Actual source code: ex20adj.c
petsc-3.6.1 2015-08-06
1: #define c11 1.0
2: #define c12 0
3: #define c21 2.0
4: #define c22 1.0
5: static char help[] = "Solves the van der Pol equation.\n\
6: Input parameters include:\n";
8: /*
9: Concepts: TS^time-dependent nonlinear problems
10: Concepts: TS^van der Pol equation DAE equivalent
11: Processors: 1
12: */
13: /* ------------------------------------------------------------------------
15: This program solves the van der Pol DAE ODE equivalent
16: y' = z (1)
17: z' = mu[(1-y^2)z-y]
18: on the domain 0 <= x <= 1, with the boundary conditions
19: y(0) = 2, y'(0) = -6.666665432100101e-01,
20: and
21: mu = 10^6.
22: This is a nonlinear equation.
24: Notes:
25: This code demonstrates the TS solver interface to a variant of
26: linear problems, u_t = f(u,t), namely turning (1) into a system of
27: first order differential equations,
29: [ y' ] = [ z ]
30: [ z' ] [ mu[(1-y^2)z-y] ]
32: which then we can write as a vector equation
34: [ u_1' ] = [ u_2 ] (2)
35: [ u_2' ] [ mu[(1-u_1^2)u_2-u_1] ]
37: which is now in the desired form of u_t = f(u,t). One way that we
38: can split f(u,t) in (2) is to split by component,
40: [ u_1' ] = [ u_2 ] + [ 0 ]
41: [ u_2' ] [ 0 ] [ mu[(1-u_1^2)u_2-u_1] ]
43: where
45: [ F(u,t) ] = [ u_2 ]
46: [ 0 ]
48: and
50: [ G(u',u,t) ] = [ u_1' ] - [ 0 ]
51: [ u_2' ] [ mu[(1-u_1^2)u_2-u_1] ]
53: Using the definition of the Jacobian of G (from the PETSc user manual),
54: in the equation G(u',u,t) = F(u,t),
56: dG dG
57: J(G) = a * -- + --
58: du' du
60: where d is the partial derivative. In this example,
62: dG [ 1 ; 0 ]
63: -- = [ ]
64: du' [ 0 ; 1 ]
66: dG [ 0 ; 0 ]
67: -- = [ ]
68: du [ mu*(1.0 + 2.0*u_1*u_2) ; -mu*(1-u_1*u_1) ]
70: Hence,
72: [ a ; 0 ]
73: J(G) = [ ]
74: [ mu*(1.0 + 2.0*u_1*u_2) ; a - mu*(1-u_1*u_1) ]
76: ------------------------------------------------------------------------- */
77: #include <petscts.h>
78: #include <petsctao.h>
80: typedef struct _n_User *User;
81: struct _n_User {
82: PetscReal mu;
83: PetscReal next_output;
84:
85: /* Sensitivity analysis support */
86: PetscInt steps;
87: PetscReal ftime;
88: Mat A; /* Jacobian matrix */
89: Mat Jacp; /* JacobianP matrix */
90: Vec x,lambda[2],mup[2]; /* adjoint variables */
91: };
93: /*
94: * User-defined routines
95: */
98: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
99: {
100: PetscErrorCode ierr;
101: User user = (User)ctx;
102: const PetscScalar *x,*xdot;
103: PetscScalar *f;
106: VecGetArrayRead(X,&x);
107: VecGetArrayRead(Xdot,&xdot);
108: VecGetArray(F,&f);
109: f[0] = xdot[0] - x[1];
110: f[1] = c21*(xdot[0]-x[1]) + xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]) ;
111: VecRestoreArrayRead(X,&x);
112: VecRestoreArrayRead(Xdot,&xdot);
113: VecRestoreArray(F,&f);
114: return(0);
115: }
119: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
120: {
121: PetscErrorCode ierr;
122: User user = (User)ctx;
123: PetscInt rowcol[] = {0,1};
124: PetscScalar J[2][2];
125: const PetscScalar *x;
128: VecGetArrayRead(X,&x);
130: J[0][0] = a; J[0][1] = -1.0;
131: 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]);
132:
133: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
134: VecRestoreArrayRead(X,&x);
136: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
137: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
138: if (A != B) {
139: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
140: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
141: }
142: return(0);
143: }
147: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
148: {
149: PetscErrorCode ierr;
150: PetscInt row[] = {0,1},col[]={0};
151: PetscScalar J[2][1];
152: const PetscScalar *x;
155: VecGetArrayRead(X,&x);
157: J[0][0] = 0;
158: J[1][0] = (1.-x[0]*x[0])*x[1]-x[0];
159: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
161: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
162: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
163: return(0);
164: }
168: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
169: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
170: {
171: PetscErrorCode ierr;
172: const PetscScalar *x;
173: PetscReal tfinal, dt;
174: User user = (User)ctx;
175: Vec interpolatedX;
178: TSGetTimeStep(ts,&dt);
179: TSGetDuration(ts,NULL,&tfinal);
181: while (user->next_output <= t && user->next_output <= tfinal) {
182: VecDuplicate(X,&interpolatedX);
183: TSInterpolate(ts,user->next_output,interpolatedX);
184: VecGetArrayRead(interpolatedX,&x);
185: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
186: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
187: (double)PetscRealPart(x[1]));
188: VecRestoreArrayRead(interpolatedX,&x);
189: VecDestroy(&interpolatedX);
190: user->next_output += 0.1;
191: }
192: return(0);
193: }
197: int main(int argc,char **argv)
198: {
199: TS ts; /* nonlinear solver */
200: PetscBool monitor = PETSC_FALSE;
201: PetscScalar *x_ptr,*y_ptr;
202: PetscMPIInt size;
203: struct _n_User user;
206: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
207: Initialize program
208: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
209: PetscInitialize(&argc,&argv,NULL,help);
210:
211: MPI_Comm_size(PETSC_COMM_WORLD,&size);
212: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
214: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
215: Set runtime options
216: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
217: user.next_output = 0.0;
218: user.mu = 1.0e6;
219: user.steps = 0;
220: user.ftime = 0.5;
221: PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);
222: PetscOptionsGetReal(NULL,"-mu",&user.mu,NULL);
224: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
225: Create necessary matrix and vectors, solve same ODE on every process
226: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
227: MatCreate(PETSC_COMM_WORLD,&user.A);
228: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
229: MatSetFromOptions(user.A);
230: MatSetUp(user.A);
231: MatCreateVecs(user.A,&user.x,NULL);
233: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
234: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
235: MatSetFromOptions(user.Jacp);
236: MatSetUp(user.Jacp);
238: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
239: Create timestepping solver context
240: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
241: TSCreate(PETSC_COMM_WORLD,&ts);
242: TSSetType(ts,TSCN);
243: TSSetIFunction(ts,NULL,IFunction,&user);
244: TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
245: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
246: TSSetDuration(ts,200000,user.ftime);
247: if (monitor) {
248: TSMonitorSet(ts,Monitor,&user,NULL);
249: }
251: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
252: Set initial conditions
253: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
254: VecGetArray(user.x,&x_ptr);
255: x_ptr[0] = 2.0; x_ptr[1] = -0.66666654321;
256: VecRestoreArray(user.x,&x_ptr);
257: TSSetInitialTimeStep(ts,0.0,.0001);
259: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
260: Save trajectory of solution so that TSAdjointSolve() may be used
261: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
262: TSSetSaveTrajectory(ts);
264: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
265: Set runtime options
266: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
267: TSSetFromOptions(ts);
269: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
270: Solve nonlinear system
271: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
272: TSSolve(ts,user.x);
273: TSGetSolveTime(ts,&user.ftime);
274: TSGetTimeStepNumber(ts,&user.steps);
275: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)user.ftime);
276: PetscPrintf(PETSC_COMM_WORLD,"\n ode solution \n");
277: VecView(user.x,PETSC_VIEWER_STDOUT_WORLD);
279: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
280: Adjoint model starts here
281: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
282: MatCreateVecs(user.A,&user.lambda[0],NULL);
283: /* Set initial conditions for the adjoint integration */
284: VecGetArray(user.lambda[0],&y_ptr);
285: y_ptr[0] = 1.0; y_ptr[1] = 0.0;
286: VecRestoreArray(user.lambda[0],&y_ptr);
287: MatCreateVecs(user.A,&user.lambda[1],NULL);
288: VecGetArray(user.lambda[1],&y_ptr);
289: y_ptr[0] = 0.0; y_ptr[1] = 1.0;
290: VecRestoreArray(user.lambda[1],&y_ptr);
292: MatCreateVecs(user.Jacp,&user.mup[0],NULL);
293: VecGetArray(user.mup[0],&x_ptr);
294: x_ptr[0] = 0.0;
295: VecRestoreArray(user.mup[0],&x_ptr);
296: MatCreateVecs(user.Jacp,&user.mup[1],NULL);
297: VecGetArray(user.mup[1],&x_ptr);
298: x_ptr[0] = 0.0;
299: VecRestoreArray(user.mup[1],&x_ptr);
301: TSSetCostGradients(ts,2,user.lambda,user.mup);
303: /* Set RHS JacobianP */
304: TSAdjointSetRHSJacobian(ts,user.Jacp,RHSJacobianP,&user);
306: TSAdjointSolve(ts);
308: PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[y(tf)]/d[y0] d[y(tf)]/d[z0]\n");
309: VecView(user.lambda[0],PETSC_VIEWER_STDOUT_WORLD);
310: PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[z(tf)]/d[y0] d[z(tf)]/d[z0]\n");
311: VecView(user.lambda[1],PETSC_VIEWER_STDOUT_WORLD);
312: PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt parameters: d[y(tf)]/d[mu]\n");
313: VecView(user.mup[0],PETSC_VIEWER_STDOUT_WORLD);
314: PetscPrintf(PETSC_COMM_WORLD,"\n sensivitity wrt parameters: d[z(tf)]/d[mu]\n");
315: VecView(user.mup[1],PETSC_VIEWER_STDOUT_WORLD);
317: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
318: Free work space. All PETSc objects should be destroyed when they
319: are no longer needed.
320: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
321: MatDestroy(&user.A);
322: MatDestroy(&user.Jacp);
323: VecDestroy(&user.x);
324: VecDestroy(&user.lambda[0]);
325: VecDestroy(&user.lambda[1]);
326: VecDestroy(&user.mup[0]);
327: VecDestroy(&user.mup[1]);
328: TSDestroy(&ts);
330: PetscFinalize();
331: return(0);
332: }