Actual source code: ex24.c
petsc-3.4.5 2014-06-29
1: static char help[] = "Pseudotransient continuation to solve a many-variable system that comes from the 2 variable Rosenbrock function + trivial.\n\n";
3: #include <petscts.h>
5: static PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat*,Mat*,MatStructure*,void*);
6: static PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*);
7: static PetscErrorCode MonitorObjective(TS,PetscInt,PetscReal,Vec,void*);
9: typedef struct {
10: PetscInt n;
11: PetscBool monitor_short;
12: } Ctx;
16: int main(int argc,char **argv)
17: {
18: TS ts; /* time integration context */
19: Vec X; /* solution, residual vectors */
20: Mat J; /* Jacobian matrix */
22: PetscScalar *x;
23: PetscReal ftime;
24: PetscInt i,steps,nits,lits;
25: PetscBool view_final;
26: Ctx ctx;
28: PetscInitialize(&argc,&argv,(char*)0,help);
29: ctx.n = 3;
30: PetscOptionsGetInt(NULL,"-n",&ctx.n,NULL);
31: if (ctx.n < 2) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_OUTOFRANGE,"The dimension specified with -n must be at least 2");
33: view_final = PETSC_FALSE;
34: PetscOptionsGetBool(NULL,"-view_final",&view_final,NULL);
36: ctx.monitor_short = PETSC_FALSE;
37: PetscOptionsGetBool(NULL,"-monitor_short",&ctx.monitor_short,NULL);
39: /*
40: Create Jacobian matrix data structure and state vector
41: */
42: MatCreate(PETSC_COMM_WORLD,&J);
43: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx.n,ctx.n);
44: MatSetFromOptions(J);
45: MatSetUp(J);
46: MatGetVecs(J,&X,NULL);
48: /* Create time integration context */
49: TSCreate(PETSC_COMM_WORLD,&ts);
50: TSSetType(ts,TSPSEUDO);
51: TSSetIFunction(ts,NULL,FormIFunction,&ctx);
52: TSSetIJacobian(ts,J,J,FormIJacobian,&ctx);
53: TSSetDuration(ts,1000,1e14);
54: TSSetInitialTimeStep(ts,0.0,1e-3);
55: TSMonitorSet(ts,MonitorObjective,&ctx,NULL);
57: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58: Customize time integrator; set runtime options
59: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: TSSetFromOptions(ts);
62: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
63: Evaluate initial guess; then solve nonlinear system
64: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
65: VecSet(X,0.0);
66: VecGetArray(X,&x);
67: #if 1
68: x[0] = 5.;
69: x[1] = -5.;
70: for (i=2; i<ctx.n; i++) x[i] = 5.;
71: #else
72: x[0] = 1.0;
73: x[1] = 15.0;
74: for (i=2; i<ctx.n; i++) x[i] = 10.0;
75: #endif
76: VecRestoreArray(X,&x);
78: TSSolve(ts,X);
79: TSGetSolveTime(ts,&ftime);
80: TSGetTimeStepNumber(ts,&steps);
81: TSGetSNESIterations(ts,&nits);
82: TSGetKSPIterations(ts,&lits);
83: PetscPrintf(PETSC_COMM_WORLD,"Time integrator took (%D,%D,%D) iterations to reach final time %G\n",steps,nits,lits,ftime);
84: if (view_final) {
85: VecView(X,PETSC_VIEWER_STDOUT_WORLD);
86: }
88: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
89: Free work space. All PETSc objects should be destroyed when they
90: are no longer needed.
91: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
93: VecDestroy(&X);
94: MatDestroy(&J);
95: TSDestroy(&ts);
96: PetscFinalize();
97: return 0;
98: }
102: static PetscErrorCode MonitorObjective(TS ts,PetscInt step,PetscReal t,Vec X,void *ictx)
103: {
104: Ctx *ctx = (Ctx*)ictx;
105: PetscErrorCode ierr;
106: const PetscScalar *x;
107: PetscScalar f;
108: PetscReal dt,gnorm;
109: PetscInt i,snesit,linit;
110: SNES snes;
111: Vec Xdot,F;
114: /* Compute objective functional */
115: VecGetArrayRead(X,&x);
116: f = 0;
117: for (i=0; i<ctx->n-1; i++) f += PetscSqr(1. - x[i]) + 100. * PetscSqr(x[i+1] - PetscSqr(x[i]));
118: VecRestoreArrayRead(X,&x);
120: /* Compute norm of gradient */
121: VecDuplicate(X,&Xdot);
122: VecDuplicate(X,&F);
123: VecZeroEntries(Xdot);
124: FormIFunction(ts,t,X,Xdot,F,ictx);
125: VecNorm(F,NORM_2,&gnorm);
126: VecDestroy(&Xdot);
127: VecDestroy(&F);
129: TSGetTimeStep(ts,&dt);
130: TSGetSNES(ts,&snes);
131: SNESGetIterationNumber(snes,&snesit);
132: SNESGetLinearSolveIterations(snes,&linit);
133: PetscPrintf(PETSC_COMM_WORLD,
134: (ctx->monitor_short
135: ? "%3D t=%10.1e dt=%10.1e f=%10.1e df=%10.1e it=(%2D,%3D)\n"
136: : "%3D t=%10.4e dt=%10.4e f=%10.4e df=%10.4e it=(%2D,%3D)\n"),
137: step,(double)t,(double)dt,(double)PetscRealPart(f),(double)gnorm,snesit,linit);
138: return(0);
139: }
142: /* ------------------------------------------------------------------- */
145: /*
146: FormIFunction - Evaluates nonlinear function, F(X,Xdot) = Xdot + grad(objective(X))
148: Input Parameters:
149: + ts - the TS context
150: . t - time
151: . X - input vector
152: . Xdot - time derivative
153: - ctx - optional user-defined context
155: Output Parameter:
156: . F - function vector
157: */
158: static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ictx)
159: {
160: PetscErrorCode ierr;
161: const PetscScalar *x;
162: PetscScalar *f;
163: PetscInt i;
164: Ctx *ctx = (Ctx*)ictx;
167: /*
168: Get pointers to vector data.
169: - For default PETSc vectors, VecGetArray() returns a pointer to
170: the data array. Otherwise, the routine is implementation dependent.
171: - You MUST call VecRestoreArray() when you no longer need access to
172: the array.
173: */
174: VecGetArrayRead(X,&x);
175: VecZeroEntries(F);
176: VecGetArray(F,&f);
178: /* Compute gradient of objective */
179: for (i=0; i<ctx->n-1; i++) {
180: PetscScalar a,a0,a1;
181: a = x[i+1] - PetscSqr(x[i]);
182: a0 = -2.*x[i];
183: a1 = 1.;
184: f[i] += -2.*(1. - x[i]) + 200.*a*a0;
185: f[i+1] += 200.*a*a1;
186: }
187: /* Restore vectors */
188: VecRestoreArrayRead(X,&x);
189: VecRestoreArray(F,&f);
190: VecAXPY(F,1.0,Xdot);
191: return(0);
192: }
193: /* ------------------------------------------------------------------- */
196: /*
197: FormIJacobian - Evaluates Jacobian matrix.
199: Input Parameters:
200: + ts - the TS context
201: . t - pseudo-time
202: . X - input vector
203: . Xdot - time derivative
204: . shift - multiplier for mass matrix
205: . dummy - user-defined context
207: Output Parameters:
208: . J - Jacobian matrix
209: . B - optionally different preconditioning matrix
210: . flag - flag indicating matrix structure
211: */
212: static PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal shift,Mat *J,Mat *B,MatStructure *flag,void *ictx)
213: {
214: const PetscScalar *x;
215: PetscErrorCode ierr;
216: PetscInt i;
217: Ctx *ctx = (Ctx*)ictx;
220: MatZeroEntries(*B);
221: /*
222: Get pointer to vector data
223: */
224: VecGetArrayRead(X,&x);
226: /*
227: Compute Jacobian entries and insert into matrix.
228: */
229: for (i=0; i<ctx->n-1; i++) {
230: PetscInt rowcol[2];
231: PetscScalar v[2][2],a,a0,a1,a00,a01,a10,a11;
232: rowcol[0] = i;
233: rowcol[1] = i+1;
234: a = x[i+1] - PetscSqr(x[i]);
235: a0 = -2.*x[i];
236: a00 = -2.;
237: a01 = 0.;
238: a1 = 1.;
239: a10 = 0.;
240: a11 = 0.;
241: v[0][0] = 2. + 200.*(a*a00 + a0*a0);
242: v[0][1] = 200.*(a*a01 + a1*a0);
243: v[1][0] = 200.*(a*a10 + a0*a1);
244: v[1][1] = 200.*(a*a11 + a1*a1);
245: MatSetValues(*B,2,rowcol,2,rowcol,&v[0][0],ADD_VALUES);
246: }
247: for (i=0; i<ctx->n; i++) {
248: MatSetValue(*B,i,i,(PetscScalar)shift,ADD_VALUES);
249: }
251: VecRestoreArrayRead(X,&x);
253: /*
254: Assemble matrix
255: */
256: MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
257: MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
258: if (*J != *B) {
259: MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
260: MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
261: }
262: return(0);
263: }