetscBool monitor = PETSC_FALSE;
175: PetscScalar *x_ptr,*y_ptr;
176: PetscMPIInt size;
177: struct _n_User user;
180: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181: Initialize program
182: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183: PetscInitialize(&argc,&argv,NULL,help);
185: MPI_Comm_size(PETSC_COMM_WORLD,&size);
186: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
188: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189: Set runtime options
190: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
191: user.next_output = 0.0;
192: user.mu = 1.0e6;
193: user.steps = 0;
194: user.ftime = 0.5;
195: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
196: PetscOptionsGetReal(NULL,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: TSSetDuration(ts,200000,user.ftime);
220: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
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: Save trajectory of solution so that TSAdjointSolve() may be used
235: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
236: TSSetSaveTrajectory(ts);
238: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
239: Set runtime options
240: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
241: TSSetFromOptions(ts);
243: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
244: Solve nonlinear system
245: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
246: TSSolve(ts,user.x);
247: TSGetSolveTime(ts,&user.ftime);
248: TSGetTimeStepNumber(ts,&user.steps);
250: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
251: Adjoint model starts here
252: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
253: MatCreateVecs(user.A,&user.lambda[0],NULL);
254: /* Set initial conditions for the adjoint integration */
255: VecGetArray(user.lambda[0],&y_ptr);
256: y_ptr[0] = 1.0; y_ptr[1] = 0.0;
257: VecRestoreArray(user.lambda[0],&y_ptr);
258: MatCreateVecs(user.A,&user.lambda[1],NULL);
259: VecGetArray(user.lambda[1],&y_ptr);
260: y_ptr[0] = 0.0; y_ptr[1] = 1.0;
261: VecRestoreArray(user.lambda[1],&y_ptr);
263: MatCreateVecs(user.Jacp,&user.mup[0],NULL);
264: VecGetArray(user.mup[0],&x_ptr);
265: x_ptr[0] = 0.0;
266: VecRestoreArray(user.mup[0],&x_ptr);
267: MatCreateVecs(user.Jacp,&user.mup[1],NULL);
268: VecGetArray(user.mup[1],&x_ptr);
269: x_ptr[0] = 0.0;
270: VecRestoreArray(user.mup[1],&x_ptr);
272: TSSetCostGradients(ts,2,user.lambda,user.mup);
274: /* Set RHS JacobianP */
275: TSAdjointSetRHSJacobian(ts,user.Jacp,RHSJacobianP,&user);
277: TSAdjointSolve(ts);
279: PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[y(tf)]/d[y0] d[y(tf)]/d[z0]\n");
280: VecView(user.lambda[0],PETSC_VIEWER_STDOUT_WORLD);
281: PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[z(tf)]/d[y0] d[z(tf)]/d[z0]\n");
282: VecView(user.lambda[1],PETSC_VIEWER_STDOUT_WORLD);
283: PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt parameters: d[y(tf)]/d[mu]\n");
284: VecView(user.mup[0],PETSC_VIEWER_STDOUT_WORLD);
285: PetscPrintf(PETSC_COMM_WORLD,"\n sensivitity wrt parameters: d[z(tf)]/d[mu]\n");
286: VecView(user.mup[1],PETSC_VIEWER_STDOUT_WORLD);
288: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
289: Free work space. All PETSc objects should be destroyed when they
290: are no longer needed.
291: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
292: MatDestroy(&user.A);
293: MatDestroy(&user.Jacp);
294: VecDestroy(&user.x);
295: VecDestroy(&user.lambda[0]);
296: VecDestroy(&user.lambda[1]);
297: VecDestroy(&user.mup[0]);
298: VecDestroy(&user.mup[1]);
299: TSDestroy(&ts);
301: PetscFinalize();
302: return(0);
303: }