Actual source code: ex24.c

petsc-master 2016-07-22
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  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,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);if (ierr) return ierr;
 29:   ctx.n = 3;
 30:   PetscOptionsGetInt(NULL,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,NULL,"-view_final",&view_final,NULL);

 36:   ctx.monitor_short = PETSC_FALSE;
 37:   PetscOptionsGetBool(NULL,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:   MatCreateVecs(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:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
 55:   TSSetInitialTimeStep(ts,0.0,1e-3);
 56:   TSMonitorSet(ts,MonitorObjective,&ctx,NULL);

 58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59:      Customize time integrator; set runtime options
 60:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 61:   TSSetFromOptions(ts);

 63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 64:      Evaluate initial guess; then solve nonlinear system
 65:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 66:   VecSet(X,0.0);
 67:   VecGetArray(X,&x);
 68: #if 1
 69:   x[0] = 5.;
 70:   x[1] = -5.;
 71:   for (i=2; i<ctx.n; i++) x[i] = 5.;
 72: #else
 73:   x[0] = 1.0;
 74:   x[1] = 15.0;
 75:   for (i=2; i<ctx.n; i++) x[i] = 10.0;
 76: #endif
 77:   VecRestoreArray(X,&x);

 79:   TSSolve(ts,X);
 80:   TSGetSolveTime(ts,&ftime);
 81:   TSGetTimeStepNumber(ts,&steps);
 82:   TSGetSNESIterations(ts,&nits);
 83:   TSGetKSPIterations(ts,&lits);
 84:   PetscPrintf(PETSC_COMM_WORLD,"Time integrator took (%D,%D,%D) iterations to reach final time %g\n",steps,nits,lits,(double)ftime);
 85:   if (view_final) {
 86:     VecView(X,PETSC_VIEWER_STDOUT_WORLD);
 87:   }

 89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90:      Free work space.  All PETSc objects should be destroyed when they
 91:      are no longer needed.
 92:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 94:   VecDestroy(&X);
 95:   MatDestroy(&J);
 96:   TSDestroy(&ts);
 97:   PetscFinalize();
 98:   return ierr;
 99: }

103: static PetscErrorCode MonitorObjective(TS ts,PetscInt step,PetscReal t,Vec X,void *ictx)
104: {
105:   Ctx               *ctx = (Ctx*)ictx;
106:   PetscErrorCode    ierr;
107:   const PetscScalar *x;
108:   PetscScalar       f;
109:   PetscReal         dt,gnorm;
110:   PetscInt          i,snesit,linit;
111:   SNES              snes;
112:   Vec               Xdot,F;

115:   /* Compute objective functional */
116:   VecGetArrayRead(X,&x);
117:   f    = 0;
118:   for (i=0; i<ctx->n-1; i++) f += PetscSqr(1. - x[i]) + 100. * PetscSqr(x[i+1] - PetscSqr(x[i]));
119:   VecRestoreArrayRead(X,&x);

121:   /* Compute norm of gradient */
122:   VecDuplicate(X,&Xdot);
123:   VecDuplicate(X,&F);
124:   VecZeroEntries(Xdot);
125:   FormIFunction(ts,t,X,Xdot,F,ictx);
126:   VecNorm(F,NORM_2,&gnorm);
127:   VecDestroy(&Xdot);
128:   VecDestroy(&F);

130:   TSGetTimeStep(ts,&dt);
131:   TSGetSNES(ts,&snes);
132:   SNESGetIterationNumber(snes,&snesit);
133:   SNESGetLinearSolveIterations(snes,&linit);
134:   PetscPrintf(PETSC_COMM_WORLD,
135:                      (ctx->monitor_short
136:                       ? "%3D t=%10.1e  dt=%10.1e  f=%10.1e  df=%10.1e  it=(%2D,%3D)\n"
137:                       : "%3D t=%10.4e  dt=%10.4e  f=%10.4e  df=%10.4e  it=(%2D,%3D)\n"),
138:                      step,(double)t,(double)dt,(double)PetscRealPart(f),(double)gnorm,snesit,linit);
139:   return(0);
140: }


143: /* ------------------------------------------------------------------- */
146: /*
147:    FormIFunction - Evaluates nonlinear function, F(X,Xdot) = Xdot + grad(objective(X))

149:    Input Parameters:
150: +  ts   - the TS context
151: .  t - time
152: .  X    - input vector
153: .  Xdot - time derivative
154: -  ctx  - optional user-defined context

156:    Output Parameter:
157: .  F - function vector
158:  */
159: static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ictx)
160: {
161:   PetscErrorCode    ierr;
162:   const PetscScalar *x;
163:   PetscScalar       *f;
164:   PetscInt          i;
165:   Ctx               *ctx = (Ctx*)ictx;

168:   /*
169:     Get pointers to vector data.
170:     - For default PETSc vectors, VecGetArray() returns a pointer to
171:     the data array.  Otherwise, the routine is implementation dependent.
172:     - You MUST call VecRestoreArray() when you no longer need access to
173:     the array.
174:   */
175:   VecGetArrayRead(X,&x);
176:   VecZeroEntries(F);
177:   VecGetArray(F,&f);

179:   /* Compute gradient of objective */
180:   for (i=0; i<ctx->n-1; i++) {
181:     PetscScalar a,a0,a1;
182:     a       = x[i+1] - PetscSqr(x[i]);
183:     a0      = -2.*x[i];
184:     a1      = 1.;
185:     f[i]   += -2.*(1. - x[i]) + 200.*a*a0;
186:     f[i+1] += 200.*a*a1;
187:   }
188:   /* Restore vectors */
189:   VecRestoreArrayRead(X,&x);
190:   VecRestoreArray(F,&f);
191:   VecAXPY(F,1.0,Xdot);
192:   return(0);
193: }
194: /* ------------------------------------------------------------------- */
197: /*
198:    FormIJacobian - Evaluates Jacobian matrix.

200:    Input Parameters:
201: +  ts - the TS context
202: .  t - pseudo-time
203: .  X - input vector
204: .  Xdot - time derivative
205: .  shift - multiplier for mass matrix
206: .  dummy - user-defined context

208:    Output Parameters:
209: .  J - Jacobian matrix
210: .  B - optionally different preconditioning matrix
211: .  flag - flag indicating matrix structure
212: */
213: static PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal shift,Mat J,Mat B,void *ictx)
214: {
215:   const PetscScalar *x;
216:   PetscErrorCode    ierr;
217:   PetscInt          i;
218:   Ctx               *ctx = (Ctx*)ictx;

221:   MatZeroEntries(B);
222:   /*
223:      Get pointer to vector data
224:   */
225:   VecGetArrayRead(X,&x);

227:   /*
228:      Compute Jacobian entries and insert into matrix.
229:   */
230:   for (i=0; i<ctx->n-1; i++) {
231:     PetscInt    rowcol[2];
232:     PetscScalar v[2][2],a,a0,a1,a00,a01,a10,a11;
233:     rowcol[0] = i;
234:     rowcol[1] = i+1;
235:     a         = x[i+1] - PetscSqr(x[i]);
236:     a0        = -2.*x[i];
237:     a00       = -2.;
238:     a01       = 0.;
239:     a1        = 1.;
240:     a10       = 0.;
241:     a11       = 0.;
242:     v[0][0]   = 2. + 200.*(a*a00 + a0*a0);
243:     v[0][1]   = 200.*(a*a01 + a1*a0);
244:     v[1][0]   = 200.*(a*a10 + a0*a1);
245:     v[1][1]   = 200.*(a*a11 + a1*a1);
246:     MatSetValues(B,2,rowcol,2,rowcol,&v[0][0],ADD_VALUES);
247:   }
248:   for (i=0; i<ctx->n; i++) {
249:     MatSetValue(B,i,i,(PetscScalar)shift,ADD_VALUES);
250:   }

252:   VecRestoreArrayRead(X,&x);

254:   /*
255:      Assemble matrix
256:   */
257:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
258:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
259:   if (J != B) {
260:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
261:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
262:   }
263:   return(0);
264: }