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;
98: PetscInitialize(&argc,&argv,NULL,help);
100: MPI_Comm_size(PETSC_COMM_WORLD,&size);
103: user.a = 2.0;
104: user.b = 4.0;
105: user.c = 3.0;
106: user.steps = 0;
107: user.ftime = 1.0;
108: user.der = 1;
109: PetscOptionsGetInt(NULL,NULL,"-der",&user.der,NULL);
111: rows = 1;
112: cols = 1;
113: MatCreate(PETSC_COMM_WORLD,&user.Jac);
114: MatSetSizes(user.Jac,PETSC_DECIDE,PETSC_DECIDE,1,1);
115: MatSetFromOptions(user.Jac);
116: MatSetUp(user.Jac);
117: MatCreateVecs(user.Jac,&user.x,NULL);
119: TSCreate(PETSC_COMM_WORLD,&ts);
120: TSSetType(ts,TSBEULER);
121: TSSetIFunction(ts,NULL,IFunction,&user);
122: TSSetIJacobian(ts,user.Jac,user.Jac,IJacobian,&user);
123: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
124: TSSetMaxTime(ts,user.ftime);
126: VecGetArrayWrite(user.x,&x_ptr);
127: x_ptr[0] = user.a;
128: VecRestoreArrayWrite(user.x,&x_ptr);
129: TSSetTimeStep(ts,0.001);
131: /* Set up forward sensitivity */
132: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
133: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,rows,cols);
134: MatSetFromOptions(user.Jacp);
135: MatSetUp(user.Jacp);
136: MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,rows,cols,NULL,&user.sp);
137: MatZeroEntries(user.sp);
138: TSForwardSetSensitivities(ts,cols,user.sp);
139: TSSetIJacobianP(ts,user.Jacp,IJacobianP,&user);
141: TSSetSaveTrajectory(ts);
142: TSSetFromOptions(ts);
144: TSSolve(ts,user.x);
145: TSGetSolveTime(ts,&user.ftime);
146: TSGetStepNumber(ts,&user.steps);
147: VecGetArray(user.x,&x_ptr);
148: PetscPrintf(PETSC_COMM_WORLD,"\n ode solution %g\n",(double)PetscRealPart(x_ptr[0]));
149: VecRestoreArray(user.x,&x_ptr);
150: PetscPrintf(PETSC_COMM_WORLD,"\n analytical solution %g\n",(double)user.a*PetscExpReal(user.b/user.c*user.ftime));
152: if (user.der == 1) {
153: 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: }
155: if (user.der == 2) {
156: PetscPrintf(PETSC_COMM_WORLD,"\n analytical derivative w.r.t. b %g\n",user.a*user.ftime/user.c*PetscExpReal(user.b/user.c*user.ftime));
157: }
158: PetscPrintf(PETSC_COMM_WORLD,"\n forward sensitivity:\n");
159: MatView(user.sp,PETSC_VIEWER_STDOUT_WORLD);
161: MatCreateVecs(user.Jac,&user.lambda[0],NULL);
162: /* Set initial conditions for the adjoint integration */
163: VecGetArrayWrite(user.lambda[0],&x_ptr);
164: x_ptr[0] = 1.0;
165: VecRestoreArrayWrite(user.lambda[0],&x_ptr);
166: MatCreateVecs(user.Jacp,&user.mup[0],NULL);
167: VecGetArrayWrite(user.mup[0],&x_ptr);
168: x_ptr[0] = 0.0;
169: VecRestoreArrayWrite(user.mup[0],&x_ptr);
171: TSSetCostGradients(ts,1,user.lambda,user.mup);
172: TSAdjointSolve(ts);
174: PetscPrintf(PETSC_COMM_WORLD,"\n adjoint sensitivity:\n");
175: VecView(user.mup[0],PETSC_VIEWER_STDOUT_WORLD);
177: MatDestroy(&user.Jac);
178: MatDestroy(&user.sp);
179: MatDestroy(&user.Jacp);
180: VecDestroy(&user.x);
181: VecDestroy(&user.lambda[0]);
182: VecDestroy(&user.mup[0]);
183: TSDestroy(&ts);
185: PetscFinalize();
186: return 0;
187: }
189: /*TEST
191: test:
192: args: -ts_type beuler
194: test:
195: suffix: 2
196: args: -ts_type cn
197: output_file: output/ex23fwdadj_1.out
199: TEST*/