xref: /petsc/src/snes/impls/vi/vi.c (revision fcb1c9af1a39adbb75e1011fa083d9d197867fec)
1 
2 #include <../src/snes/impls/vi/viimpl.h> /*I "petscsnes.h" I*/
3 #include <../include/private/kspimpl.h>
4 #include <../include/private/matimpl.h>
5 
6 #undef __FUNCT__
7 #define __FUNCT__ "SNESMonitorVI"
8 PetscErrorCode  SNESMonitorVI(SNES snes,PetscInt its,PetscReal fgnorm,void *dummy)
9 {
10   PetscErrorCode          ierr;
11   SNES_VI                 *vi = (SNES_VI*)snes->data;
12   PetscViewerASCIIMonitor viewer = (PetscViewerASCIIMonitor) dummy;
13   const PetscScalar       *x,*xl,*xu,*f;
14   PetscInt                i,n,act = 0;
15   PetscReal               rnorm,fnorm;
16 
17   PetscFunctionBegin;
18   if (!dummy) {
19     ierr = PetscViewerASCIIMonitorCreate(((PetscObject)snes)->comm,"stdout",0,&viewer);CHKERRQ(ierr);
20   }
21   ierr = VecGetLocalSize(snes->vec_sol,&n);CHKERRQ(ierr);
22   ierr = VecGetArrayRead(vi->xl,&xl);CHKERRQ(ierr);
23   ierr = VecGetArrayRead(vi->xu,&xu);CHKERRQ(ierr);
24   ierr = VecGetArrayRead(snes->vec_sol,&x);CHKERRQ(ierr);
25   ierr = VecGetArrayRead(snes->vec_func,&f);CHKERRQ(ierr);
26 
27   rnorm = 0.0;
28   for (i=0; i<n; i++) {
29     if (((x[i] > xl[i] + 1.e-8 || (f[i] < 0.0)) && ((x[i] < xu[i] - 1.e-8) || f[i] > 0.0))) rnorm += f[i]*f[i];
30     else act++;
31   }
32   ierr = VecRestoreArrayRead(snes->vec_func,&f);CHKERRQ(ierr);
33   ierr = VecRestoreArrayRead(vi->xl,&xl);CHKERRQ(ierr);
34   ierr = VecRestoreArrayRead(vi->xu,&xu);CHKERRQ(ierr);
35   ierr = VecRestoreArrayRead(snes->vec_sol,&x);CHKERRQ(ierr);
36   ierr = MPI_Allreduce(&rnorm,&fnorm,1,MPIU_REAL,MPIU_SUM,((PetscObject)snes)->comm);CHKERRQ(ierr);
37   fnorm = sqrt(fnorm);
38   ierr = PetscViewerASCIIMonitorPrintf(viewer,"%3D SNES VI Function norm %14.12e Active constraints %D\n",its,fnorm,act);CHKERRQ(ierr);
39   if (!dummy) {
40     ierr = PetscViewerASCIIMonitorDestroy(&viewer);CHKERRQ(ierr);
41   }
42   PetscFunctionReturn(0);
43 }
44 
45 /*
46      Checks if J^T F = 0 which implies we've found a local minimum of the norm of the function,
47     || F(u) ||_2 but not a zero, F(u) = 0. In the case when one cannot compute J^T F we use the fact that
48     0 = (J^T F)^T W = F^T J W iff W not in the null space of J. Thanks for Jorge More
49     for this trick. One assumes that the probability that W is in the null space of J is very, very small.
50 */
51 #undef __FUNCT__
52 #define __FUNCT__ "SNESVICheckLocalMin_Private"
53 PetscErrorCode SNESVICheckLocalMin_Private(SNES snes,Mat A,Vec F,Vec W,PetscReal fnorm,PetscBool *ismin)
54 {
55   PetscReal      a1;
56   PetscErrorCode ierr;
57   PetscBool     hastranspose;
58 
59   PetscFunctionBegin;
60   *ismin = PETSC_FALSE;
61   ierr = MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);CHKERRQ(ierr);
62   if (hastranspose) {
63     /* Compute || J^T F|| */
64     ierr = MatMultTranspose(A,F,W);CHKERRQ(ierr);
65     ierr = VecNorm(W,NORM_2,&a1);CHKERRQ(ierr);
66     ierr = PetscInfo1(snes,"|| J^T F|| %G near zero implies found a local minimum\n",a1/fnorm);CHKERRQ(ierr);
67     if (a1/fnorm < 1.e-4) *ismin = PETSC_TRUE;
68   } else {
69     Vec         work;
70     PetscScalar result;
71     PetscReal   wnorm;
72 
73     ierr = VecSetRandom(W,PETSC_NULL);CHKERRQ(ierr);
74     ierr = VecNorm(W,NORM_2,&wnorm);CHKERRQ(ierr);
75     ierr = VecDuplicate(W,&work);CHKERRQ(ierr);
76     ierr = MatMult(A,W,work);CHKERRQ(ierr);
77     ierr = VecDot(F,work,&result);CHKERRQ(ierr);
78     ierr = VecDestroy(&work);CHKERRQ(ierr);
79     a1   = PetscAbsScalar(result)/(fnorm*wnorm);
80     ierr = PetscInfo1(snes,"(F^T J random)/(|| F ||*||random|| %G near zero implies found a local minimum\n",a1);CHKERRQ(ierr);
81     if (a1 < 1.e-4) *ismin = PETSC_TRUE;
82   }
83   PetscFunctionReturn(0);
84 }
85 
86 /*
87      Checks if J^T(F - J*X) = 0
88 */
89 #undef __FUNCT__
90 #define __FUNCT__ "SNESVICheckResidual_Private"
91 PetscErrorCode SNESVICheckResidual_Private(SNES snes,Mat A,Vec F,Vec X,Vec W1,Vec W2)
92 {
93   PetscReal      a1,a2;
94   PetscErrorCode ierr;
95   PetscBool     hastranspose;
96 
97   PetscFunctionBegin;
98   ierr = MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);CHKERRQ(ierr);
99   if (hastranspose) {
100     ierr = MatMult(A,X,W1);CHKERRQ(ierr);
101     ierr = VecAXPY(W1,-1.0,F);CHKERRQ(ierr);
102 
103     /* Compute || J^T W|| */
104     ierr = MatMultTranspose(A,W1,W2);CHKERRQ(ierr);
105     ierr = VecNorm(W1,NORM_2,&a1);CHKERRQ(ierr);
106     ierr = VecNorm(W2,NORM_2,&a2);CHKERRQ(ierr);
107     if (a1 != 0.0) {
108       ierr = PetscInfo1(snes,"||J^T(F-Ax)||/||F-AX|| %G near zero implies inconsistent rhs\n",a2/a1);CHKERRQ(ierr);
109     }
110   }
111   PetscFunctionReturn(0);
112 }
113 
114 /*
115   SNESDefaultConverged_VI - Checks the convergence of the semismooth newton algorithm.
116 
117   Notes:
118   The convergence criterion currently implemented is
119   merit < abstol
120   merit < rtol*merit_initial
121 */
122 #undef __FUNCT__
123 #define __FUNCT__ "SNESDefaultConverged_VI"
124 PetscErrorCode SNESDefaultConverged_VI(SNES snes,PetscInt it,PetscReal xnorm,PetscReal gradnorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
125 {
126   PetscErrorCode ierr;
127 
128   PetscFunctionBegin;
129   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
130   PetscValidPointer(reason,6);
131 
132   *reason = SNES_CONVERGED_ITERATING;
133 
134   if (!it) {
135     /* set parameter for default relative tolerance convergence test */
136     snes->ttol = fnorm*snes->rtol;
137   }
138   if (fnorm != fnorm) {
139     ierr = PetscInfo(snes,"Failed to converged, function norm is NaN\n");CHKERRQ(ierr);
140     *reason = SNES_DIVERGED_FNORM_NAN;
141   } else if (fnorm < snes->abstol) {
142     ierr = PetscInfo2(snes,"Converged due to function norm %G < %G\n",fnorm,snes->abstol);CHKERRQ(ierr);
143     *reason = SNES_CONVERGED_FNORM_ABS;
144   } else if (snes->nfuncs >= snes->max_funcs) {
145     ierr = PetscInfo2(snes,"Exceeded maximum number of function evaluations: %D > %D\n",snes->nfuncs,snes->max_funcs);CHKERRQ(ierr);
146     *reason = SNES_DIVERGED_FUNCTION_COUNT;
147   }
148 
149   if (it && !*reason) {
150     if (fnorm < snes->ttol) {
151       ierr = PetscInfo2(snes,"Converged due to function norm %G < %G (relative tolerance)\n",fnorm,snes->ttol);CHKERRQ(ierr);
152       *reason = SNES_CONVERGED_FNORM_RELATIVE;
153     }
154   }
155   PetscFunctionReturn(0);
156 }
157 
158 /*
159   SNESVIComputeMeritFunction - Evaluates the merit function for the mixed complementarity problem.
160 
161   Input Parameter:
162 . phi - the semismooth function
163 
164   Output Parameter:
165 . merit - the merit function
166 . phinorm - ||phi||
167 
168   Notes:
169   The merit function for the mixed complementarity problem is defined as
170      merit = 0.5*phi^T*phi
171 */
172 #undef __FUNCT__
173 #define __FUNCT__ "SNESVIComputeMeritFunction"
174 static PetscErrorCode SNESVIComputeMeritFunction(Vec phi, PetscReal* merit,PetscReal* phinorm)
175 {
176   PetscErrorCode ierr;
177 
178   PetscFunctionBegin;
179   ierr = VecNormBegin(phi,NORM_2,phinorm);CHKERRQ(ierr);
180   ierr = VecNormEnd(phi,NORM_2,phinorm);CHKERRQ(ierr);
181 
182   *merit = 0.5*(*phinorm)*(*phinorm);
183   PetscFunctionReturn(0);
184 }
185 
186 PETSC_STATIC_INLINE PetscScalar Phi(PetscScalar a,PetscScalar b)
187 {
188   return a + b - sqrt(a*a + b*b);
189 }
190 
191 PETSC_STATIC_INLINE PetscScalar DPhi(PetscScalar a,PetscScalar b)
192 {
193   if ((PetscAbsScalar(a) >= 1.e-6) || (PetscAbsScalar(b) >= 1.e-6)) return  1.0 - a/ sqrt(a*a + b*b);
194   else return .5;
195 }
196 
197 /*
198    SNESVIComputeFunction - Reformulates a system of nonlinear equations in mixed complementarity form to a system of nonlinear equations in semismooth form.
199 
200    Input Parameters:
201 .  snes - the SNES context
202 .  x - current iterate
203 .  functx - user defined function context
204 
205    Output Parameters:
206 .  phi - Semismooth function
207 
208 */
209 #undef __FUNCT__
210 #define __FUNCT__ "SNESVIComputeFunction"
211 static PetscErrorCode SNESVIComputeFunction(SNES snes,Vec X,Vec phi,void* functx)
212 {
213   PetscErrorCode  ierr;
214   SNES_VI         *vi = (SNES_VI*)snes->data;
215   Vec             Xl = vi->xl,Xu = vi->xu,F = snes->vec_func;
216   PetscScalar     *phi_arr,*x_arr,*f_arr,*l,*u;
217   PetscInt        i,nlocal;
218 
219   PetscFunctionBegin;
220   ierr = (*vi->computeuserfunction)(snes,X,F,functx);CHKERRQ(ierr);
221   ierr = VecGetLocalSize(X,&nlocal);CHKERRQ(ierr);
222   ierr = VecGetArray(X,&x_arr);CHKERRQ(ierr);
223   ierr = VecGetArray(F,&f_arr);CHKERRQ(ierr);
224   ierr = VecGetArray(Xl,&l);CHKERRQ(ierr);
225   ierr = VecGetArray(Xu,&u);CHKERRQ(ierr);
226   ierr = VecGetArray(phi,&phi_arr);CHKERRQ(ierr);
227 
228   for (i=0;i < nlocal;i++) {
229     if ((l[i] <= PETSC_VI_NINF) && (u[i] >= PETSC_VI_INF)) { /* no constraints on variable */
230       phi_arr[i] = f_arr[i];
231     } else if (l[i] <= PETSC_VI_NINF) {                      /* upper bound on variable only */
232       phi_arr[i] = -Phi(u[i] - x_arr[i],-f_arr[i]);
233     } else if (u[i] >= PETSC_VI_INF) {                       /* lower bound on variable only */
234       phi_arr[i] = Phi(x_arr[i] - l[i],f_arr[i]);
235     } else if (l[i] == u[i]) {
236       phi_arr[i] = l[i] - x_arr[i];
237     } else {                                                /* both bounds on variable */
238       phi_arr[i] = Phi(x_arr[i] - l[i],-Phi(u[i] - x_arr[i],-f_arr[i]));
239     }
240   }
241 
242   ierr = VecRestoreArray(X,&x_arr);CHKERRQ(ierr);
243   ierr = VecRestoreArray(F,&f_arr);CHKERRQ(ierr);
244   ierr = VecRestoreArray(Xl,&l);CHKERRQ(ierr);
245   ierr = VecRestoreArray(Xu,&u);CHKERRQ(ierr);
246   ierr = VecRestoreArray(phi,&phi_arr);CHKERRQ(ierr);
247   PetscFunctionReturn(0);
248 }
249 
250 /*
251    SNESVIComputeBsubdifferentialVectors - Computes the diagonal shift (Da) and row scaling (Db) vectors needed for the
252                                           the semismooth jacobian.
253 */
254 #undef __FUNCT__
255 #define __FUNCT__ "SNESVIComputeBsubdifferentialVectors"
256 PetscErrorCode SNESVIComputeBsubdifferentialVectors(SNES snes,Vec X,Vec F,Mat jac,Vec Da,Vec Db)
257 {
258   PetscErrorCode ierr;
259   SNES_VI      *vi = (SNES_VI*)snes->data;
260   PetscScalar    *l,*u,*x,*f,*da,*db,da1,da2,db1,db2;
261   PetscInt       i,nlocal;
262 
263   PetscFunctionBegin;
264 
265   ierr = VecGetArray(X,&x);CHKERRQ(ierr);
266   ierr = VecGetArray(F,&f);CHKERRQ(ierr);
267   ierr = VecGetArray(vi->xl,&l);CHKERRQ(ierr);
268   ierr = VecGetArray(vi->xu,&u);CHKERRQ(ierr);
269   ierr = VecGetArray(Da,&da);CHKERRQ(ierr);
270   ierr = VecGetArray(Db,&db);CHKERRQ(ierr);
271   ierr = VecGetLocalSize(X,&nlocal);CHKERRQ(ierr);
272 
273   for (i=0;i< nlocal;i++) {
274     if ((l[i] <= PETSC_VI_NINF) && (u[i] >= PETSC_VI_INF)) {/* no constraints on variable */
275       da[i] = 0;
276       db[i] = 1;
277     } else if (l[i] <= PETSC_VI_NINF) {                     /* upper bound on variable only */
278       da[i] = DPhi(u[i] - x[i], -f[i]);
279       db[i] = DPhi(-f[i],u[i] - x[i]);
280     } else if (u[i] >= PETSC_VI_INF) {                      /* lower bound on variable only */
281       da[i] = DPhi(x[i] - l[i], f[i]);
282       db[i] = DPhi(f[i],x[i] - l[i]);
283     } else if (l[i] == u[i]) {                              /* fixed variable */
284       da[i] = 1;
285       db[i] = 0;
286     } else {                                                /* upper and lower bounds on variable */
287       da1 = DPhi(x[i] - l[i], -Phi(u[i] - x[i], -f[i]));
288       db1 = DPhi(-Phi(u[i] - x[i], -f[i]),x[i] - l[i]);
289       da2 = DPhi(u[i] - x[i], -f[i]);
290       db2 = DPhi(-f[i],u[i] - x[i]);
291       da[i] = da1 + db1*da2;
292       db[i] = db1*db2;
293     }
294   }
295 
296   ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
297   ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
298   ierr = VecRestoreArray(vi->xl,&l);CHKERRQ(ierr);
299   ierr = VecRestoreArray(vi->xu,&u);CHKERRQ(ierr);
300   ierr = VecRestoreArray(Da,&da);CHKERRQ(ierr);
301   ierr = VecRestoreArray(Db,&db);CHKERRQ(ierr);
302   PetscFunctionReturn(0);
303 }
304 
305 /*
306    SNESVIComputeJacobian - Computes the jacobian of the semismooth function.The Jacobian for the semismooth function is an element of the B-subdifferential of the Fischer-Burmeister function for complementarity problems.
307 
308    Input Parameters:
309 .  Da       - Diagonal shift vector for the semismooth jacobian.
310 .  Db       - Row scaling vector for the semismooth jacobian.
311 
312    Output Parameters:
313 .  jac      - semismooth jacobian
314 .  jac_pre  - optional preconditioning matrix
315 
316    Notes:
317    The semismooth jacobian matrix is given by
318    jac = Da + Db*jacfun
319    where Db is the row scaling matrix stored as a vector,
320          Da is the diagonal perturbation matrix stored as a vector
321    and   jacfun is the jacobian of the original nonlinear function.
322 */
323 #undef __FUNCT__
324 #define __FUNCT__ "SNESVIComputeJacobian"
325 PetscErrorCode SNESVIComputeJacobian(Mat jac, Mat jac_pre,Vec Da, Vec Db)
326 {
327   PetscErrorCode ierr;
328 
329   /* Do row scaling  and add diagonal perturbation */
330   ierr = MatDiagonalScale(jac,Db,PETSC_NULL);CHKERRQ(ierr);
331   ierr = MatDiagonalSet(jac,Da,ADD_VALUES);CHKERRQ(ierr);
332   if (jac != jac_pre) { /* If jac and jac_pre are different */
333     ierr = MatDiagonalScale(jac_pre,Db,PETSC_NULL);
334     ierr = MatDiagonalSet(jac_pre,Da,ADD_VALUES);CHKERRQ(ierr);
335   }
336   PetscFunctionReturn(0);
337 }
338 
339 /*
340    SNESVIComputeMeritFunctionGradient - Computes the gradient of the merit function psi.
341 
342    Input Parameters:
343    phi - semismooth function.
344    H   - semismooth jacobian
345 
346    Output Parameters:
347    dpsi - merit function gradient
348 
349    Notes:
350   The merit function gradient is computed as follows
351         dpsi = H^T*phi
352 */
353 #undef __FUNCT__
354 #define __FUNCT__ "SNESVIComputeMeritFunctionGradient"
355 PetscErrorCode SNESVIComputeMeritFunctionGradient(Mat H, Vec phi, Vec dpsi)
356 {
357   PetscErrorCode ierr;
358 
359   PetscFunctionBegin;
360   ierr = MatMultTranspose(H,phi,dpsi);CHKERRQ(ierr);
361   PetscFunctionReturn(0);
362 }
363 
364 /* -------------------------------------------------------------------------- */
365 /*
366    SNESVIProjectOntoBounds - Projects X onto the feasible region so that Xl[i] <= X[i] <= Xu[i] for i = 1...n.
367 
368    Input Parameters:
369 .  SNES - nonlinear solver context
370 
371    Output Parameters:
372 .  X - Bound projected X
373 
374 */
375 
376 #undef __FUNCT__
377 #define __FUNCT__ "SNESVIProjectOntoBounds"
378 PetscErrorCode SNESVIProjectOntoBounds(SNES snes,Vec X)
379 {
380   PetscErrorCode    ierr;
381   SNES_VI           *vi = (SNES_VI*)snes->data;
382   const PetscScalar *xl,*xu;
383   PetscScalar       *x;
384   PetscInt          i,n;
385 
386   PetscFunctionBegin;
387   ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
388   ierr = VecGetArray(X,&x);CHKERRQ(ierr);
389   ierr = VecGetArrayRead(vi->xl,&xl);CHKERRQ(ierr);
390   ierr = VecGetArrayRead(vi->xu,&xu);CHKERRQ(ierr);
391 
392   for(i = 0;i<n;i++) {
393     if (x[i] < xl[i]) x[i] = xl[i];
394     else if (x[i] > xu[i]) x[i] = xu[i];
395   }
396   ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
397   ierr = VecRestoreArrayRead(vi->xl,&xl);CHKERRQ(ierr);
398   ierr = VecRestoreArrayRead(vi->xu,&xu);CHKERRQ(ierr);
399   PetscFunctionReturn(0);
400 }
401 
402 /*  --------------------------------------------------------------------
403 
404      This file implements a semismooth truncated Newton method with a line search,
405      for solving a system of nonlinear equations in complementarity form, using the KSP, Vec,
406      and Mat interfaces for linear solvers, vectors, and matrices,
407      respectively.
408 
409      The following basic routines are required for each nonlinear solver:
410           SNESCreate_XXX()          - Creates a nonlinear solver context
411           SNESSetFromOptions_XXX()  - Sets runtime options
412           SNESSolve_XXX()           - Solves the nonlinear system
413           SNESDestroy_XXX()         - Destroys the nonlinear solver context
414      The suffix "_XXX" denotes a particular implementation, in this case
415      we use _VI (e.g., SNESCreate_VI, SNESSolve_VI) for solving
416      systems of nonlinear equations with a line search (LS) method.
417      These routines are actually called via the common user interface
418      routines SNESCreate(), SNESSetFromOptions(), SNESSolve(), and
419      SNESDestroy(), so the application code interface remains identical
420      for all nonlinear solvers.
421 
422      Another key routine is:
423           SNESSetUp_XXX()           - Prepares for the use of a nonlinear solver
424      by setting data structures and options.   The interface routine SNESSetUp()
425      is not usually called directly by the user, but instead is called by
426      SNESSolve() if necessary.
427 
428      Additional basic routines are:
429           SNESView_XXX()            - Prints details of runtime options that
430                                       have actually been used.
431      These are called by application codes via the interface routines
432      SNESView().
433 
434      The various types of solvers (preconditioners, Krylov subspace methods,
435      nonlinear solvers, timesteppers) are all organized similarly, so the
436      above description applies to these categories also.
437 
438     -------------------------------------------------------------------- */
439 /*
440    SNESSolveVI_SS - Solves the complementarity problem with a semismooth Newton
441    method using a line search.
442 
443    Input Parameters:
444 .  snes - the SNES context
445 
446    Output Parameter:
447 .  outits - number of iterations until termination
448 
449    Application Interface Routine: SNESSolve()
450 
451    Notes:
452    This implements essentially a semismooth Newton method with a
453    line search. The default line search does not do any line seach
454    but rather takes a full newton step.
455 */
456 #undef __FUNCT__
457 #define __FUNCT__ "SNESSolveVI_SS"
458 PetscErrorCode SNESSolveVI_SS(SNES snes)
459 {
460   SNES_VI            *vi = (SNES_VI*)snes->data;
461   PetscErrorCode     ierr;
462   PetscInt           maxits,i,lits;
463   PetscBool          lssucceed;
464   MatStructure       flg = DIFFERENT_NONZERO_PATTERN;
465   PetscReal          gnorm,xnorm=0,ynorm;
466   Vec                Y,X,F,G,W;
467   KSPConvergedReason kspreason;
468 
469   PetscFunctionBegin;
470   vi->computeuserfunction    = snes->ops->computefunction;
471   snes->ops->computefunction = SNESVIComputeFunction;
472 
473   snes->numFailures            = 0;
474   snes->numLinearSolveFailures = 0;
475   snes->reason                 = SNES_CONVERGED_ITERATING;
476 
477   maxits	= snes->max_its;	/* maximum number of iterations */
478   X		= snes->vec_sol;	/* solution vector */
479   F		= snes->vec_func;	/* residual vector */
480   Y		= snes->work[0];	/* work vectors */
481   G		= snes->work[1];
482   W		= snes->work[2];
483 
484   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
485   snes->iter = 0;
486   snes->norm = 0.0;
487   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
488 
489   ierr = SNESVIProjectOntoBounds(snes,X);CHKERRQ(ierr);
490   ierr = SNESComputeFunction(snes,X,vi->phi);CHKERRQ(ierr);
491   if (snes->domainerror) {
492     snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
493     snes->ops->computefunction = vi->computeuserfunction;
494     PetscFunctionReturn(0);
495   }
496    /* Compute Merit function */
497   ierr = SNESVIComputeMeritFunction(vi->phi,&vi->merit,&vi->phinorm);CHKERRQ(ierr);
498 
499   ierr = VecNormBegin(X,NORM_2,&xnorm);CHKERRQ(ierr);	/* xnorm <- ||x||  */
500   ierr = VecNormEnd(X,NORM_2,&xnorm);CHKERRQ(ierr);
501   if (PetscIsInfOrNanReal(vi->merit)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
502 
503   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
504   snes->norm = vi->phinorm;
505   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
506   SNESLogConvHistory(snes,vi->phinorm,0);
507   ierr = SNESMonitor(snes,0,vi->phinorm);CHKERRQ(ierr);
508 
509   /* set parameter for default relative tolerance convergence test */
510   snes->ttol = vi->phinorm*snes->rtol;
511   /* test convergence */
512   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,vi->phinorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
513   if (snes->reason) {
514     snes->ops->computefunction = vi->computeuserfunction;
515     PetscFunctionReturn(0);
516   }
517 
518   for (i=0; i<maxits; i++) {
519 
520     /* Call general purpose update function */
521     if (snes->ops->update) {
522       ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
523     }
524 
525     /* Solve J Y = Phi, where J is the semismooth jacobian */
526     /* Get the nonlinear function jacobian */
527     ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr);
528     /* Get the diagonal shift and row scaling vectors */
529     ierr = SNESVIComputeBsubdifferentialVectors(snes,X,F,snes->jacobian,vi->Da,vi->Db);CHKERRQ(ierr);
530     /* Compute the semismooth jacobian */
531     ierr = SNESVIComputeJacobian(snes->jacobian,snes->jacobian_pre,vi->Da,vi->Db);CHKERRQ(ierr);
532     /* Compute the merit function gradient */
533     ierr = SNESVIComputeMeritFunctionGradient(snes->jacobian,vi->phi,vi->dpsi);CHKERRQ(ierr);
534     ierr = KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);CHKERRQ(ierr);
535     ierr = SNES_KSPSolve(snes,snes->ksp,vi->phi,Y);CHKERRQ(ierr);
536     ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr);
537 
538     if (kspreason < 0) {
539       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
540         ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr);
541         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
542         break;
543       }
544     }
545     ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr);
546     snes->linear_its += lits;
547     ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr);
548     /*
549     if (vi->precheckstep) {
550       PetscBool changed_y = PETSC_FALSE;
551       ierr = (*vi->precheckstep)(snes,X,Y,vi->precheck,&changed_y);CHKERRQ(ierr);
552     }
553 
554     if (PetscLogPrintInfo){
555       ierr = SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr);
556     }
557     */
558     /* Compute a (scaled) negative update in the line search routine:
559          Y <- X - lambda*Y
560        and evaluate G = function(Y) (depends on the line search).
561     */
562     ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr);
563     ynorm = 1; gnorm = vi->phinorm;
564     ierr = (*vi->LineSearch)(snes,vi->lsP,X,vi->phi,G,Y,W,vi->phinorm,xnorm,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
565     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",vi->phinorm,gnorm,ynorm,(int)lssucceed);CHKERRQ(ierr);
566     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
567     if (snes->domainerror) {
568       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
569       snes->ops->computefunction = vi->computeuserfunction;
570       PetscFunctionReturn(0);
571     }
572     if (!lssucceed) {
573       if (++snes->numFailures >= snes->maxFailures) {
574 	PetscBool ismin;
575         snes->reason = SNES_DIVERGED_LINE_SEARCH;
576         ierr = SNESVICheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr);
577         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
578         break;
579       }
580     }
581     /* Update function and solution vectors */
582     vi->phinorm = gnorm;
583     vi->merit = 0.5*vi->phinorm*vi->phinorm;
584     ierr = VecCopy(G,vi->phi);CHKERRQ(ierr);
585     ierr = VecCopy(W,X);CHKERRQ(ierr);
586     /* Monitor convergence */
587     ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
588     snes->iter = i+1;
589     snes->norm = vi->phinorm;
590     ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
591     SNESLogConvHistory(snes,snes->norm,lits);
592     ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr);
593     /* Test for convergence, xnorm = || X || */
594     if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); }
595     ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,vi->phinorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
596     if (snes->reason) break;
597   }
598   if (i == maxits) {
599     ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr);
600     if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
601   }
602   snes->ops->computefunction = vi->computeuserfunction;
603   PetscFunctionReturn(0);
604 }
605 
606 #undef __FUNCT__
607 #define __FUNCT__ "SNESVIGetActiveSetIS"
608 /*
609    SNESVIGetActiveSetIndices - Gets the global indices for the active set variables
610 
611    Input parameter
612 .  snes - the SNES context
613 .  X    - the snes solution vector
614 .  F    - the nonlinear function vector
615 
616    Output parameter
617 .  ISact - active set index set
618  */
619 PetscErrorCode SNESVIGetActiveSetIS(SNES snes,Vec X,Vec F,IS* ISact)
620 {
621   PetscErrorCode   ierr;
622   SNES_VI          *vi = (SNES_VI*)snes->data;
623   Vec               Xl=vi->xl,Xu=vi->xu;
624   const PetscScalar *x,*f,*xl,*xu;
625   PetscInt          *idx_act,i,nlocal,nloc_isact=0,ilow,ihigh,i1=0;
626 
627   PetscFunctionBegin;
628   ierr = VecGetLocalSize(X,&nlocal);CHKERRQ(ierr);
629   ierr = VecGetOwnershipRange(X,&ilow,&ihigh);CHKERRQ(ierr);
630   ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
631   ierr = VecGetArrayRead(Xl,&xl);CHKERRQ(ierr);
632   ierr = VecGetArrayRead(Xu,&xu);CHKERRQ(ierr);
633   ierr = VecGetArrayRead(F,&f);CHKERRQ(ierr);
634   /* Compute active set size */
635   for (i=0; i < nlocal;i++) {
636     if (!((x[i] > xl[i] + 1.e-8 || (f[i] < 0.0)) && ((x[i] < xu[i] - 1.e-8) || f[i] > 0.0))) nloc_isact++;
637   }
638 
639   ierr = PetscMalloc(nloc_isact*sizeof(PetscInt),&idx_act);CHKERRQ(ierr);
640 
641   /* Set active set indices */
642   for(i=0; i < nlocal; i++) {
643     if (!((x[i] > xl[i] + 1.e-8 || (f[i] < 0.0)) && ((x[i] < xu[i] - 1.e-8) || f[i] > 0.0))) idx_act[i1++] = ilow+i;
644   }
645 
646    /* Create active set IS */
647   ierr = ISCreateGeneral(((PetscObject)snes)->comm,nloc_isact,idx_act,PETSC_OWN_POINTER,ISact);CHKERRQ(ierr);
648 
649   ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
650   ierr = VecRestoreArrayRead(Xl,&xl);CHKERRQ(ierr);
651   ierr = VecRestoreArrayRead(Xu,&xu);CHKERRQ(ierr);
652   ierr = VecRestoreArrayRead(F,&f);CHKERRQ(ierr);
653   PetscFunctionReturn(0);
654 }
655 
656 #undef __FUNCT__
657 #define __FUNCT__ "SNESVICreateIndexSets_RS"
658 PetscErrorCode SNESVICreateIndexSets_RS(SNES snes,Vec X,Vec F,IS* ISact,IS* ISinact)
659 {
660   PetscErrorCode     ierr;
661 
662   PetscFunctionBegin;
663   ierr = SNESVIGetActiveSetIS(snes,X,F,ISact);CHKERRQ(ierr);
664   ierr = ISComplement(*ISact,X->map->rstart,X->map->rend,ISinact);CHKERRQ(ierr);
665   PetscFunctionReturn(0);
666 }
667 
668 /* Create active and inactive set vectors. The local size of this vector is set and petsc computes the global size */
669 #undef __FUNCT__
670 #define __FUNCT__ "SNESVICreateSubVectors"
671 PetscErrorCode SNESVICreateSubVectors(SNES snes,PetscInt n,Vec* newv)
672 {
673   PetscErrorCode ierr;
674   Vec            v;
675 
676   PetscFunctionBegin;
677   ierr = VecCreate(((PetscObject)snes)->comm,&v);CHKERRQ(ierr);
678   ierr = VecSetSizes(v,n,PETSC_DECIDE);CHKERRQ(ierr);
679   ierr = VecSetFromOptions(v);CHKERRQ(ierr);
680   *newv = v;
681 
682   PetscFunctionReturn(0);
683 }
684 
685 /* Resets the snes PC and KSP when the active set sizes change */
686 #undef __FUNCT__
687 #define __FUNCT__ "SNESVIResetPCandKSP"
688 PetscErrorCode SNESVIResetPCandKSP(SNES snes,Mat Amat,Mat Pmat)
689 {
690   PetscErrorCode         ierr;
691   KSP                    kspnew,snesksp;
692   PC                     pcnew;
693   const MatSolverPackage stype;
694 
695   PetscFunctionBegin;
696   /* The active and inactive set sizes have changed so need to create a new snes->ksp object */
697   ierr = SNESGetKSP(snes,&snesksp);CHKERRQ(ierr);
698   ierr = KSPCreate(((PetscObject)snes)->comm,&kspnew);CHKERRQ(ierr);
699   /* Copy over snes->ksp info */
700   kspnew->pc_side = snesksp->pc_side;
701   kspnew->rtol    = snesksp->rtol;
702   kspnew->abstol    = snesksp->abstol;
703   kspnew->max_it  = snesksp->max_it;
704   ierr = KSPSetType(kspnew,((PetscObject)snesksp)->type_name);CHKERRQ(ierr);
705   ierr = KSPGetPC(kspnew,&pcnew);CHKERRQ(ierr);
706   ierr = PCSetType(kspnew->pc,((PetscObject)snesksp->pc)->type_name);CHKERRQ(ierr);
707   ierr = PCSetOperators(kspnew->pc,Amat,Pmat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
708   ierr = PCFactorGetMatSolverPackage(snesksp->pc,&stype);CHKERRQ(ierr);
709   ierr = PCFactorSetMatSolverPackage(kspnew->pc,stype);CHKERRQ(ierr);
710   ierr = KSPDestroy(&snesksp);CHKERRQ(ierr);
711   snes->ksp = kspnew;
712   ierr = PetscLogObjectParent(snes,kspnew);CHKERRQ(ierr);
713   ierr = KSPSetFromOptions(kspnew);CHKERRQ(ierr);
714   PetscFunctionReturn(0);
715 }
716 
717 
718 #undef __FUNCT__
719 #define __FUNCT__ "SNESVIComputeInactiveSetFnorm"
720 PetscErrorCode SNESVIComputeInactiveSetFnorm(SNES snes,Vec F,Vec X,PetscScalar *fnorm)
721 {
722   PetscErrorCode    ierr;
723   SNES_VI           *vi = (SNES_VI*)snes->data;
724   const PetscScalar *x,*xl,*xu,*f;
725   PetscInt          i,n;
726   PetscReal         rnorm;
727 
728   PetscFunctionBegin;
729   ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
730   ierr = VecGetArrayRead(vi->xl,&xl);CHKERRQ(ierr);
731   ierr = VecGetArrayRead(vi->xu,&xu);CHKERRQ(ierr);
732   ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
733   ierr = VecGetArrayRead(F,&f);CHKERRQ(ierr);
734   rnorm = 0.0;
735   for (i=0; i<n; i++) {
736     if (((x[i] > xl[i] + 1.e-8 || (f[i] < 0.0)) && ((x[i] < xu[i] - 1.e-8) || f[i] > 0.0))) rnorm += f[i]*f[i];
737   }
738   ierr = VecRestoreArrayRead(F,&f);CHKERRQ(ierr);
739   ierr = VecRestoreArrayRead(vi->xl,&xl);CHKERRQ(ierr);
740   ierr = VecRestoreArrayRead(vi->xu,&xu);CHKERRQ(ierr);
741   ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
742   ierr = MPI_Allreduce(&rnorm,fnorm,1,MPIU_REAL,MPIU_SUM,((PetscObject)snes)->comm);CHKERRQ(ierr);
743   *fnorm = sqrt(*fnorm);
744   PetscFunctionReturn(0);
745 }
746 
747 /* Variational Inequality solver using reduce space method. No semismooth algorithm is
748    implemented in this algorithm. It basically identifies the active variables and does
749    a linear solve on the inactive variables. */
750 #undef __FUNCT__
751 #define __FUNCT__ "SNESSolveVI_RS"
752 PetscErrorCode SNESSolveVI_RS(SNES snes)
753 {
754   SNES_VI          *vi = (SNES_VI*)snes->data;
755   PetscErrorCode    ierr;
756   PetscInt          maxits,i,lits;
757   PetscBool         lssucceed;
758   MatStructure      flg = DIFFERENT_NONZERO_PATTERN;
759   PetscReal         fnorm,gnorm,xnorm=0,ynorm;
760   Vec                Y,X,F,G,W;
761   KSPConvergedReason kspreason;
762 
763   PetscFunctionBegin;
764   snes->numFailures            = 0;
765   snes->numLinearSolveFailures = 0;
766   snes->reason                 = SNES_CONVERGED_ITERATING;
767 
768   maxits	= snes->max_its;	/* maximum number of iterations */
769   X		= snes->vec_sol;	/* solution vector */
770   F		= snes->vec_func;	/* residual vector */
771   Y		= snes->work[0];	/* work vectors */
772   G		= snes->work[1];
773   W		= snes->work[2];
774 
775   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
776   snes->iter = 0;
777   snes->norm = 0.0;
778   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
779 
780   ierr = SNESVIProjectOntoBounds(snes,X);CHKERRQ(ierr);
781   ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);
782   if (snes->domainerror) {
783     snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
784     PetscFunctionReturn(0);
785   }
786   ierr = SNESVIComputeInactiveSetFnorm(snes,F,X,&fnorm);CHKERRQ(ierr);
787   ierr = VecNormBegin(X,NORM_2,&xnorm);CHKERRQ(ierr);	/* xnorm <- ||x||  */
788   ierr = VecNormEnd(X,NORM_2,&xnorm);CHKERRQ(ierr);
789   if (PetscIsInfOrNanReal(fnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
790 
791   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
792   snes->norm = fnorm;
793   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
794   SNESLogConvHistory(snes,fnorm,0);
795   ierr = SNESMonitor(snes,0,fnorm);CHKERRQ(ierr);
796 
797   /* set parameter for default relative tolerance convergence test */
798   snes->ttol = fnorm*snes->rtol;
799   /* test convergence */
800   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
801   if (snes->reason) PetscFunctionReturn(0);
802 
803   for (i=0; i<maxits; i++) {
804 
805     IS         IS_act,IS_inact; /* _act -> active set _inact -> inactive set */
806     VecScatter scat_act,scat_inact;
807     PetscInt   nis_act,nis_inact;
808     Vec        Y_act,Y_inact,F_inact;
809     Mat        jac_inact_inact,prejac_inact_inact;
810     IS         keptrows;
811     PetscBool  isequal;
812 
813     /* Call general purpose update function */
814     if (snes->ops->update) {
815       ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
816     }
817     ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr);
818 
819     /* Create active and inactive index sets */
820     ierr = SNESVICreateIndexSets_RS(snes,X,F,&IS_act,&IS_inact);CHKERRQ(ierr);
821 
822     /* Create inactive set submatrix */
823     ierr = MatGetSubMatrix(snes->jacobian,IS_inact,IS_inact,MAT_INITIAL_MATRIX,&jac_inact_inact);CHKERRQ(ierr);
824     ierr = MatFindNonzeroRows(jac_inact_inact,&keptrows);CHKERRQ(ierr);
825     if (keptrows) {
826       PetscInt       cnt,*nrows,k;
827       const PetscInt *krows,*inact;
828       PetscInt       rstart=jac_inact_inact->rmap->rstart;
829 
830       ierr = MatDestroy(&jac_inact_inact);CHKERRQ(ierr);
831       ierr = ISDestroy(&IS_act);CHKERRQ(ierr);
832 
833       ierr = ISGetLocalSize(keptrows,&cnt);CHKERRQ(ierr);
834       ierr = ISGetIndices(keptrows,&krows);CHKERRQ(ierr);
835       ierr = ISGetIndices(IS_inact,&inact);CHKERRQ(ierr);
836       ierr = PetscMalloc(cnt*sizeof(PetscInt),&nrows);CHKERRQ(ierr);
837       for (k=0; k<cnt; k++) {
838         nrows[k] = inact[krows[k]-rstart];
839       }
840       ierr = ISRestoreIndices(keptrows,&krows);CHKERRQ(ierr);
841       ierr = ISRestoreIndices(IS_inact,&inact);CHKERRQ(ierr);
842       ierr = ISDestroy(&keptrows);CHKERRQ(ierr);
843       ierr = ISDestroy(&IS_inact);CHKERRQ(ierr);
844 
845       ierr = ISCreateGeneral(PETSC_COMM_WORLD,cnt,nrows,PETSC_OWN_POINTER,&IS_inact);CHKERRQ(ierr);
846       ierr = ISComplement(IS_inact,F->map->rstart,F->map->rend,&IS_act);CHKERRQ(ierr);
847       ierr = MatGetSubMatrix(snes->jacobian,IS_inact,IS_inact,MAT_INITIAL_MATRIX,&jac_inact_inact);CHKERRQ(ierr);
848     }
849 
850     /* Get sizes of active and inactive sets */
851     ierr = ISGetLocalSize(IS_act,&nis_act);CHKERRQ(ierr);
852     ierr = ISGetLocalSize(IS_inact,&nis_inact);CHKERRQ(ierr);
853 
854     /* Create active and inactive set vectors */
855     ierr = SNESVICreateSubVectors(snes,nis_inact,&F_inact);CHKERRQ(ierr);
856     ierr = SNESVICreateSubVectors(snes,nis_act,&Y_act);CHKERRQ(ierr);
857     ierr = SNESVICreateSubVectors(snes,nis_inact,&Y_inact);CHKERRQ(ierr);
858 
859     /* Create scatter contexts */
860     ierr = VecScatterCreate(Y,IS_act,Y_act,PETSC_NULL,&scat_act);CHKERRQ(ierr);
861     ierr = VecScatterCreate(Y,IS_inact,Y_inact,PETSC_NULL,&scat_inact);CHKERRQ(ierr);
862 
863     /* Do a vec scatter to active and inactive set vectors */
864     ierr = VecScatterBegin(scat_inact,F,F_inact,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
865     ierr = VecScatterEnd(scat_inact,F,F_inact,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
866 
867     ierr = VecScatterBegin(scat_act,Y,Y_act,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
868     ierr = VecScatterEnd(scat_act,Y,Y_act,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
869 
870     ierr = VecScatterBegin(scat_inact,Y,Y_inact,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
871     ierr = VecScatterEnd(scat_inact,Y,Y_inact,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
872 
873     /* Active set direction = 0 */
874     ierr = VecSet(Y_act,0);CHKERRQ(ierr);
875     if (snes->jacobian != snes->jacobian_pre) {
876       ierr = MatGetSubMatrix(snes->jacobian_pre,IS_inact,IS_inact,MAT_INITIAL_MATRIX,&prejac_inact_inact);CHKERRQ(ierr);
877     } else prejac_inact_inact = jac_inact_inact;
878 
879     ierr = ISEqual(vi->IS_inact_prev,IS_inact,&isequal);CHKERRQ(ierr);
880     if (!isequal) {
881       ierr = SNESVIResetPCandKSP(snes,jac_inact_inact,prejac_inact_inact);CHKERRQ(ierr);
882     }
883 
884     /*      ierr = ISView(IS_inact,0);CHKERRQ(ierr); */
885     /*      ierr = ISView(IS_act,0);CHKERRQ(ierr);*/
886     /*      ierr = MatView(snes->jacobian_pre,0); */
887 
888     ierr = KSPSetOperators(snes->ksp,jac_inact_inact,prejac_inact_inact,flg);CHKERRQ(ierr);
889     ierr = KSPSetUp(snes->ksp);CHKERRQ(ierr);
890     {
891       PC        pc;
892       PetscBool flg;
893       ierr = KSPGetPC(snes->ksp,&pc);CHKERRQ(ierr);
894       ierr = PetscTypeCompare((PetscObject)pc,PCFIELDSPLIT,&flg);CHKERRQ(ierr);
895       if (flg) {
896         KSP      *subksps;
897         ierr = PCFieldSplitGetSubKSP(pc,PETSC_NULL,&subksps);CHKERRQ(ierr);
898         ierr = KSPGetPC(subksps[0],&pc);CHKERRQ(ierr);
899         ierr = PetscFree(subksps);CHKERRQ(ierr);
900         ierr = PetscTypeCompare((PetscObject)pc,PCBJACOBI,&flg);CHKERRQ(ierr);
901         if (flg) {
902           PetscInt       n,N = 101*101,j,cnts[3] = {0,0,0};
903           const PetscInt *ii;
904 
905           ierr = ISGetSize(IS_inact,&n);CHKERRQ(ierr);
906           ierr = ISGetIndices(IS_inact,&ii);CHKERRQ(ierr);
907           for (j=0; j<n; j++) {
908             if (ii[j] < N) cnts[0]++;
909             else if (ii[j] < 2*N) cnts[1]++;
910             else if (ii[j] < 3*N) cnts[2]++;
911           }
912           ierr = ISRestoreIndices(IS_inact,&ii);CHKERRQ(ierr);
913 
914           ierr = PCBJacobiSetTotalBlocks(pc,3,cnts);CHKERRQ(ierr);
915         }
916       }
917     }
918 
919     ierr = SNES_KSPSolve(snes,snes->ksp,F_inact,Y_inact);CHKERRQ(ierr);
920     ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr);
921     if (kspreason < 0) {
922       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
923         ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr);
924         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
925         break;
926       }
927      }
928 
929     ierr = VecScatterBegin(scat_act,Y_act,Y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
930     ierr = VecScatterEnd(scat_act,Y_act,Y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
931     ierr = VecScatterBegin(scat_inact,Y_inact,Y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
932     ierr = VecScatterEnd(scat_inact,Y_inact,Y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
933 
934     ierr = VecDestroy(&F_inact);CHKERRQ(ierr);
935     ierr = VecDestroy(&Y_act);CHKERRQ(ierr);
936     ierr = VecDestroy(&Y_inact);CHKERRQ(ierr);
937     ierr = VecScatterDestroy(&scat_act);CHKERRQ(ierr);
938     ierr = VecScatterDestroy(&scat_inact);CHKERRQ(ierr);
939     ierr = ISDestroy(&IS_act);CHKERRQ(ierr);
940     if (!isequal) {
941       ierr = ISDestroy(&vi->IS_inact_prev);CHKERRQ(ierr);
942       ierr = ISDuplicate(IS_inact,&vi->IS_inact_prev);CHKERRQ(ierr);
943     }
944     ierr = ISDestroy(&IS_inact);CHKERRQ(ierr);
945     ierr = MatDestroy(&jac_inact_inact);CHKERRQ(ierr);
946     if (snes->jacobian != snes->jacobian_pre) {
947       ierr = MatDestroy(&prejac_inact_inact);CHKERRQ(ierr);
948     }
949     ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr);
950     snes->linear_its += lits;
951     ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr);
952     /*
953     if (vi->precheckstep) {
954       PetscBool changed_y = PETSC_FALSE;
955       ierr = (*vi->precheckstep)(snes,X,Y,vi->precheck,&changed_y);CHKERRQ(ierr);
956     }
957 
958     if (PetscLogPrintInfo){
959       ierr = SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr);
960     }
961     */
962     /* Compute a (scaled) negative update in the line search routine:
963          Y <- X - lambda*Y
964        and evaluate G = function(Y) (depends on the line search).
965     */
966     ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr);
967     ynorm = 1; gnorm = fnorm;
968     ierr = (*vi->LineSearch)(snes,vi->lsP,X,F,G,Y,W,fnorm,xnorm,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
969     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",fnorm,gnorm,ynorm,(int)lssucceed);CHKERRQ(ierr);
970     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
971     if (snes->domainerror) {
972       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
973       PetscFunctionReturn(0);
974     }
975     if (!lssucceed) {
976       if (++snes->numFailures >= snes->maxFailures) {
977 	PetscBool ismin;
978         snes->reason = SNES_DIVERGED_LINE_SEARCH;
979         ierr = SNESVICheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr);
980         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
981         break;
982       }
983     }
984     /* Update function and solution vectors */
985     fnorm = gnorm;
986     ierr = VecCopy(G,F);CHKERRQ(ierr);
987     ierr = VecCopy(W,X);CHKERRQ(ierr);
988     /* Monitor convergence */
989     ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
990     snes->iter = i+1;
991     snes->norm = fnorm;
992     ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
993     SNESLogConvHistory(snes,snes->norm,lits);
994     ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr);
995     /* Test for convergence, xnorm = || X || */
996     if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); }
997     ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
998     if (snes->reason) break;
999   }
1000   if (i == maxits) {
1001     ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr);
1002     if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
1003   }
1004   PetscFunctionReturn(0);
1005 }
1006 
1007 #undef __FUNCT__
1008 #define __FUNCT__ "SNESVISetRedundancyCheck"
1009 PetscErrorCode SNESVISetRedundancyCheck(SNES snes,PetscErrorCode (*func)(SNES,IS,IS*,void*),void *ctx)
1010 {
1011   SNES_VI         *vi = (SNES_VI*)snes->data;
1012 
1013   PetscFunctionBegin;
1014   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
1015   vi->checkredundancy = func;
1016   vi->ctxP            = ctx;
1017   PetscFunctionReturn(0);
1018 }
1019 
1020 #if defined(PETSC_HAVE_MATLAB_ENGINE)
1021 #include <engine.h>
1022 #include <mex.h>
1023 typedef struct {char *funcname; mxArray *ctx;} SNESMatlabContext;
1024 
1025 #undef __FUNCT__
1026 #define __FUNCT__ "SNESVIRedundancyCheck_Matlab"
1027 PetscErrorCode SNESVIRedundancyCheck_Matlab(SNES snes,IS is_act,IS* is_redact,void* ctx)
1028 {
1029   PetscErrorCode      ierr;
1030   SNESMatlabContext   *sctx = (SNESMatlabContext*)ctx;
1031   int                 nlhs = 1, nrhs = 5;
1032   mxArray             *plhs[1], *prhs[5];
1033   long long int       l1 = 0, l2 = 0,ls = 0;
1034   PetscInt            *indices=PETSC_NULL;
1035 
1036   PetscFunctionBegin;
1037   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
1038   PetscValidHeaderSpecific(is_act,IS_CLASSID,2);
1039   PetscValidPointer(is_redact,3);
1040   PetscCheckSameComm(snes,1,is_act,2);
1041 
1042   /* Create IS for reduced active set, its size and indices will be changed by the Matlab function */
1043   ierr = ISCreateGeneral(((PetscObject)snes)->comm,0,indices,PETSC_OWN_POINTER,is_redact);CHKERRQ(ierr);
1044   /* call Matlab function in ctx */
1045   ierr = PetscMemcpy(&ls,&snes,sizeof(snes));CHKERRQ(ierr);
1046   ierr = PetscMemcpy(&l1,&is_act,sizeof(is_act));CHKERRQ(ierr);
1047   ierr = PetscMemcpy(&l2,is_redact,sizeof(is_act));CHKERRQ(ierr);
1048   prhs[0] = mxCreateDoubleScalar((double)ls);
1049   prhs[1] = mxCreateDoubleScalar((double)l1);
1050   prhs[2] = mxCreateDoubleScalar((double)l2);
1051   prhs[3] = mxCreateString(sctx->funcname);
1052   prhs[4] = sctx->ctx;
1053   ierr    = mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscSNESVIRedundancyCheckInternal");CHKERRQ(ierr);
1054   ierr    = mxGetScalar(plhs[0]);CHKERRQ(ierr);
1055   mxDestroyArray(prhs[0]);
1056   mxDestroyArray(prhs[1]);
1057   mxDestroyArray(prhs[2]);
1058   mxDestroyArray(prhs[3]);
1059   mxDestroyArray(plhs[0]);
1060   PetscFunctionReturn(0);
1061 }
1062 
1063 #undef __FUNCT__
1064 #define __FUNCT__ "SNESVISetRedundancyCheckMatlab"
1065 PetscErrorCode SNESVISetRedundancyCheckMatlab(SNES snes,const char* func,mxArray* ctx)
1066 {
1067   PetscErrorCode      ierr;
1068   SNESMatlabContext   *sctx;
1069 
1070   PetscFunctionBegin;
1071   /* currently sctx is memory bleed */
1072   ierr = PetscMalloc(sizeof(SNESMatlabContext),&sctx);CHKERRQ(ierr);
1073   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
1074   sctx->ctx = mxDuplicateArray(ctx);
1075   ierr = SNESVISetRedundancyCheck(snes,SNESVIRedundancyCheck_Matlab,sctx);CHKERRQ(ierr);
1076   PetscFunctionReturn(0);
1077 }
1078 
1079 #endif
1080 
1081 
1082 /* Variational Inequality solver using augmented space method. It does the opposite of the
1083    reduced space method i.e. it identifies the active set variables and instead of discarding
1084    them it augments the original system by introducing additional equality
1085    constraint equations for active set variables. The user can optionally provide an IS for
1086    a subset of 'redundant' active set variables which will treated as free variables.
1087    Specific implementation for Allen-Cahn problem
1088 */
1089 #undef __FUNCT__
1090 #define __FUNCT__ "SNESSolveVI_RS2"
1091 PetscErrorCode SNESSolveVI_RS2(SNES snes)
1092 {
1093   SNES_VI          *vi = (SNES_VI*)snes->data;
1094   PetscErrorCode    ierr;
1095   PetscInt          maxits,i,lits;
1096   PetscBool         lssucceed;
1097   MatStructure      flg = DIFFERENT_NONZERO_PATTERN;
1098   PetscReal         fnorm,gnorm,xnorm=0,ynorm;
1099   Vec                Y,X,F,G,W;
1100   KSPConvergedReason kspreason;
1101 
1102   PetscFunctionBegin;
1103   snes->numFailures            = 0;
1104   snes->numLinearSolveFailures = 0;
1105   snes->reason                 = SNES_CONVERGED_ITERATING;
1106 
1107   maxits	= snes->max_its;	/* maximum number of iterations */
1108   X		= snes->vec_sol;	/* solution vector */
1109   F		= snes->vec_func;	/* residual vector */
1110   Y		= snes->work[0];	/* work vectors */
1111   G		= snes->work[1];
1112   W		= snes->work[2];
1113 
1114   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1115   snes->iter = 0;
1116   snes->norm = 0.0;
1117   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1118 
1119   ierr = SNESVIProjectOntoBounds(snes,X);CHKERRQ(ierr);
1120   ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);
1121   if (snes->domainerror) {
1122     snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
1123     PetscFunctionReturn(0);
1124   }
1125   ierr = SNESVIComputeInactiveSetFnorm(snes,F,X,&fnorm);CHKERRQ(ierr);
1126   ierr = VecNormBegin(X,NORM_2,&xnorm);CHKERRQ(ierr);	/* xnorm <- ||x||  */
1127   ierr = VecNormEnd(X,NORM_2,&xnorm);CHKERRQ(ierr);
1128   if (PetscIsInfOrNanReal(fnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1129 
1130   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1131   snes->norm = fnorm;
1132   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1133   SNESLogConvHistory(snes,fnorm,0);
1134   ierr = SNESMonitor(snes,0,fnorm);CHKERRQ(ierr);
1135 
1136   /* set parameter for default relative tolerance convergence test */
1137   snes->ttol = fnorm*snes->rtol;
1138   /* test convergence */
1139   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
1140   if (snes->reason) PetscFunctionReturn(0);
1141 
1142   for (i=0; i<maxits; i++) {
1143     IS             IS_act,IS_inact; /* _act -> active set _inact -> inactive set */
1144     IS             IS_redact; /* redundant active set */
1145     Mat            J_aug,Jpre_aug;
1146     Vec            F_aug,Y_aug;
1147     PetscInt       nis_redact,nis_act;
1148     const PetscInt *idx_redact,*idx_act;
1149     PetscInt       k;
1150     PetscInt       *idx_actkept=PETSC_NULL,nkept; /* list of kept active set */
1151     PetscScalar    *f,*f2;
1152     PetscBool      isequal;
1153     PetscInt       i1=0,j1=0;
1154 
1155     /* Call general purpose update function */
1156     if (snes->ops->update) {
1157       ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
1158     }
1159     ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr);
1160 
1161     /* Create active and inactive index sets */
1162     ierr = SNESVICreateIndexSets_RS(snes,X,F,&IS_act,&IS_inact);CHKERRQ(ierr);
1163 
1164     /* Get local active set size */
1165     ierr = ISGetLocalSize(IS_act,&nis_act);CHKERRQ(ierr);
1166     ierr = ISGetIndices(IS_act,&idx_act);CHKERRQ(ierr);
1167     if(nis_act) {
1168       if(vi->checkredundancy) {
1169 	(*vi->checkredundancy)(snes,IS_act,&IS_redact,vi->ctxP);
1170       }
1171 
1172       if(!IS_redact) {
1173 	/* User called checkredundancy function but didn't create IS_redact because
1174            there were no redundant active set variables */
1175 	/* Copy over all active set indices to the list */
1176 	ierr = PetscMalloc(nis_act*sizeof(PetscInt),&idx_actkept);CHKERRQ(ierr);
1177 	for(k=0;k < nis_act;k++) idx_actkept[k] = idx_act[k];
1178 	nkept = nis_act;
1179       } else {
1180 	ierr = ISGetLocalSize(IS_redact,&nis_redact);CHKERRQ(ierr);
1181 	ierr = PetscMalloc((nis_act-nis_redact)*sizeof(PetscInt),&idx_actkept);CHKERRQ(ierr);
1182 
1183 	/* Create reduced active set list */
1184 	ierr = ISGetIndices(IS_act,&idx_act);CHKERRQ(ierr);
1185 	ierr = ISGetIndices(IS_redact,&idx_redact);CHKERRQ(ierr);
1186 	j1 = 0;nkept = 0;
1187 	for(k=0;k<nis_act;k++) {
1188 	  if(j1 < nis_redact && idx_act[k] == idx_redact[j1]) j1++;
1189 	  else idx_actkept[nkept++] = idx_act[k];
1190 	}
1191 	ierr = ISRestoreIndices(IS_act,&idx_act);CHKERRQ(ierr);
1192 	ierr = ISRestoreIndices(IS_redact,&idx_redact);CHKERRQ(ierr);
1193 
1194         ierr = ISDestroy(&IS_redact);CHKERRQ(ierr);
1195       }
1196 
1197       /* Create augmented F and Y */
1198       ierr = VecCreate(((PetscObject)snes)->comm,&F_aug);CHKERRQ(ierr);
1199       ierr = VecSetSizes(F_aug,F->map->n+nkept,PETSC_DECIDE);CHKERRQ(ierr);
1200       ierr = VecSetFromOptions(F_aug);CHKERRQ(ierr);
1201       ierr = VecDuplicate(F_aug,&Y_aug);CHKERRQ(ierr);
1202 
1203       /* Copy over F to F_aug in the first n locations */
1204       ierr = VecGetArray(F,&f);CHKERRQ(ierr);
1205       ierr = VecGetArray(F_aug,&f2);CHKERRQ(ierr);
1206       ierr = PetscMemcpy(f2,f,F->map->n*sizeof(PetscScalar));CHKERRQ(ierr);
1207       ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
1208       ierr = VecRestoreArray(F_aug,&f2);CHKERRQ(ierr);
1209 
1210       /* Create the augmented jacobian matrix */
1211       ierr = MatCreate(((PetscObject)snes)->comm,&J_aug);CHKERRQ(ierr);
1212       ierr = MatSetSizes(J_aug,X->map->n+nkept,X->map->n+nkept,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
1213       ierr = MatSetFromOptions(J_aug);CHKERRQ(ierr);
1214 
1215 
1216       { /* local vars */
1217       /* Preallocate augmented matrix and set values in it...Doing only sequential case first*/
1218       PetscInt          ncols;
1219       const PetscInt    *cols;
1220       const PetscScalar *vals;
1221       PetscScalar        value=1.0;
1222       PetscInt           row,col;
1223       PetscInt           *d_nnz;
1224 
1225       ierr = PetscMalloc((X->map->n+nkept)*sizeof(PetscInt),&d_nnz);CHKERRQ(ierr);
1226       ierr = PetscMemzero(d_nnz,(X->map->n+nkept)*sizeof(PetscInt));CHKERRQ(ierr);
1227       for(row=0;row<snes->jacobian->rmap->n;row++) {
1228         ierr = MatGetRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1229         d_nnz[row] += ncols;
1230         ierr = MatRestoreRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1231       }
1232 
1233       for(k=0;k<nkept;k++) {
1234         d_nnz[idx_actkept[k]] += 1;
1235         d_nnz[snes->jacobian->rmap->n+k] += 1;
1236       }
1237       ierr = MatSeqAIJSetPreallocation(J_aug,PETSC_NULL,d_nnz);CHKERRQ(ierr);
1238 
1239       ierr = PetscFree(d_nnz);CHKERRQ(ierr);
1240 
1241       /* Set the original jacobian matrix in J_aug */
1242       for(row=0;row<snes->jacobian->rmap->n;row++) {
1243 	ierr = MatGetRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1244 	ierr = MatSetValues(J_aug,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
1245 	ierr = MatRestoreRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1246       }
1247       /* Add the augmented part */
1248       for(k=0;k<nkept;k++) {
1249 	row = idx_actkept[k];
1250 	col = snes->jacobian->rmap->n+k;
1251 	ierr = MatSetValues(J_aug,1,&row,1,&col,&value,INSERT_VALUES);CHKERRQ(ierr);
1252 	ierr = MatSetValues(J_aug,1,&col,1,&row,&value,INSERT_VALUES);CHKERRQ(ierr);
1253       }
1254       ierr = MatAssemblyBegin(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1255       ierr = MatAssemblyEnd(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1256       /* Only considering prejac = jac for now */
1257       Jpre_aug = J_aug;
1258       } /* local vars*/
1259     } else {
1260       F_aug = F; J_aug = snes->jacobian; Y_aug = Y; Jpre_aug = snes->jacobian_pre;
1261     }
1262 
1263     ierr = ISEqual(vi->IS_inact_prev,IS_inact,&isequal);CHKERRQ(ierr);
1264     if (!isequal) {
1265       ierr = SNESVIResetPCandKSP(snes,J_aug,Jpre_aug);CHKERRQ(ierr);
1266     }
1267     ierr = KSPSetOperators(snes->ksp,J_aug,Jpre_aug,flg);CHKERRQ(ierr);
1268     ierr = KSPSetUp(snes->ksp);CHKERRQ(ierr);
1269     /*  {
1270       PC        pc;
1271       PetscBool flg;
1272       ierr = KSPGetPC(snes->ksp,&pc);CHKERRQ(ierr);
1273       ierr = PetscTypeCompare((PetscObject)pc,PCFIELDSPLIT,&flg);CHKERRQ(ierr);
1274       if (flg) {
1275         KSP      *subksps;
1276         ierr = PCFieldSplitGetSubKSP(pc,PETSC_NULL,&subksps);CHKERRQ(ierr);
1277         ierr = KSPGetPC(subksps[0],&pc);CHKERRQ(ierr);
1278         ierr = PetscFree(subksps);CHKERRQ(ierr);
1279         ierr = PetscTypeCompare((PetscObject)pc,PCBJACOBI,&flg);CHKERRQ(ierr);
1280         if (flg) {
1281           PetscInt       n,N = 101*101,j,cnts[3] = {0,0,0};
1282           const PetscInt *ii;
1283 
1284           ierr = ISGetSize(IS_inact,&n);CHKERRQ(ierr);
1285           ierr = ISGetIndices(IS_inact,&ii);CHKERRQ(ierr);
1286           for (j=0; j<n; j++) {
1287             if (ii[j] < N) cnts[0]++;
1288             else if (ii[j] < 2*N) cnts[1]++;
1289             else if (ii[j] < 3*N) cnts[2]++;
1290           }
1291           ierr = ISRestoreIndices(IS_inact,&ii);CHKERRQ(ierr);
1292 
1293           ierr = PCBJacobiSetTotalBlocks(pc,3,cnts);CHKERRQ(ierr);
1294         }
1295       }
1296     }
1297     */
1298     ierr = SNES_KSPSolve(snes,snes->ksp,F_aug,Y_aug);CHKERRQ(ierr);
1299     ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr);
1300     if (kspreason < 0) {
1301       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
1302         ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr);
1303         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
1304         break;
1305       }
1306     }
1307 
1308     if(nis_act) {
1309       PetscScalar *y1,*y2;
1310       ierr = VecGetArray(Y,&y1);CHKERRQ(ierr);
1311       ierr = VecGetArray(Y_aug,&y2);CHKERRQ(ierr);
1312       /* Copy over inactive Y_aug to Y */
1313       j1 = 0;
1314       for(i1=Y->map->rstart;i1 < Y->map->rend;i1++) {
1315 	if(j1 < nkept && idx_actkept[j1] == i1) j1++;
1316 	else y1[i1-Y->map->rstart] = y2[i1-Y->map->rstart];
1317       }
1318       ierr = VecRestoreArray(Y,&y1);CHKERRQ(ierr);
1319       ierr = VecRestoreArray(Y_aug,&y2);CHKERRQ(ierr);
1320 
1321       ierr = VecDestroy(&F_aug);CHKERRQ(ierr);
1322       ierr = VecDestroy(&Y_aug);CHKERRQ(ierr);
1323       ierr = MatDestroy(&J_aug);CHKERRQ(ierr);
1324       ierr = PetscFree(idx_actkept);CHKERRQ(ierr);
1325     }
1326 
1327     if (!isequal) {
1328       ierr = ISDestroy(&vi->IS_inact_prev);CHKERRQ(ierr);
1329       ierr = ISDuplicate(IS_inact,&vi->IS_inact_prev);CHKERRQ(ierr);
1330     }
1331     ierr = ISDestroy(&IS_inact);CHKERRQ(ierr);
1332 
1333     ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr);
1334     snes->linear_its += lits;
1335     ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr);
1336     /*
1337     if (vi->precheckstep) {
1338       PetscBool changed_y = PETSC_FALSE;
1339       ierr = (*vi->precheckstep)(snes,X,Y,vi->precheck,&changed_y);CHKERRQ(ierr);
1340     }
1341 
1342     if (PetscLogPrintInfo){
1343       ierr = SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr);
1344     }
1345     */
1346     /* Compute a (scaled) negative update in the line search routine:
1347          Y <- X - lambda*Y
1348        and evaluate G = function(Y) (depends on the line search).
1349     */
1350     ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr);
1351     ynorm = 1; gnorm = fnorm;
1352     ierr = (*vi->LineSearch)(snes,vi->lsP,X,F,G,Y,W,fnorm,xnorm,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
1353     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",fnorm,gnorm,ynorm,(int)lssucceed);CHKERRQ(ierr);
1354     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
1355     if (snes->domainerror) {
1356       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
1357       PetscFunctionReturn(0);
1358     }
1359     if (!lssucceed) {
1360       if (++snes->numFailures >= snes->maxFailures) {
1361 	PetscBool ismin;
1362         snes->reason = SNES_DIVERGED_LINE_SEARCH;
1363         ierr = SNESVICheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr);
1364         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
1365         break;
1366       }
1367     }
1368     /* Update function and solution vectors */
1369     fnorm = gnorm;
1370     ierr = VecCopy(G,F);CHKERRQ(ierr);
1371     ierr = VecCopy(W,X);CHKERRQ(ierr);
1372     /* Monitor convergence */
1373     ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1374     snes->iter = i+1;
1375     snes->norm = fnorm;
1376     ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1377     SNESLogConvHistory(snes,snes->norm,lits);
1378     ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr);
1379     /* Test for convergence, xnorm = || X || */
1380     if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); }
1381     ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
1382     if (snes->reason) break;
1383   }
1384   if (i == maxits) {
1385     ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr);
1386     if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
1387   }
1388   PetscFunctionReturn(0);
1389 }
1390 
1391 /* -------------------------------------------------------------------------- */
1392 /*
1393    SNESSetUp_VI - Sets up the internal data structures for the later use
1394    of the SNESVI nonlinear solver.
1395 
1396    Input Parameter:
1397 .  snes - the SNES context
1398 .  x - the solution vector
1399 
1400    Application Interface Routine: SNESSetUp()
1401 
1402    Notes:
1403    For basic use of the SNES solvers, the user need not explicitly call
1404    SNESSetUp(), since these actions will automatically occur during
1405    the call to SNESSolve().
1406  */
1407 #undef __FUNCT__
1408 #define __FUNCT__ "SNESSetUp_VI"
1409 PetscErrorCode SNESSetUp_VI(SNES snes)
1410 {
1411   PetscErrorCode ierr;
1412   SNES_VI        *vi = (SNES_VI*) snes->data;
1413   PetscInt       i_start[3],i_end[3];
1414 
1415   PetscFunctionBegin;
1416 
1417   ierr = SNESDefaultGetWork(snes,3);CHKERRQ(ierr);
1418 
1419   /* If the lower and upper bound on variables are not set, set it to
1420      -Inf and Inf */
1421   if (!vi->xl && !vi->xu) {
1422     vi->usersetxbounds = PETSC_FALSE;
1423     ierr = VecDuplicate(snes->vec_sol, &vi->xl); CHKERRQ(ierr);
1424     ierr = VecSet(vi->xl,PETSC_VI_NINF);CHKERRQ(ierr);
1425     ierr = VecDuplicate(snes->vec_sol, &vi->xu); CHKERRQ(ierr);
1426     ierr = VecSet(vi->xu,PETSC_VI_INF);CHKERRQ(ierr);
1427   } else {
1428     /* Check if lower bound, upper bound and solution vector distribution across the processors is identical */
1429     ierr = VecGetOwnershipRange(snes->vec_sol,i_start,i_end);CHKERRQ(ierr);
1430     ierr = VecGetOwnershipRange(vi->xl,i_start+1,i_end+1);CHKERRQ(ierr);
1431     ierr = VecGetOwnershipRange(vi->xu,i_start+2,i_end+2);CHKERRQ(ierr);
1432     if ((i_start[0] != i_start[1]) || (i_start[0] != i_start[2]) || (i_end[0] != i_end[1]) || (i_end[0] != i_end[2]))
1433       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Distribution of lower bound, upper bound and the solution vector should be identical across all the processors.");
1434   }
1435   if (snes->ops->solve != SNESSolveVI_SS) {
1436     /* Set up previous active index set for the first snes solve
1437        vi->IS_inact_prev = 0,1,2,....N */
1438     PetscInt *indices;
1439     PetscInt  i,n,rstart,rend;
1440 
1441     ierr = VecGetOwnershipRange(snes->vec_sol,&rstart,&rend);CHKERRQ(ierr);
1442     ierr = VecGetLocalSize(snes->vec_sol,&n);CHKERRQ(ierr);
1443     ierr = PetscMalloc(n*sizeof(PetscInt),&indices);CHKERRQ(ierr);
1444     for(i=0;i < n; i++) indices[i] = rstart + i;
1445     ierr = ISCreateGeneral(((PetscObject)snes)->comm,n,indices,PETSC_OWN_POINTER,&vi->IS_inact_prev);
1446   }
1447 
1448   if (snes->ops->solve == SNESSolveVI_SS) {
1449     ierr = VecDuplicate(snes->vec_sol, &vi->dpsi);CHKERRQ(ierr);
1450     ierr = VecDuplicate(snes->vec_sol, &vi->phi); CHKERRQ(ierr);
1451     ierr = VecDuplicate(snes->vec_sol, &vi->Da); CHKERRQ(ierr);
1452     ierr = VecDuplicate(snes->vec_sol, &vi->Db); CHKERRQ(ierr);
1453     ierr = VecDuplicate(snes->vec_sol, &vi->z);CHKERRQ(ierr);
1454     ierr = VecDuplicate(snes->vec_sol, &vi->t); CHKERRQ(ierr);
1455   }
1456   PetscFunctionReturn(0);
1457 }
1458 /* -------------------------------------------------------------------------- */
1459 /*
1460    SNESDestroy_VI - Destroys the private SNES_VI context that was created
1461    with SNESCreate_VI().
1462 
1463    Input Parameter:
1464 .  snes - the SNES context
1465 
1466    Application Interface Routine: SNESDestroy()
1467  */
1468 #undef __FUNCT__
1469 #define __FUNCT__ "SNESDestroy_VI"
1470 PetscErrorCode SNESDestroy_VI(SNES snes)
1471 {
1472   SNES_VI        *vi = (SNES_VI*) snes->data;
1473   PetscErrorCode ierr;
1474 
1475   PetscFunctionBegin;
1476   if (snes->ops->solve != SNESSolveVI_SS) {
1477     ierr = ISDestroy(&vi->IS_inact_prev);
1478   }
1479 
1480   if (snes->ops->solve == SNESSolveVI_SS) {
1481     /* clear vectors */
1482     ierr = VecDestroy(&vi->dpsi);CHKERRQ(ierr);
1483     ierr = VecDestroy(&vi->phi); CHKERRQ(ierr);
1484     ierr = VecDestroy(&vi->Da); CHKERRQ(ierr);
1485     ierr = VecDestroy(&vi->Db); CHKERRQ(ierr);
1486     ierr = VecDestroy(&vi->z); CHKERRQ(ierr);
1487     ierr = VecDestroy(&vi->t); CHKERRQ(ierr);
1488   }
1489 
1490   if (!vi->usersetxbounds) {
1491     ierr = VecDestroy(&vi->xl); CHKERRQ(ierr);
1492     ierr = VecDestroy(&vi->xu); CHKERRQ(ierr);
1493   }
1494 
1495   ierr = PetscViewerASCIIMonitorDestroy(&vi->lsmonitor);CHKERRQ(ierr);
1496   ierr = PetscFree(snes->data);CHKERRQ(ierr);
1497 
1498   /* clear composed functions */
1499   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","",PETSC_NULL);CHKERRQ(ierr);
1500   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","",PETSC_NULL);CHKERRQ(ierr);
1501   PetscFunctionReturn(0);
1502 }
1503 
1504 /* -------------------------------------------------------------------------- */
1505 #undef __FUNCT__
1506 #define __FUNCT__ "SNESLineSearchNo_VI"
1507 
1508 /*
1509   This routine does not actually do a line search but it takes a full newton
1510   step while ensuring that the new iterates remain within the constraints.
1511 
1512 */
1513 PetscErrorCode SNESLineSearchNo_VI(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal xnorm,PetscReal *ynorm,PetscReal *gnorm,PetscBool *flag)
1514 {
1515   PetscErrorCode ierr;
1516   SNES_VI        *vi = (SNES_VI*)snes->data;
1517   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1518 
1519   PetscFunctionBegin;
1520   *flag = PETSC_TRUE;
1521   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1522   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);         /* ynorm = || y || */
1523   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1524   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1525   if (vi->postcheckstep) {
1526    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1527   }
1528   if (changed_y) {
1529     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1530     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1531   }
1532   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1533   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1534   if (!snes->domainerror) {
1535     if (snes->ops->solve != SNESSolveVI_SS) {
1536        ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1537     } else {
1538       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);  /* gnorm = || g || */
1539     }
1540     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1541   }
1542   if (vi->lsmonitor) {
1543     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1544   }
1545   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1546   PetscFunctionReturn(0);
1547 }
1548 
1549 /* -------------------------------------------------------------------------- */
1550 #undef __FUNCT__
1551 #define __FUNCT__ "SNESLineSearchNoNorms_VI"
1552 
1553 /*
1554   This routine is a copy of SNESLineSearchNoNorms in snes/impls/ls/ls.c
1555 */
1556 PetscErrorCode SNESLineSearchNoNorms_VI(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal xnorm,PetscReal *ynorm,PetscReal *gnorm,PetscBool *flag)
1557 {
1558   PetscErrorCode ierr;
1559   SNES_VI        *vi = (SNES_VI*)snes->data;
1560   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1561 
1562   PetscFunctionBegin;
1563   *flag = PETSC_TRUE;
1564   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1565   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y      */
1566   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1567   if (vi->postcheckstep) {
1568    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1569   }
1570   if (changed_y) {
1571     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1572     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1573   }
1574 
1575   /* don't evaluate function the last time through */
1576   if (snes->iter < snes->max_its-1) {
1577     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1578   }
1579   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1580   PetscFunctionReturn(0);
1581 }
1582 
1583 /* -------------------------------------------------------------------------- */
1584 #undef __FUNCT__
1585 #define __FUNCT__ "SNESLineSearchCubic_VI"
1586 /*
1587   This routine implements a cubic line search while doing a projection on the variable bounds
1588 */
1589 PetscErrorCode SNESLineSearchCubic_VI(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal xnorm,PetscReal *ynorm,PetscReal *gnorm,PetscBool *flag)
1590 {
1591   PetscReal      initslope,lambdaprev,gnormprev,a,b,d,t1,t2,rellength;
1592   PetscReal      minlambda,lambda,lambdatemp;
1593 #if defined(PETSC_USE_COMPLEX)
1594   PetscScalar    cinitslope;
1595 #endif
1596   PetscErrorCode ierr;
1597   PetscInt       count;
1598   SNES_VI        *vi = (SNES_VI*)snes->data;
1599   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1600   MPI_Comm       comm;
1601 
1602   PetscFunctionBegin;
1603   ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr);
1604   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1605   *flag   = PETSC_TRUE;
1606 
1607   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1608   if (*ynorm == 0.0) {
1609     if (vi->lsmonitor) {
1610       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Initial direction and size is 0\n");CHKERRQ(ierr);
1611     }
1612     *gnorm = fnorm;
1613     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1614     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1615     *flag  = PETSC_FALSE;
1616     goto theend1;
1617   }
1618   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1619     if (vi->lsmonitor) {
1620       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Scaling step by %G old ynorm %G\n",vi->maxstep/(*ynorm),*ynorm);CHKERRQ(ierr);
1621     }
1622     ierr = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1623     *ynorm = vi->maxstep;
1624   }
1625   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1626   minlambda = vi->minlambda/rellength;
1627   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1628 #if defined(PETSC_USE_COMPLEX)
1629   ierr = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1630   initslope = PetscRealPart(cinitslope);
1631 #else
1632   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1633 #endif
1634   if (initslope > 0.0)  initslope = -initslope;
1635   if (initslope == 0.0) initslope = -1.0;
1636 
1637   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1638   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1639   if (snes->nfuncs >= snes->max_funcs) {
1640     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1641     *flag = PETSC_FALSE;
1642     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1643     goto theend1;
1644   }
1645   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1646   if (snes->ops->solve != SNESSolveVI_SS) {
1647     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1648   } else {
1649     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1650   }
1651   if (snes->domainerror) {
1652     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1653     PetscFunctionReturn(0);
1654   }
1655   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1656   ierr = PetscInfo2(snes,"Initial fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1657   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1658     if (vi->lsmonitor) {
1659       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1660     }
1661     goto theend1;
1662   }
1663 
1664   /* Fit points with quadratic */
1665   lambda     = 1.0;
1666   lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1667   lambdaprev = lambda;
1668   gnormprev  = *gnorm;
1669   if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1670   if (lambdatemp <= .1*lambda) lambda = .1*lambda;
1671   else                         lambda = lambdatemp;
1672 
1673   ierr  = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1674   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1675   if (snes->nfuncs >= snes->max_funcs) {
1676     ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while attempting quadratic backtracking! %D \n",snes->nfuncs);CHKERRQ(ierr);
1677     *flag = PETSC_FALSE;
1678     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1679     goto theend1;
1680   }
1681   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1682   if (snes->ops->solve != SNESSolveVI_SS) {
1683     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1684   } else {
1685     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1686   }
1687   if (snes->domainerror) {
1688     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1689     PetscFunctionReturn(0);
1690   }
1691   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1692   if (vi->lsmonitor) {
1693     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: gnorm after quadratic fit %G\n",*gnorm);CHKERRQ(ierr);
1694   }
1695   if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1696     if (vi->lsmonitor) {
1697       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Quadratically determined step, lambda=%18.16e\n",lambda);CHKERRQ(ierr);
1698     }
1699     goto theend1;
1700   }
1701 
1702   /* Fit points with cubic */
1703   count = 1;
1704   while (PETSC_TRUE) {
1705     if (lambda <= minlambda) {
1706       if (vi->lsmonitor) {
1707 	ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: unable to find good step length! After %D tries \n",count);CHKERRQ(ierr);
1708 	ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, minlambda=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",fnorm,*gnorm,*ynorm,minlambda,lambda,initslope);CHKERRQ(ierr);
1709       }
1710       *flag = PETSC_FALSE;
1711       break;
1712     }
1713     t1 = .5*((*gnorm)*(*gnorm) - fnorm*fnorm) - lambda*initslope;
1714     t2 = .5*(gnormprev*gnormprev  - fnorm*fnorm) - lambdaprev*initslope;
1715     a  = (t1/(lambda*lambda) - t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1716     b  = (-lambdaprev*t1/(lambda*lambda) + lambda*t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1717     d  = b*b - 3*a*initslope;
1718     if (d < 0.0) d = 0.0;
1719     if (a == 0.0) {
1720       lambdatemp = -initslope/(2.0*b);
1721     } else {
1722       lambdatemp = (-b + sqrt(d))/(3.0*a);
1723     }
1724     lambdaprev = lambda;
1725     gnormprev  = *gnorm;
1726     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1727     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1728     else                         lambda     = lambdatemp;
1729     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1730     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1731     if (snes->nfuncs >= snes->max_funcs) {
1732       ierr = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1733       ierr = PetscInfo5(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",fnorm,*gnorm,*ynorm,lambda,initslope);CHKERRQ(ierr);
1734       *flag = PETSC_FALSE;
1735       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1736       break;
1737     }
1738     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1739     if (snes->ops->solve != SNESSolveVI_SS) {
1740       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1741     } else {
1742       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1743     }
1744     if (snes->domainerror) {
1745       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1746       PetscFunctionReturn(0);
1747     }
1748     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1749     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* is reduction enough? */
1750       if (vi->lsmonitor) {
1751 	ierr = PetscPrintf(comm,"    Line search: Cubically determined step, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1752       }
1753       break;
1754     } else {
1755       if (vi->lsmonitor) {
1756         ierr = PetscPrintf(comm,"    Line search: Cubic step no good, shrinking lambda, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1757       }
1758     }
1759     count++;
1760   }
1761   theend1:
1762   /* Optional user-defined check for line search step validity */
1763   if (vi->postcheckstep && *flag) {
1764     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1765     if (changed_y) {
1766       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1767       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1768     }
1769     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1770       ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1771       if (snes->ops->solve != SNESSolveVI_SS) {
1772         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1773       } else {
1774         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1775       }
1776       if (snes->domainerror) {
1777         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1778         PetscFunctionReturn(0);
1779       }
1780       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1781       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1782       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1783     }
1784   }
1785   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1786   PetscFunctionReturn(0);
1787 }
1788 
1789 #undef __FUNCT__
1790 #define __FUNCT__ "SNESLineSearchQuadratic_VI"
1791 /*
1792   This routine does a quadratic line search while keeping the iterates within the variable bounds
1793 */
1794 PetscErrorCode SNESLineSearchQuadratic_VI(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal xnorm,PetscReal *ynorm,PetscReal *gnorm,PetscBool *flag)
1795 {
1796   /*
1797      Note that for line search purposes we work with with the related
1798      minimization problem:
1799         min  z(x):  R^n -> R,
1800      where z(x) = .5 * fnorm*fnorm,and fnorm = || f ||_2.
1801    */
1802   PetscReal      initslope,minlambda,lambda,lambdatemp,rellength;
1803 #if defined(PETSC_USE_COMPLEX)
1804   PetscScalar    cinitslope;
1805 #endif
1806   PetscErrorCode ierr;
1807   PetscInt       count;
1808   SNES_VI        *vi = (SNES_VI*)snes->data;
1809   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1810 
1811   PetscFunctionBegin;
1812   ierr    = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1813   *flag   = PETSC_TRUE;
1814 
1815   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1816   if (*ynorm == 0.0) {
1817     if (vi->lsmonitor) {
1818       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Direction and size is 0\n");CHKERRQ(ierr);
1819     }
1820     *gnorm = fnorm;
1821     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1822     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1823     *flag  = PETSC_FALSE;
1824     goto theend2;
1825   }
1826   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1827     ierr   = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1828     *ynorm = vi->maxstep;
1829   }
1830   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1831   minlambda = vi->minlambda/rellength;
1832   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1833 #if defined(PETSC_USE_COMPLEX)
1834   ierr      = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1835   initslope = PetscRealPart(cinitslope);
1836 #else
1837   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1838 #endif
1839   if (initslope > 0.0)  initslope = -initslope;
1840   if (initslope == 0.0) initslope = -1.0;
1841   ierr = PetscInfo1(snes,"Initslope %G \n",initslope);CHKERRQ(ierr);
1842 
1843   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1844   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1845   if (snes->nfuncs >= snes->max_funcs) {
1846     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1847     *flag = PETSC_FALSE;
1848     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1849     goto theend2;
1850   }
1851   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1852   if (snes->ops->solve != SNESSolveVI_SS) {
1853     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1854   } else {
1855     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1856   }
1857   if (snes->domainerror) {
1858     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1859     PetscFunctionReturn(0);
1860   }
1861   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1862   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1863     if (vi->lsmonitor) {
1864       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1865     }
1866     goto theend2;
1867   }
1868 
1869   /* Fit points with quadratic */
1870   lambda = 1.0;
1871   count = 1;
1872   while (PETSC_TRUE) {
1873     if (lambda <= minlambda) { /* bad luck; use full step */
1874       if (vi->lsmonitor) {
1875         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Unable to find good step length! %D \n",count);CHKERRQ(ierr);
1876         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: fnorm=%G, gnorm=%G, ynorm=%G, lambda=%G, initial slope=%G\n",fnorm,*gnorm,*ynorm,lambda,initslope);CHKERRQ(ierr);
1877       }
1878       ierr = VecCopy(x,w);CHKERRQ(ierr);
1879       *flag = PETSC_FALSE;
1880       break;
1881     }
1882     lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1883     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1884     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1885     else                         lambda     = lambdatemp;
1886 
1887     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1888     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1889     if (snes->nfuncs >= snes->max_funcs) {
1890       ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1891       ierr  = PetscInfo5(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",fnorm,*gnorm,*ynorm,lambda,initslope);CHKERRQ(ierr);
1892       *flag = PETSC_FALSE;
1893       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1894       break;
1895     }
1896     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1897     if (snes->domainerror) {
1898       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1899       PetscFunctionReturn(0);
1900     }
1901     if (snes->ops->solve != SNESSolveVI_SS) {
1902       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1903     } else {
1904       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1905     }
1906     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1907     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1908       if (vi->lsmonitor) {
1909         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line Search: Quadratically determined step, lambda=%G\n",lambda);CHKERRQ(ierr);
1910       }
1911       break;
1912     }
1913     count++;
1914   }
1915   theend2:
1916   /* Optional user-defined check for line search step validity */
1917   if (vi->postcheckstep) {
1918     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1919     if (changed_y) {
1920       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1921       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1922     }
1923     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1924       ierr = SNESComputeFunction(snes,w,g);
1925       if (snes->domainerror) {
1926         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1927         PetscFunctionReturn(0);
1928       }
1929       if (snes->ops->solve != SNESSolveVI_SS) {
1930         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1931       } else {
1932         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1933       }
1934 
1935       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1936       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1937       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1938     }
1939   }
1940   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1941   PetscFunctionReturn(0);
1942 }
1943 
1944 typedef PetscErrorCode (*FCN2)(SNES,void*,Vec,Vec,Vec,Vec,Vec,PetscReal,PetscReal,PetscReal*,PetscReal*,PetscBool*); /* force argument to next function to not be extern C*/
1945 /* -------------------------------------------------------------------------- */
1946 EXTERN_C_BEGIN
1947 #undef __FUNCT__
1948 #define __FUNCT__ "SNESLineSearchSet_VI"
1949 PetscErrorCode  SNESLineSearchSet_VI(SNES snes,FCN2 func,void *lsctx)
1950 {
1951   PetscFunctionBegin;
1952   ((SNES_VI *)(snes->data))->LineSearch = func;
1953   ((SNES_VI *)(snes->data))->lsP        = lsctx;
1954   PetscFunctionReturn(0);
1955 }
1956 EXTERN_C_END
1957 
1958 /* -------------------------------------------------------------------------- */
1959 EXTERN_C_BEGIN
1960 #undef __FUNCT__
1961 #define __FUNCT__ "SNESLineSearchSetMonitor_VI"
1962 PetscErrorCode  SNESLineSearchSetMonitor_VI(SNES snes,PetscBool flg)
1963 {
1964   SNES_VI        *vi = (SNES_VI*)snes->data;
1965   PetscErrorCode ierr;
1966 
1967   PetscFunctionBegin;
1968   if (flg && !vi->lsmonitor) {
1969     ierr = PetscViewerASCIIMonitorCreate(((PetscObject)snes)->comm,"stdout",((PetscObject)snes)->tablevel,&vi->lsmonitor);CHKERRQ(ierr);
1970   } else if (!flg && vi->lsmonitor) {
1971     ierr = PetscViewerASCIIMonitorDestroy(&vi->lsmonitor);CHKERRQ(ierr);
1972   }
1973   PetscFunctionReturn(0);
1974 }
1975 EXTERN_C_END
1976 
1977 /*
1978    SNESView_VI - Prints info from the SNESVI data structure.
1979 
1980    Input Parameters:
1981 .  SNES - the SNES context
1982 .  viewer - visualization context
1983 
1984    Application Interface Routine: SNESView()
1985 */
1986 #undef __FUNCT__
1987 #define __FUNCT__ "SNESView_VI"
1988 static PetscErrorCode SNESView_VI(SNES snes,PetscViewer viewer)
1989 {
1990   SNES_VI        *vi = (SNES_VI *)snes->data;
1991   const char     *cstr,*tstr;
1992   PetscErrorCode ierr;
1993   PetscBool     iascii;
1994 
1995   PetscFunctionBegin;
1996   ierr = PetscTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1997   if (iascii) {
1998     if (vi->LineSearch == SNESLineSearchNo_VI)             cstr = "SNESLineSearchNo";
1999     else if (vi->LineSearch == SNESLineSearchQuadratic_VI) cstr = "SNESLineSearchQuadratic";
2000     else if (vi->LineSearch == SNESLineSearchCubic_VI)     cstr = "SNESLineSearchCubic";
2001     else                                                             cstr = "unknown";
2002     if (snes->ops->solve == SNESSolveVI_SS)      tstr = "Semismooth";
2003     else if (snes->ops->solve == SNESSolveVI_RS) tstr = "Reduced Space";
2004     else if (snes->ops->solve == SNESSolveVI_RS2) tstr = "Augmented Space";
2005     else                                         tstr = "unknown";
2006     ierr = PetscViewerASCIIPrintf(viewer,"  VI algorithm: %s\n",tstr);CHKERRQ(ierr);
2007     ierr = PetscViewerASCIIPrintf(viewer,"  line search variant: %s\n",cstr);CHKERRQ(ierr);
2008     ierr = PetscViewerASCIIPrintf(viewer,"  alpha=%G, maxstep=%G, minlambda=%G\n",vi->alpha,vi->maxstep,vi->minlambda);CHKERRQ(ierr);
2009   } else {
2010     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Viewer type %s not supported for SNES EQ VI",((PetscObject)viewer)->type_name);
2011   }
2012   PetscFunctionReturn(0);
2013 }
2014 
2015 #undef __FUNCT__
2016 #define __FUNCT__ "SNESVISetVariableBounds"
2017 /*@
2018    SNESVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu.
2019 
2020    Input Parameters:
2021 .  snes - the SNES context.
2022 .  xl   - lower bound.
2023 .  xu   - upper bound.
2024 
2025    Notes:
2026    If this routine is not called then the lower and upper bounds are set to
2027    PETSC_VI_INF and PETSC_VI_NINF respectively during SNESSetUp().
2028 
2029 @*/
2030 PetscErrorCode SNESVISetVariableBounds(SNES snes, Vec xl, Vec xu)
2031 {
2032   SNES_VI  *vi = (SNES_VI*)snes->data;
2033 
2034   PetscFunctionBegin;
2035   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
2036   PetscValidHeaderSpecific(xl,VEC_CLASSID,2);
2037   PetscValidHeaderSpecific(xu,VEC_CLASSID,3);
2038   if (!snes->vec_func) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call SNESSetFunction() first");
2039   if (xl->map->N != snes->vec_func->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incompatible vector lengths lower bound = %D solution vector = %D",xl->map->N,snes->vec_func->map->N);
2040   if (xu->map->N != snes->vec_func->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incompatible vector lengths: upper bound = %D solution vector = %D",xu->map->N,snes->vec_func->map->N);
2041 
2042   vi->usersetxbounds = PETSC_TRUE;
2043   vi->xl = xl;
2044   vi->xu = xu;
2045   PetscFunctionReturn(0);
2046 }
2047 
2048 /* -------------------------------------------------------------------------- */
2049 /*
2050    SNESSetFromOptions_VI - Sets various parameters for the SNESVI method.
2051 
2052    Input Parameter:
2053 .  snes - the SNES context
2054 
2055    Application Interface Routine: SNESSetFromOptions()
2056 */
2057 #undef __FUNCT__
2058 #define __FUNCT__ "SNESSetFromOptions_VI"
2059 static PetscErrorCode SNESSetFromOptions_VI(SNES snes)
2060 {
2061   SNES_VI        *vi = (SNES_VI *)snes->data;
2062   const char     *lses[] = {"basic","basicnonorms","quadratic","cubic"};
2063   const char     *vies[] = {"ss","rs","rs2"};
2064   PetscErrorCode ierr;
2065   PetscInt       indx;
2066   PetscBool      flg,set,flg2;
2067 
2068   PetscFunctionBegin;
2069   ierr = PetscOptionsHead("SNES semismooth method options");CHKERRQ(ierr);
2070   ierr = PetscOptionsBool("-snes_vi_monitor","Monitor all non-active variables","None",PETSC_FALSE,&flg,0);CHKERRQ(ierr);
2071   if (flg) {
2072     ierr = SNESMonitorSet(snes,SNESMonitorVI,0,0);CHKERRQ(ierr);
2073   }
2074   ierr = PetscOptionsReal("-snes_ls_alpha","Function norm must decrease by","None",vi->alpha,&vi->alpha,0);CHKERRQ(ierr);
2075   ierr = PetscOptionsReal("-snes_ls_maxstep","Step must be less than","None",vi->maxstep,&vi->maxstep,0);CHKERRQ(ierr);
2076   ierr = PetscOptionsReal("-snes_ls_minlambda","Minimum lambda allowed","None",vi->minlambda,&vi->minlambda,0);CHKERRQ(ierr);
2077   ierr = PetscOptionsReal("-snes_vi_const_tol","constraint tolerance","None",vi->const_tol,&vi->const_tol,0);CHKERRQ(ierr);
2078   ierr = PetscOptionsBool("-snes_ls_monitor","Print progress of line searches","SNESLineSearchSetMonitor",vi->lsmonitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);CHKERRQ(ierr);
2079   if (set) {ierr = SNESLineSearchSetMonitor(snes,flg);CHKERRQ(ierr);}
2080   ierr = PetscOptionsEList("-snes_vi_type","Semismooth algorithm used","",vies,3,"ss",&indx,&flg2);CHKERRQ(ierr);
2081   if (flg2) {
2082     switch (indx) {
2083     case 0:
2084       snes->ops->solve = SNESSolveVI_SS;
2085       break;
2086     case 1:
2087       snes->ops->solve = SNESSolveVI_RS;
2088       break;
2089     case 2:
2090       snes->ops->solve = SNESSolveVI_RS2;
2091     }
2092   }
2093   ierr = PetscOptionsEList("-snes_ls","Line search used","SNESLineSearchSet",lses,4,"basic",&indx,&flg);CHKERRQ(ierr);
2094   if (flg) {
2095     switch (indx) {
2096     case 0:
2097       ierr = SNESLineSearchSet(snes,SNESLineSearchNo_VI,PETSC_NULL);CHKERRQ(ierr);
2098       break;
2099     case 1:
2100       ierr = SNESLineSearchSet(snes,SNESLineSearchNoNorms_VI,PETSC_NULL);CHKERRQ(ierr);
2101       break;
2102     case 2:
2103       ierr = SNESLineSearchSet(snes,SNESLineSearchQuadratic_VI,PETSC_NULL);CHKERRQ(ierr);
2104       break;
2105     case 3:
2106       ierr = SNESLineSearchSet(snes,SNESLineSearchCubic_VI,PETSC_NULL);CHKERRQ(ierr);
2107       break;
2108     }
2109   }
2110   ierr = PetscOptionsTail();CHKERRQ(ierr);
2111   PetscFunctionReturn(0);
2112 }
2113 /* -------------------------------------------------------------------------- */
2114 /*MC
2115       SNESVI - Semismooth newton method based nonlinear solver that uses a line search
2116 
2117    Options Database:
2118 +   -snes_ls [cubic,quadratic,basic,basicnonorms] - Selects line search
2119 .   -snes_ls_alpha <alpha> - Sets alpha
2120 .   -snes_ls_maxstep <maxstep> - Sets the maximum stepsize the line search will use (if the 2-norm(y) > maxstep then scale y to be y = (maxstep/2-norm(y)) *y)
2121 .   -snes_ls_minlambda <minlambda>  - Sets the minimum lambda the line search will use  minlambda / max_i ( y[i]/x[i] )
2122 -   -snes_ls_monitor - print information about progress of line searches
2123 
2124 
2125    Level: beginner
2126 
2127 .seealso:  SNESCreate(), SNES, SNESSetType(), SNESTR, SNESLineSearchSet(),
2128            SNESLineSearchSetPostCheck(), SNESLineSearchNo(), SNESLineSearchCubic(), SNESLineSearchQuadratic(),
2129            SNESLineSearchSet(), SNESLineSearchNoNorms(), SNESLineSearchSetPreCheck(), SNESLineSearchSetParams(), SNESLineSearchGetParams()
2130 
2131 M*/
2132 EXTERN_C_BEGIN
2133 #undef __FUNCT__
2134 #define __FUNCT__ "SNESCreate_VI"
2135 PetscErrorCode  SNESCreate_VI(SNES snes)
2136 {
2137   PetscErrorCode ierr;
2138   SNES_VI      *vi;
2139 
2140   PetscFunctionBegin;
2141   snes->ops->setup           = SNESSetUp_VI;
2142   snes->ops->solve           = SNESSolveVI_SS;
2143   snes->ops->destroy         = SNESDestroy_VI;
2144   snes->ops->setfromoptions  = SNESSetFromOptions_VI;
2145   snes->ops->view            = SNESView_VI;
2146   snes->ops->reset           = 0; /* XXX Implement!!! */
2147   snes->ops->converged       = SNESDefaultConverged_VI;
2148 
2149   ierr                  = PetscNewLog(snes,SNES_VI,&vi);CHKERRQ(ierr);
2150   snes->data            = (void*)vi;
2151   vi->alpha             = 1.e-4;
2152   vi->maxstep           = 1.e8;
2153   vi->minlambda         = 1.e-12;
2154   vi->LineSearch        = SNESLineSearchNo_VI;
2155   vi->lsP               = PETSC_NULL;
2156   vi->postcheckstep     = PETSC_NULL;
2157   vi->postcheck         = PETSC_NULL;
2158   vi->precheckstep      = PETSC_NULL;
2159   vi->precheck          = PETSC_NULL;
2160   vi->const_tol         =  2.2204460492503131e-16;
2161   vi->checkredundancy   = PETSC_NULL;
2162 
2163   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","SNESLineSearchSetMonitor_VI",SNESLineSearchSetMonitor_VI);CHKERRQ(ierr);
2164   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","SNESLineSearchSet_VI",SNESLineSearchSet_VI);CHKERRQ(ierr);
2165 
2166   PetscFunctionReturn(0);
2167 }
2168 EXTERN_C_END
2169