Actual source code: ex20adj.c
petsc-3.8.4 2018-03-24
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: */
70: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
71: {
72: PetscErrorCode ierr;
73: User user = (User)ctx;
74: const PetscScalar *x,*xdot;
75: PetscScalar *f;
78: VecGetArrayRead(X,&x);
79: VecGetArrayRead(Xdot,&xdot);
80: VecGetArray(F,&f);
81: f[0] = xdot[0] - x[1];
82: f[1] = c21*(xdot[0]-x[1]) + xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]) ;
83: VecRestoreArrayRead(X,&x);
84: VecRestoreArrayRead(Xdot,&xdot);
85: VecRestoreArray(F,&f);
86: return(0);
87: }
89: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
90: {
91: PetscErrorCode ierr;
92: User user = (User)ctx;
93: PetscInt rowcol[] = {0,1};
94: PetscScalar J[2][2];
95: const PetscScalar *x;
98: VecGetArrayRead(X,&x);
100: J[0][0] = a; J[0][1] = -1.0;
101: 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]);
103: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
104: VecRestoreArrayRead(X,&x);
106: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
107: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
108: if (A != B) {
109: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
110: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
111: }
112: return(0);
113: }
115: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
116: {
117: PetscErrorCode ierr;
118: PetscInt row[] = {0,1},col[]={0};
119: PetscScalar J[2][1];
120: const PetscScalar *x;
123: VecGetArrayRead(X,&x);
125: J[0][0] = 0;
126: J[1][0] = (1.-x[0]*x[0])*x[1]-x[0];
127: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
129: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
130: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
131: return(0);
132: }
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;
140: User user = (User)ctx;
141: Vec interpolatedX;
144: TSGetTimeStep(ts,&dt);
145: TSGetMaxTime(ts,&tfinal);
147: while (user->next_output <= t && user->next_output <= tfinal) {
148: VecDuplicate(X,&interpolatedX);
149: TSInterpolate(ts,user->next_output,interpolatedX);
150: VecGetArrayRead(interpolatedX,&x);
151: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
152: user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(x[0]),
153: (double)PetscRealPart(x[1]));
154: VecRestoreArrayRead(interpolatedX,&x);
155: VecDestroy(&interpolatedX);
156: user->next_output += 0.1;
157: }
158: return(0);
159: }
161: int main(int argc,char **argv)
162: {
163: TS ts; /* nonlinear solver */
164: PetscBool monitor = PETSC_FALSE;
165: PetscScalar *x_ptr,*y_ptr;
166: PetscMPIInt size;
167: struct _n_User user;
170: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171: Initialize program
172: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
173: PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
174: MPI_Comm_size(PETSC_COMM_WORLD,&size);
175: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
177: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: Set runtime options
179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
180: user.next_output = 0.0;
181: user.mu = 1.0e6;
182: user.steps = 0;
183: user.ftime = 0.5;
184: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
185: PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
187: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: Create necessary matrix and vectors, solve same ODE on every process
189: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
190: MatCreate(PETSC_COMM_WORLD,&user.A);
191: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
192: MatSetFromOptions(user.A);
193: MatSetUp(user.A);
194: MatCreateVecs(user.A,&user.x,NULL);
196: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
197: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
198: MatSetFromOptions(user.Jacp);
199: MatSetUp(user.Jacp);
201: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202: Create timestepping solver context
203: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
204: TSCreate(PETSC_COMM_WORLD,&ts);
205: TSSetType(ts,TSCN);
206: TSSetIFunction(ts,NULL,IFunction,&user);
207: TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
208: TSSetMaxTime(ts,user.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(user.x,&x_ptr);
218: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
219: VecRestoreArray(user.x,&x_ptr);
220: TSSetTimeStep(ts,.0001);
222: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
223: Save trajectory of solution so that TSAdjointSolve() may be used
224: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
225: TSSetSaveTrajectory(ts);
227: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
228: Set runtime options
229: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
230: TSSetFromOptions(ts);
232: TSSolve(ts,user.x);
233: TSGetSolveTime(ts,&user.ftime);
234: TSGetStepNumber(ts,&user.steps);
236: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
237: Adjoint model starts here
238: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
239: MatCreateVecs(user.A,&user.lambda[0],NULL);
240: /* Set initial conditions for the adjoint integration */
241: VecGetArray(user.lambda[0],&y_ptr);
242: y_ptr[0] = 1.0; y_ptr[1] = 0.0;
243: VecRestoreArray(user.lambda[0],&y_ptr);
244: MatCreateVecs(user.A,&user.lambda[1],NULL);
245: VecGetArray(user.lambda[1],&y_ptr);
246: y_ptr[0] = 0.0; y_ptr[1] = 1.0;
247: VecRestoreArray(user.lambda[1],&y_ptr);
249: MatCreateVecs(user.Jacp,&user.mup[0],NULL);
250: VecGetArray(user.mup[0],&x_ptr);
251: x_ptr[0] = 0.0;
252: VecRestoreArray(user.mup[0],&x_ptr);
253: MatCreateVecs(user.Jacp,&user.mup[1],NULL);
254: VecGetArray(user.mup[1],&x_ptr);
255: x_ptr[0] = 0.0;
256: VecRestoreArray(user.mup[1],&x_ptr);
258: TSSetCostGradients(ts,2,user.lambda,user.mup);
260: /* Set RHS JacobianP */
261: TSAdjointSetRHSJacobian(ts,user.Jacp,RHSJacobianP,&user);
263: TSAdjointSolve(ts);
265: PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[y(tf)]/d[y0] d[y(tf)]/d[z0]\n");
266: VecView(user.lambda[0],PETSC_VIEWER_STDOUT_WORLD);
267: PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[z(tf)]/d[y0] d[z(tf)]/d[z0]\n");
268: VecView(user.lambda[1],PETSC_VIEWER_STDOUT_WORLD);
269: PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt parameters: d[y(tf)]/d[mu]\n");
270: VecView(user.mup[0],PETSC_VIEWER_STDOUT_WORLD);
271: PetscPrintf(PETSC_COMM_WORLD,"\n sensivitity wrt parameters: d[z(tf)]/d[mu]\n");
272: VecView(user.mup[1],PETSC_VIEWER_STDOUT_WORLD);
274: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
275: Free work space. All PETSc objects should be destroyed when they
276: are no longer needed.
277: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
278: MatDestroy(&user.A);
279: MatDestroy(&user.Jacp);
280: VecDestroy(&user.x);
281: VecDestroy(&user.lambda[0]);
282: VecDestroy(&user.lambda[1]);
283: VecDestroy(&user.mup[0]);
284: VecDestroy(&user.mup[1]);
285: TSDestroy(&ts);
287: PetscFinalize();
288: return(ierr);
289: }