Actual source code: ex23fwdadj.c
1: static char help[] = "A toy example for testing forward and adjoint sensitivity analysis of an implicit ODE with a paramerized mass matrice.\n";
3: /*
4: This example solves the simple ODE
5: c x' = b x, x(0) = a,
6: whose analytical solution is x(T)=a*exp(b/c*T), and calculates the derivative of x(T) w.r.t. c (by default) or w.r.t. b (can be enabled with command line option -der 2).
8: */
10: #include <petscts.h>
12: typedef struct _n_User *User;
13: struct _n_User {
14: PetscReal a;
15: PetscReal b;
16: PetscReal c;
17: /* Sensitivity analysis support */
18: PetscInt steps;
19: PetscReal ftime;
20: Mat Jac; /* Jacobian matrix */
21: Mat Jacp; /* JacobianP matrix */
22: Vec x;
23: Mat sp; /* forward sensitivity variables */
24: Vec lambda[1]; /* adjoint sensitivity variables */
25: Vec mup[1]; /* adjoint sensitivity variables */
26: PetscInt der;
27: };
29: static PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, void *ctx)
30: {
31: User user = (User)ctx;
32: const PetscScalar *x, *xdot;
33: PetscScalar *f;
36: VecGetArrayRead(X, &x);
37: VecGetArrayRead(Xdot, &xdot);
38: VecGetArrayWrite(F, &f);
39: f[0] = user->c * xdot[0] - user->b * x[0];
40: VecRestoreArrayRead(X, &x);
41: VecRestoreArrayRead(Xdot, &xdot);
42: VecRestoreArrayWrite(F, &f);
43: return 0;
44: }
46: static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat A, Mat B, void *ctx)
47: {
48: User user = (User)ctx;
49: PetscInt rowcol[] = {0};
50: PetscScalar J[1][1];
51: const PetscScalar *x;
54: VecGetArrayRead(X, &x);
55: J[0][0] = user->c * a - user->b * 1.0;
56: MatSetValues(B, 1, rowcol, 1, rowcol, &J[0][0], INSERT_VALUES);
57: VecRestoreArrayRead(X, &x);
59: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
60: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
61: if (A != B) {
62: MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
63: MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
64: }
65: return 0;
66: }
68: static PetscErrorCode IJacobianP(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal shift, Mat A, void *ctx)
69: {
70: User user = (User)ctx;
71: PetscInt row[] = {0}, col[] = {0};
72: PetscScalar J[1][1];
73: const PetscScalar *x, *xdot;
74: PetscReal dt;
77: VecGetArrayRead(X, &x);
78: VecGetArrayRead(Xdot, &xdot);
79: TSGetTimeStep(ts, &dt);
80: if (user->der == 1) J[0][0] = xdot[0];
81: if (user->der == 2) J[0][0] = -x[0];
82: MatSetValues(A, 1, row, 1, col, &J[0][0], INSERT_VALUES);
83: VecRestoreArrayRead(X, &x);
85: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
86: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
87: return 0;
88: }
90: int main(int argc, char **argv)
91: {
92: TS ts;
93: PetscScalar *x_ptr;
94: PetscMPIInt size;
95: struct _n_User user;
96: PetscInt rows, cols;
99: PetscInitialize(&argc, &argv, NULL, help);
101: MPI_Comm_size(PETSC_COMM_WORLD, &size);
104: user.a = 2.0;
105: user.b = 4.0;
106: user.c = 3.0;
107: user.steps = 0;
108: user.ftime = 1.0;
109: user.der = 1;
110: PetscOptionsGetInt(NULL, NULL, "-der", &user.der, NULL);
112: rows = 1;
113: cols = 1;
114: MatCreate(PETSC_COMM_WORLD, &user.Jac);
115: MatSetSizes(user.Jac, PETSC_DECIDE, PETSC_DECIDE, 1, 1);
116: MatSetFromOptions(user.Jac);
117: MatSetUp(user.Jac);
118: MatCreateVecs(user.Jac, &user.x, NULL);
120: TSCreate(PETSC_COMM_WORLD, &ts);
121: TSSetType(ts, TSBEULER);
122: TSSetIFunction(ts, NULL, IFunction, &user);
123: TSSetIJacobian(ts, user.Jac, user.Jac, IJacobian, &user);
124: TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
125: TSSetMaxTime(ts, user.ftime);
127: VecGetArrayWrite(user.x, &x_ptr);
128: x_ptr[0] = user.a;
129: VecRestoreArrayWrite(user.x, &x_ptr);
130: TSSetTimeStep(ts, 0.001);
132: /* Set up forward sensitivity */
133: MatCreate(PETSC_COMM_WORLD, &user.Jacp);
134: MatSetSizes(user.Jacp, PETSC_DECIDE, PETSC_DECIDE, rows, cols);
135: MatSetFromOptions(user.Jacp);
136: MatSetUp(user.Jacp);
137: MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, rows, cols, NULL, &user.sp);
138: MatZeroEntries(user.sp);
139: TSForwardSetSensitivities(ts, cols, user.sp);
140: TSSetIJacobianP(ts, user.Jacp, IJacobianP, &user);
142: TSSetSaveTrajectory(ts);
143: TSSetFromOptions(ts);
145: TSSolve(ts, user.x);
146: TSGetSolveTime(ts, &user.ftime);
147: TSGetStepNumber(ts, &user.steps);
148: VecGetArray(user.x, &x_ptr);
149: PetscPrintf(PETSC_COMM_WORLD, "\n ode solution %g\n", (double)PetscRealPart(x_ptr[0]));
150: VecRestoreArray(user.x, &x_ptr);
151: PetscPrintf(PETSC_COMM_WORLD, "\n analytical solution %g\n", (double)(user.a * PetscExpReal(user.b / user.c * user.ftime)));
153: if (user.der == 1) PetscPrintf(PETSC_COMM_WORLD, "\n analytical derivative w.r.t. c %g\n", (double)(-user.a * user.ftime * user.b / (user.c * user.c) * PetscExpReal(user.b / user.c * user.ftime)));
154: if (user.der == 2) PetscPrintf(PETSC_COMM_WORLD, "\n analytical derivative w.r.t. b %g\n", (double)(user.a * user.ftime / user.c * PetscExpReal(user.b / user.c * user.ftime)));
155: PetscPrintf(PETSC_COMM_WORLD, "\n forward sensitivity:\n");
156: MatView(user.sp, PETSC_VIEWER_STDOUT_WORLD);
158: MatCreateVecs(user.Jac, &user.lambda[0], NULL);
159: /* Set initial conditions for the adjoint integration */
160: VecGetArrayWrite(user.lambda[0], &x_ptr);
161: x_ptr[0] = 1.0;
162: VecRestoreArrayWrite(user.lambda[0], &x_ptr);
163: MatCreateVecs(user.Jacp, &user.mup[0], NULL);
164: VecGetArrayWrite(user.mup[0], &x_ptr);
165: x_ptr[0] = 0.0;
166: VecRestoreArrayWrite(user.mup[0], &x_ptr);
168: TSSetCostGradients(ts, 1, user.lambda, user.mup);
169: TSAdjointSolve(ts);
171: PetscPrintf(PETSC_COMM_WORLD, "\n adjoint sensitivity:\n");
172: VecView(user.mup[0], PETSC_VIEWER_STDOUT_WORLD);
174: MatDestroy(&user.Jac);
175: MatDestroy(&user.sp);
176: MatDestroy(&user.Jacp);
177: VecDestroy(&user.x);
178: VecDestroy(&user.lambda[0]);
179: VecDestroy(&user.mup[0]);
180: TSDestroy(&ts);
182: PetscFinalize();
183: return 0;
184: }
186: /*TEST
188: test:
189: args: -ts_type beuler
191: test:
192: suffix: 2
193: args: -ts_type cn
194: output_file: output/ex23fwdadj_1.out
196: TEST*/