xref: /petsc/src/snes/impls/vi/vi.c (revision d372ba47371068bdce79d7d3cf159aa0df7e4cba)
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   SNESMonitor(snes,0,vi->phinorm);
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     SNESMonitor(snes,snes->iter,snes->norm);
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   SNESMonitor(snes,0,fnorm);
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     SNESMonitor(snes,snes->iter,snes->norm);
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 
1035   PetscFunctionBegin;
1036   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
1037   PetscValidHeaderSpecific(is_act,IS_CLASSID,2);
1038   PetscValidPointer(is_redact,3);
1039   PetscCheckSameComm(snes,1,is_act,2);
1040 
1041   /* Create IS for reduced active set, its size and indices will be set by the Matlab function */
1042   ierr = ISCreate(((PetscObject)snes)->comm,is_redact);CHKERRQ(ierr);
1043   /* call Matlab function in ctx */
1044   ierr = PetscMemcpy(&ls,&snes,sizeof(snes));CHKERRQ(ierr);
1045   ierr = PetscMemcpy(&l1,&is_act,sizeof(is_act));CHKERRQ(ierr);
1046   ierr = PetscMemcpy(&l2,is_redact,sizeof(is_act));CHKERRQ(ierr);
1047   prhs[0] = mxCreateDoubleScalar((double)ls);
1048   prhs[1] = mxCreateDoubleScalar((double)l1);
1049   prhs[2] = mxCreateDoubleScalar((double)l2);
1050   prhs[3] = mxCreateString(sctx->funcname);
1051   prhs[4] = sctx->ctx;
1052   ierr    = mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscSNESVIRedundancyCheckInternal");CHKERRQ(ierr);
1053   ierr    = mxGetScalar(plhs[0]);CHKERRQ(ierr);
1054   PetscInt n;
1055   ierr = ISGetSize(*is_redact,&n);CHKERRQ(ierr);
1056   PetscPrintf(PETSC_COMM_SELF,"IS_size = %d\n",n);
1057   mxDestroyArray(prhs[0]);
1058   mxDestroyArray(prhs[1]);
1059   mxDestroyArray(prhs[2]);
1060   mxDestroyArray(prhs[3]);
1061   mxDestroyArray(prhs[4]);
1062   mxDestroyArray(plhs[0]);
1063   PetscFunctionReturn(0);
1064 }
1065 
1066 #undef __FUNCT__
1067 #define __FUNCT__ "SNESVISetRedundancyCheckMatlab"
1068 PetscErrorCode SNESVISetRedundancyCheckMatlab(SNES snes,const char* func,mxArray* ctx)
1069 {
1070   PetscErrorCode      ierr;
1071   SNESMatlabContext   *sctx;
1072 
1073   PetscFunctionBegin;
1074   /* currently sctx is memory bleed */
1075   ierr = PetscMalloc(sizeof(SNESMatlabContext),&sctx);CHKERRQ(ierr);
1076   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
1077   sctx->ctx = mxDuplicateArray(ctx);
1078   ierr = SNESVISetRedundancyCheck(snes,SNESVIRedundancyCheck_Matlab,sctx);CHKERRQ(ierr);
1079   PetscFunctionReturn(0);
1080 }
1081 
1082 #endif
1083 
1084 
1085 /* Variational Inequality solver using augmented space method. It does the opposite of the
1086    reduced space method i.e. it identifies the active set variables and instead of discarding
1087    them it augments the original system by introducing additional equality
1088    constraint equations for active set variables. The user can optionally provide an IS for
1089    a subset of 'redundant' active set variables which will treated as free variables.
1090    Specific implementation for Allen-Cahn problem
1091 */
1092 #undef __FUNCT__
1093 #define __FUNCT__ "SNESSolveVI_RS2"
1094 PetscErrorCode SNESSolveVI_RS2(SNES snes)
1095 {
1096   SNES_VI          *vi = (SNES_VI*)snes->data;
1097   PetscErrorCode    ierr;
1098   PetscInt          maxits,i,lits;
1099   PetscBool         lssucceed;
1100   MatStructure      flg = DIFFERENT_NONZERO_PATTERN;
1101   PetscReal         fnorm,gnorm,xnorm=0,ynorm;
1102   Vec                Y,X,F,G,W;
1103   KSPConvergedReason kspreason;
1104 
1105   PetscFunctionBegin;
1106   snes->numFailures            = 0;
1107   snes->numLinearSolveFailures = 0;
1108   snes->reason                 = SNES_CONVERGED_ITERATING;
1109 
1110   maxits	= snes->max_its;	/* maximum number of iterations */
1111   X		= snes->vec_sol;	/* solution vector */
1112   F		= snes->vec_func;	/* residual vector */
1113   Y		= snes->work[0];	/* work vectors */
1114   G		= snes->work[1];
1115   W		= snes->work[2];
1116 
1117   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1118   snes->iter = 0;
1119   snes->norm = 0.0;
1120   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1121 
1122   ierr = SNESVIProjectOntoBounds(snes,X);CHKERRQ(ierr);
1123   ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);
1124   if (snes->domainerror) {
1125     snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
1126     PetscFunctionReturn(0);
1127   }
1128   ierr = SNESVIComputeInactiveSetFnorm(snes,F,X,&fnorm);CHKERRQ(ierr);
1129   ierr = VecNormBegin(X,NORM_2,&xnorm);CHKERRQ(ierr);	/* xnorm <- ||x||  */
1130   ierr = VecNormEnd(X,NORM_2,&xnorm);CHKERRQ(ierr);
1131   if (PetscIsInfOrNanReal(fnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1132 
1133   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1134   snes->norm = fnorm;
1135   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1136   SNESLogConvHistory(snes,fnorm,0);
1137   SNESMonitor(snes,0,fnorm);
1138 
1139   /* set parameter for default relative tolerance convergence test */
1140   snes->ttol = fnorm*snes->rtol;
1141   /* test convergence */
1142   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
1143   if (snes->reason) PetscFunctionReturn(0);
1144 
1145   for (i=0; i<maxits; i++) {
1146     IS             IS_act,IS_inact; /* _act -> active set _inact -> inactive set */
1147     IS             IS_redact; /* redundant active set */
1148     Mat            J_aug,Jpre_aug;
1149     Vec            F_aug,Y_aug;
1150     PetscInt       nis_redact,nis_act;
1151     const PetscInt *idx_redact,*idx_act;
1152     PetscInt       k;
1153     PetscInt       *idx_actkept=PETSC_NULL,nkept; /* list of kept active set */
1154     PetscScalar    *f,*f2;
1155     PetscBool      isequal;
1156     PetscInt       i1=0,j1=0;
1157 
1158     /* Call general purpose update function */
1159     if (snes->ops->update) {
1160       ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
1161     }
1162     ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr);
1163 
1164     /* Create active and inactive index sets */
1165     ierr = SNESVICreateIndexSets_RS(snes,X,F,&IS_act,&IS_inact);CHKERRQ(ierr);
1166 
1167     /* Get local active set size */
1168     ierr = ISGetLocalSize(IS_act,&nis_act);CHKERRQ(ierr);
1169     ierr = ISGetIndices(IS_act,&idx_act);CHKERRQ(ierr);
1170     if(nis_act) {
1171       if(vi->checkredundancy) {
1172 	(*vi->checkredundancy)(snes,IS_act,&IS_redact,vi->ctxP);
1173       }
1174 
1175       if(!IS_redact) {
1176 	/* User called checkredundancy function but didn't create IS_redact because
1177            there were no redundant active set variables */
1178 	/* Copy over all active set indices to the list */
1179         PetscPrintf(PETSC_COMM_SELF,"Came here 1\n");
1180 	ierr = PetscMalloc(nis_act*sizeof(PetscInt),&idx_actkept);CHKERRQ(ierr);
1181 	for(k=0;k < nis_act;k++) idx_actkept[k] = idx_act[k];
1182 	nkept = nis_act;
1183       } else {
1184         PetscPrintf(PETSC_COMM_SELF,"Came here 2\n");
1185 	ierr = ISGetLocalSize(IS_redact,&nis_redact);CHKERRQ(ierr);
1186 	ierr = PetscMalloc((nis_act-nis_redact)*sizeof(PetscInt),&idx_actkept);CHKERRQ(ierr);
1187 
1188 	/* Create reduced active set list */
1189 	ierr = ISGetIndices(IS_act,&idx_act);CHKERRQ(ierr);
1190 	ierr = ISGetIndices(IS_redact,&idx_redact);CHKERRQ(ierr);
1191 	j1 = 0;nkept = 0;
1192 	for(k=0;k<nis_act;k++) {
1193 	  if(j1 < nis_redact && idx_act[k] == idx_redact[j1]) j1++;
1194 	  else idx_actkept[nkept++] = idx_act[k];
1195 	}
1196 	ierr = ISRestoreIndices(IS_act,&idx_act);CHKERRQ(ierr);
1197 	ierr = ISRestoreIndices(IS_redact,&idx_redact);CHKERRQ(ierr);
1198 
1199         ierr = ISDestroy(&IS_redact);CHKERRQ(ierr);
1200       }
1201 
1202       /* Create augmented F and Y */
1203       ierr = VecCreate(((PetscObject)snes)->comm,&F_aug);CHKERRQ(ierr);
1204       ierr = VecSetSizes(F_aug,F->map->n+nkept,PETSC_DECIDE);CHKERRQ(ierr);
1205       ierr = VecSetFromOptions(F_aug);CHKERRQ(ierr);
1206       ierr = VecDuplicate(F_aug,&Y_aug);CHKERRQ(ierr);
1207 
1208       /* Copy over F to F_aug in the first n locations */
1209       ierr = VecGetArray(F,&f);CHKERRQ(ierr);
1210       ierr = VecGetArray(F_aug,&f2);CHKERRQ(ierr);
1211       ierr = PetscMemcpy(f2,f,F->map->n*sizeof(PetscScalar));CHKERRQ(ierr);
1212       ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
1213       ierr = VecRestoreArray(F_aug,&f2);CHKERRQ(ierr);
1214 
1215       /* Create the augmented jacobian matrix */
1216       ierr = MatCreate(((PetscObject)snes)->comm,&J_aug);CHKERRQ(ierr);
1217       ierr = MatSetSizes(J_aug,X->map->n+nkept,X->map->n+nkept,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
1218       ierr = MatSetFromOptions(J_aug);CHKERRQ(ierr);
1219 
1220 
1221       { /* local vars */
1222       /* Preallocate augmented matrix and set values in it...Doing only sequential case first*/
1223       PetscInt          ncols;
1224       const PetscInt    *cols;
1225       const PetscScalar *vals;
1226       PetscScalar        value=1.0;
1227       PetscInt           row,col;
1228       PetscInt           *d_nnz;
1229 
1230       ierr = PetscMalloc((X->map->n+nkept)*sizeof(PetscInt),&d_nnz);CHKERRQ(ierr);
1231       ierr = PetscMemzero(d_nnz,(X->map->n+nkept)*sizeof(PetscInt));CHKERRQ(ierr);
1232       for(row=0;row<snes->jacobian->rmap->n;row++) {
1233         ierr = MatGetRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1234         d_nnz[row] += ncols;
1235         ierr = MatRestoreRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1236       }
1237 
1238       for(k=0;k<nkept;k++) {
1239         d_nnz[idx_actkept[k]] += 1;
1240         d_nnz[snes->jacobian->rmap->n+k] += 1;
1241       }
1242       ierr = MatSeqAIJSetPreallocation(J_aug,PETSC_NULL,d_nnz);CHKERRQ(ierr);
1243 
1244       ierr = PetscFree(d_nnz);CHKERRQ(ierr);
1245 
1246       /* Set the original jacobian matrix in J_aug */
1247       for(row=0;row<snes->jacobian->rmap->n;row++) {
1248 	ierr = MatGetRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1249 	ierr = MatSetValues(J_aug,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
1250 	ierr = MatRestoreRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1251       }
1252       /* Add the augmented part */
1253       for(k=0;k<nkept;k++) {
1254 	row = idx_actkept[k];
1255 	col = snes->jacobian->rmap->n+k;
1256 	ierr = MatSetValues(J_aug,1,&row,1,&col,&value,INSERT_VALUES);CHKERRQ(ierr);
1257 	ierr = MatSetValues(J_aug,1,&col,1,&row,&value,INSERT_VALUES);CHKERRQ(ierr);
1258       }
1259       ierr = MatAssemblyBegin(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1260       ierr = MatAssemblyEnd(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1261       /* Only considering prejac = jac for now */
1262       Jpre_aug = J_aug;
1263       } /* local vars*/
1264     } else {
1265       F_aug = F; J_aug = snes->jacobian; Y_aug = Y; Jpre_aug = snes->jacobian_pre;
1266     }
1267 
1268     ierr = ISEqual(vi->IS_inact_prev,IS_inact,&isequal);CHKERRQ(ierr);
1269     if (!isequal) {
1270       ierr = SNESVIResetPCandKSP(snes,J_aug,Jpre_aug);CHKERRQ(ierr);
1271     }
1272     ierr = KSPSetOperators(snes->ksp,J_aug,Jpre_aug,flg);CHKERRQ(ierr);
1273     ierr = KSPSetUp(snes->ksp);CHKERRQ(ierr);
1274     /*  {
1275       PC        pc;
1276       PetscBool flg;
1277       ierr = KSPGetPC(snes->ksp,&pc);CHKERRQ(ierr);
1278       ierr = PetscTypeCompare((PetscObject)pc,PCFIELDSPLIT,&flg);CHKERRQ(ierr);
1279       if (flg) {
1280         KSP      *subksps;
1281         ierr = PCFieldSplitGetSubKSP(pc,PETSC_NULL,&subksps);CHKERRQ(ierr);
1282         ierr = KSPGetPC(subksps[0],&pc);CHKERRQ(ierr);
1283         ierr = PetscFree(subksps);CHKERRQ(ierr);
1284         ierr = PetscTypeCompare((PetscObject)pc,PCBJACOBI,&flg);CHKERRQ(ierr);
1285         if (flg) {
1286           PetscInt       n,N = 101*101,j,cnts[3] = {0,0,0};
1287           const PetscInt *ii;
1288 
1289           ierr = ISGetSize(IS_inact,&n);CHKERRQ(ierr);
1290           ierr = ISGetIndices(IS_inact,&ii);CHKERRQ(ierr);
1291           for (j=0; j<n; j++) {
1292             if (ii[j] < N) cnts[0]++;
1293             else if (ii[j] < 2*N) cnts[1]++;
1294             else if (ii[j] < 3*N) cnts[2]++;
1295           }
1296           ierr = ISRestoreIndices(IS_inact,&ii);CHKERRQ(ierr);
1297 
1298           ierr = PCBJacobiSetTotalBlocks(pc,3,cnts);CHKERRQ(ierr);
1299         }
1300       }
1301     }
1302     */
1303     ierr = SNES_KSPSolve(snes,snes->ksp,F_aug,Y_aug);CHKERRQ(ierr);
1304     ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr);
1305     if (kspreason < 0) {
1306       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
1307         ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr);
1308         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
1309         break;
1310       }
1311     }
1312 
1313     if(nis_act) {
1314       PetscScalar *y1,*y2;
1315       ierr = VecGetArray(Y,&y1);CHKERRQ(ierr);
1316       ierr = VecGetArray(Y_aug,&y2);CHKERRQ(ierr);
1317       /* Copy over inactive Y_aug to Y */
1318       j1 = 0;
1319       for(i1=Y->map->rstart;i1 < Y->map->rend;i1++) {
1320 	if(j1 < nkept && idx_actkept[j1] == i1) j1++;
1321 	else y1[i1-Y->map->rstart] = y2[i1-Y->map->rstart];
1322       }
1323       ierr = VecRestoreArray(Y,&y1);CHKERRQ(ierr);
1324       ierr = VecRestoreArray(Y_aug,&y2);CHKERRQ(ierr);
1325 
1326       ierr = VecDestroy(&F_aug);CHKERRQ(ierr);
1327       ierr = VecDestroy(&Y_aug);CHKERRQ(ierr);
1328       ierr = MatDestroy(&J_aug);CHKERRQ(ierr);
1329       ierr = PetscFree(idx_actkept);CHKERRQ(ierr);
1330     }
1331 
1332     if (!isequal) {
1333       ierr = ISDestroy(&vi->IS_inact_prev);CHKERRQ(ierr);
1334       ierr = ISDuplicate(IS_inact,&vi->IS_inact_prev);CHKERRQ(ierr);
1335     }
1336     ierr = ISDestroy(&IS_inact);CHKERRQ(ierr);
1337 
1338     ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr);
1339     snes->linear_its += lits;
1340     ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr);
1341     /*
1342     if (vi->precheckstep) {
1343       PetscBool changed_y = PETSC_FALSE;
1344       ierr = (*vi->precheckstep)(snes,X,Y,vi->precheck,&changed_y);CHKERRQ(ierr);
1345     }
1346 
1347     if (PetscLogPrintInfo){
1348       ierr = SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr);
1349     }
1350     */
1351     /* Compute a (scaled) negative update in the line search routine:
1352          Y <- X - lambda*Y
1353        and evaluate G = function(Y) (depends on the line search).
1354     */
1355     ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr);
1356     ynorm = 1; gnorm = fnorm;
1357     ierr = (*vi->LineSearch)(snes,vi->lsP,X,F,G,Y,W,fnorm,xnorm,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
1358     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",fnorm,gnorm,ynorm,(int)lssucceed);CHKERRQ(ierr);
1359     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
1360     if (snes->domainerror) {
1361       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
1362       PetscFunctionReturn(0);
1363     }
1364     if (!lssucceed) {
1365       if (++snes->numFailures >= snes->maxFailures) {
1366 	PetscBool ismin;
1367         snes->reason = SNES_DIVERGED_LINE_SEARCH;
1368         ierr = SNESVICheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr);
1369         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
1370         break;
1371       }
1372     }
1373     /* Update function and solution vectors */
1374     fnorm = gnorm;
1375     ierr = VecCopy(G,F);CHKERRQ(ierr);
1376     ierr = VecCopy(W,X);CHKERRQ(ierr);
1377     /* Monitor convergence */
1378     ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1379     snes->iter = i+1;
1380     snes->norm = fnorm;
1381     ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1382     SNESLogConvHistory(snes,snes->norm,lits);
1383     SNESMonitor(snes,snes->iter,snes->norm);
1384     /* Test for convergence, xnorm = || X || */
1385     if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); }
1386     ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
1387     if (snes->reason) break;
1388   }
1389   if (i == maxits) {
1390     ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr);
1391     if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
1392   }
1393   PetscFunctionReturn(0);
1394 }
1395 
1396 /* -------------------------------------------------------------------------- */
1397 /*
1398    SNESSetUp_VI - Sets up the internal data structures for the later use
1399    of the SNESVI nonlinear solver.
1400 
1401    Input Parameter:
1402 .  snes - the SNES context
1403 .  x - the solution vector
1404 
1405    Application Interface Routine: SNESSetUp()
1406 
1407    Notes:
1408    For basic use of the SNES solvers, the user need not explicitly call
1409    SNESSetUp(), since these actions will automatically occur during
1410    the call to SNESSolve().
1411  */
1412 #undef __FUNCT__
1413 #define __FUNCT__ "SNESSetUp_VI"
1414 PetscErrorCode SNESSetUp_VI(SNES snes)
1415 {
1416   PetscErrorCode ierr;
1417   SNES_VI        *vi = (SNES_VI*) snes->data;
1418   PetscInt       i_start[3],i_end[3];
1419 
1420   PetscFunctionBegin;
1421 
1422   ierr = SNESDefaultGetWork(snes,3);CHKERRQ(ierr);
1423 
1424   /* If the lower and upper bound on variables are not set, set it to
1425      -Inf and Inf */
1426   if (!vi->xl && !vi->xu) {
1427     vi->usersetxbounds = PETSC_FALSE;
1428     ierr = VecDuplicate(snes->vec_sol, &vi->xl); CHKERRQ(ierr);
1429     ierr = VecSet(vi->xl,PETSC_VI_NINF);CHKERRQ(ierr);
1430     ierr = VecDuplicate(snes->vec_sol, &vi->xu); CHKERRQ(ierr);
1431     ierr = VecSet(vi->xu,PETSC_VI_INF);CHKERRQ(ierr);
1432   } else {
1433     /* Check if lower bound, upper bound and solution vector distribution across the processors is identical */
1434     ierr = VecGetOwnershipRange(snes->vec_sol,i_start,i_end);CHKERRQ(ierr);
1435     ierr = VecGetOwnershipRange(vi->xl,i_start+1,i_end+1);CHKERRQ(ierr);
1436     ierr = VecGetOwnershipRange(vi->xu,i_start+2,i_end+2);CHKERRQ(ierr);
1437     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]))
1438       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.");
1439   }
1440   if (snes->ops->solve != SNESSolveVI_SS) {
1441     /* Set up previous active index set for the first snes solve
1442        vi->IS_inact_prev = 0,1,2,....N */
1443     PetscInt *indices;
1444     PetscInt  i,n,rstart,rend;
1445 
1446     ierr = VecGetOwnershipRange(snes->vec_sol,&rstart,&rend);CHKERRQ(ierr);
1447     ierr = VecGetLocalSize(snes->vec_sol,&n);CHKERRQ(ierr);
1448     ierr = PetscMalloc(n*sizeof(PetscInt),&indices);CHKERRQ(ierr);
1449     for(i=0;i < n; i++) indices[i] = rstart + i;
1450     ierr = ISCreateGeneral(((PetscObject)snes)->comm,n,indices,PETSC_OWN_POINTER,&vi->IS_inact_prev);
1451   }
1452 
1453   if (snes->ops->solve == SNESSolveVI_SS) {
1454     ierr = VecDuplicate(snes->vec_sol, &vi->dpsi);CHKERRQ(ierr);
1455     ierr = VecDuplicate(snes->vec_sol, &vi->phi); CHKERRQ(ierr);
1456     ierr = VecDuplicate(snes->vec_sol, &vi->Da); CHKERRQ(ierr);
1457     ierr = VecDuplicate(snes->vec_sol, &vi->Db); CHKERRQ(ierr);
1458     ierr = VecDuplicate(snes->vec_sol, &vi->z);CHKERRQ(ierr);
1459     ierr = VecDuplicate(snes->vec_sol, &vi->t); CHKERRQ(ierr);
1460   }
1461   PetscFunctionReturn(0);
1462 }
1463 /* -------------------------------------------------------------------------- */
1464 /*
1465    SNESDestroy_VI - Destroys the private SNES_VI context that was created
1466    with SNESCreate_VI().
1467 
1468    Input Parameter:
1469 .  snes - the SNES context
1470 
1471    Application Interface Routine: SNESDestroy()
1472  */
1473 #undef __FUNCT__
1474 #define __FUNCT__ "SNESDestroy_VI"
1475 PetscErrorCode SNESDestroy_VI(SNES snes)
1476 {
1477   SNES_VI        *vi = (SNES_VI*) snes->data;
1478   PetscErrorCode ierr;
1479 
1480   PetscFunctionBegin;
1481   if (snes->ops->solve != SNESSolveVI_SS) {
1482     ierr = ISDestroy(&vi->IS_inact_prev);
1483   }
1484 
1485   if (snes->ops->solve == SNESSolveVI_SS) {
1486     /* clear vectors */
1487     ierr = VecDestroy(&vi->dpsi);CHKERRQ(ierr);
1488     ierr = VecDestroy(&vi->phi); CHKERRQ(ierr);
1489     ierr = VecDestroy(&vi->Da); CHKERRQ(ierr);
1490     ierr = VecDestroy(&vi->Db); CHKERRQ(ierr);
1491     ierr = VecDestroy(&vi->z); CHKERRQ(ierr);
1492     ierr = VecDestroy(&vi->t); CHKERRQ(ierr);
1493   }
1494 
1495   if (!vi->usersetxbounds) {
1496     ierr = VecDestroy(&vi->xl); CHKERRQ(ierr);
1497     ierr = VecDestroy(&vi->xu); CHKERRQ(ierr);
1498   }
1499 
1500   ierr = PetscViewerASCIIMonitorDestroy(&vi->lsmonitor);CHKERRQ(ierr);
1501   ierr = PetscFree(snes->data);CHKERRQ(ierr);
1502 
1503   /* clear composed functions */
1504   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","",PETSC_NULL);CHKERRQ(ierr);
1505   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","",PETSC_NULL);CHKERRQ(ierr);
1506   PetscFunctionReturn(0);
1507 }
1508 
1509 /* -------------------------------------------------------------------------- */
1510 #undef __FUNCT__
1511 #define __FUNCT__ "SNESLineSearchNo_VI"
1512 
1513 /*
1514   This routine does not actually do a line search but it takes a full newton
1515   step while ensuring that the new iterates remain within the constraints.
1516 
1517 */
1518 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)
1519 {
1520   PetscErrorCode ierr;
1521   SNES_VI        *vi = (SNES_VI*)snes->data;
1522   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1523 
1524   PetscFunctionBegin;
1525   *flag = PETSC_TRUE;
1526   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1527   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);         /* ynorm = || y || */
1528   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1529   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1530   if (vi->postcheckstep) {
1531    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1532   }
1533   if (changed_y) {
1534     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1535     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1536   }
1537   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1538   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1539   if (!snes->domainerror) {
1540     if (snes->ops->solve != SNESSolveVI_SS) {
1541        ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1542     } else {
1543       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);  /* gnorm = || g || */
1544     }
1545     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1546   }
1547   if (vi->lsmonitor) {
1548     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1549   }
1550   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1551   PetscFunctionReturn(0);
1552 }
1553 
1554 /* -------------------------------------------------------------------------- */
1555 #undef __FUNCT__
1556 #define __FUNCT__ "SNESLineSearchNoNorms_VI"
1557 
1558 /*
1559   This routine is a copy of SNESLineSearchNoNorms in snes/impls/ls/ls.c
1560 */
1561 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)
1562 {
1563   PetscErrorCode ierr;
1564   SNES_VI        *vi = (SNES_VI*)snes->data;
1565   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1566 
1567   PetscFunctionBegin;
1568   *flag = PETSC_TRUE;
1569   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1570   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y      */
1571   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1572   if (vi->postcheckstep) {
1573    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1574   }
1575   if (changed_y) {
1576     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1577     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1578   }
1579 
1580   /* don't evaluate function the last time through */
1581   if (snes->iter < snes->max_its-1) {
1582     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1583   }
1584   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1585   PetscFunctionReturn(0);
1586 }
1587 
1588 /* -------------------------------------------------------------------------- */
1589 #undef __FUNCT__
1590 #define __FUNCT__ "SNESLineSearchCubic_VI"
1591 /*
1592   This routine implements a cubic line search while doing a projection on the variable bounds
1593 */
1594 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)
1595 {
1596   PetscReal      initslope,lambdaprev,gnormprev,a,b,d,t1,t2,rellength;
1597   PetscReal      minlambda,lambda,lambdatemp;
1598 #if defined(PETSC_USE_COMPLEX)
1599   PetscScalar    cinitslope;
1600 #endif
1601   PetscErrorCode ierr;
1602   PetscInt       count;
1603   SNES_VI        *vi = (SNES_VI*)snes->data;
1604   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1605   MPI_Comm       comm;
1606 
1607   PetscFunctionBegin;
1608   ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr);
1609   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1610   *flag   = PETSC_TRUE;
1611 
1612   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1613   if (*ynorm == 0.0) {
1614     if (vi->lsmonitor) {
1615       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Initial direction and size is 0\n");CHKERRQ(ierr);
1616     }
1617     *gnorm = fnorm;
1618     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1619     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1620     *flag  = PETSC_FALSE;
1621     goto theend1;
1622   }
1623   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1624     if (vi->lsmonitor) {
1625       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Scaling step by %G old ynorm %G\n",vi->maxstep/(*ynorm),*ynorm);CHKERRQ(ierr);
1626     }
1627     ierr = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1628     *ynorm = vi->maxstep;
1629   }
1630   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1631   minlambda = vi->minlambda/rellength;
1632   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1633 #if defined(PETSC_USE_COMPLEX)
1634   ierr = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1635   initslope = PetscRealPart(cinitslope);
1636 #else
1637   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1638 #endif
1639   if (initslope > 0.0)  initslope = -initslope;
1640   if (initslope == 0.0) initslope = -1.0;
1641 
1642   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1643   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1644   if (snes->nfuncs >= snes->max_funcs) {
1645     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1646     *flag = PETSC_FALSE;
1647     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1648     goto theend1;
1649   }
1650   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1651   if (snes->ops->solve != SNESSolveVI_SS) {
1652     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1653   } else {
1654     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1655   }
1656   if (snes->domainerror) {
1657     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1658     PetscFunctionReturn(0);
1659   }
1660   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1661   ierr = PetscInfo2(snes,"Initial fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1662   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1663     if (vi->lsmonitor) {
1664       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1665     }
1666     goto theend1;
1667   }
1668 
1669   /* Fit points with quadratic */
1670   lambda     = 1.0;
1671   lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1672   lambdaprev = lambda;
1673   gnormprev  = *gnorm;
1674   if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1675   if (lambdatemp <= .1*lambda) lambda = .1*lambda;
1676   else                         lambda = lambdatemp;
1677 
1678   ierr  = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1679   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1680   if (snes->nfuncs >= snes->max_funcs) {
1681     ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while attempting quadratic backtracking! %D \n",snes->nfuncs);CHKERRQ(ierr);
1682     *flag = PETSC_FALSE;
1683     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1684     goto theend1;
1685   }
1686   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1687   if (snes->ops->solve != SNESSolveVI_SS) {
1688     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1689   } else {
1690     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1691   }
1692   if (snes->domainerror) {
1693     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1694     PetscFunctionReturn(0);
1695   }
1696   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1697   if (vi->lsmonitor) {
1698     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: gnorm after quadratic fit %G\n",*gnorm);CHKERRQ(ierr);
1699   }
1700   if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1701     if (vi->lsmonitor) {
1702       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Quadratically determined step, lambda=%18.16e\n",lambda);CHKERRQ(ierr);
1703     }
1704     goto theend1;
1705   }
1706 
1707   /* Fit points with cubic */
1708   count = 1;
1709   while (PETSC_TRUE) {
1710     if (lambda <= minlambda) {
1711       if (vi->lsmonitor) {
1712 	ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: unable to find good step length! After %D tries \n",count);CHKERRQ(ierr);
1713 	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);
1714       }
1715       *flag = PETSC_FALSE;
1716       break;
1717     }
1718     t1 = .5*((*gnorm)*(*gnorm) - fnorm*fnorm) - lambda*initslope;
1719     t2 = .5*(gnormprev*gnormprev  - fnorm*fnorm) - lambdaprev*initslope;
1720     a  = (t1/(lambda*lambda) - t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1721     b  = (-lambdaprev*t1/(lambda*lambda) + lambda*t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1722     d  = b*b - 3*a*initslope;
1723     if (d < 0.0) d = 0.0;
1724     if (a == 0.0) {
1725       lambdatemp = -initslope/(2.0*b);
1726     } else {
1727       lambdatemp = (-b + sqrt(d))/(3.0*a);
1728     }
1729     lambdaprev = lambda;
1730     gnormprev  = *gnorm;
1731     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1732     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1733     else                         lambda     = lambdatemp;
1734     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1735     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1736     if (snes->nfuncs >= snes->max_funcs) {
1737       ierr = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1738       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);
1739       *flag = PETSC_FALSE;
1740       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1741       break;
1742     }
1743     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1744     if (snes->ops->solve != SNESSolveVI_SS) {
1745       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1746     } else {
1747       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1748     }
1749     if (snes->domainerror) {
1750       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1751       PetscFunctionReturn(0);
1752     }
1753     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1754     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* is reduction enough? */
1755       if (vi->lsmonitor) {
1756 	ierr = PetscPrintf(comm,"    Line search: Cubically determined step, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1757       }
1758       break;
1759     } else {
1760       if (vi->lsmonitor) {
1761         ierr = PetscPrintf(comm,"    Line search: Cubic step no good, shrinking lambda, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1762       }
1763     }
1764     count++;
1765   }
1766   theend1:
1767   /* Optional user-defined check for line search step validity */
1768   if (vi->postcheckstep && *flag) {
1769     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1770     if (changed_y) {
1771       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1772       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1773     }
1774     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1775       ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1776       if (snes->ops->solve != SNESSolveVI_SS) {
1777         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1778       } else {
1779         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1780       }
1781       if (snes->domainerror) {
1782         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1783         PetscFunctionReturn(0);
1784       }
1785       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1786       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1787       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1788     }
1789   }
1790   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1791   PetscFunctionReturn(0);
1792 }
1793 
1794 #undef __FUNCT__
1795 #define __FUNCT__ "SNESLineSearchQuadratic_VI"
1796 /*
1797   This routine does a quadratic line search while keeping the iterates within the variable bounds
1798 */
1799 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)
1800 {
1801   /*
1802      Note that for line search purposes we work with with the related
1803      minimization problem:
1804         min  z(x):  R^n -> R,
1805      where z(x) = .5 * fnorm*fnorm,and fnorm = || f ||_2.
1806    */
1807   PetscReal      initslope,minlambda,lambda,lambdatemp,rellength;
1808 #if defined(PETSC_USE_COMPLEX)
1809   PetscScalar    cinitslope;
1810 #endif
1811   PetscErrorCode ierr;
1812   PetscInt       count;
1813   SNES_VI        *vi = (SNES_VI*)snes->data;
1814   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1815 
1816   PetscFunctionBegin;
1817   ierr    = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1818   *flag   = PETSC_TRUE;
1819 
1820   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1821   if (*ynorm == 0.0) {
1822     if (vi->lsmonitor) {
1823       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Direction and size is 0\n");CHKERRQ(ierr);
1824     }
1825     *gnorm = fnorm;
1826     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1827     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1828     *flag  = PETSC_FALSE;
1829     goto theend2;
1830   }
1831   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1832     ierr   = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1833     *ynorm = vi->maxstep;
1834   }
1835   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1836   minlambda = vi->minlambda/rellength;
1837   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1838 #if defined(PETSC_USE_COMPLEX)
1839   ierr      = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1840   initslope = PetscRealPart(cinitslope);
1841 #else
1842   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1843 #endif
1844   if (initslope > 0.0)  initslope = -initslope;
1845   if (initslope == 0.0) initslope = -1.0;
1846   ierr = PetscInfo1(snes,"Initslope %G \n",initslope);CHKERRQ(ierr);
1847 
1848   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1849   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1850   if (snes->nfuncs >= snes->max_funcs) {
1851     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1852     *flag = PETSC_FALSE;
1853     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1854     goto theend2;
1855   }
1856   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1857   if (snes->ops->solve != SNESSolveVI_SS) {
1858     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1859   } else {
1860     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1861   }
1862   if (snes->domainerror) {
1863     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1864     PetscFunctionReturn(0);
1865   }
1866   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1867   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1868     if (vi->lsmonitor) {
1869       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1870     }
1871     goto theend2;
1872   }
1873 
1874   /* Fit points with quadratic */
1875   lambda = 1.0;
1876   count = 1;
1877   while (PETSC_TRUE) {
1878     if (lambda <= minlambda) { /* bad luck; use full step */
1879       if (vi->lsmonitor) {
1880         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Unable to find good step length! %D \n",count);CHKERRQ(ierr);
1881         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);
1882       }
1883       ierr = VecCopy(x,w);CHKERRQ(ierr);
1884       *flag = PETSC_FALSE;
1885       break;
1886     }
1887     lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1888     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1889     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1890     else                         lambda     = lambdatemp;
1891 
1892     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1893     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1894     if (snes->nfuncs >= snes->max_funcs) {
1895       ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1896       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);
1897       *flag = PETSC_FALSE;
1898       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1899       break;
1900     }
1901     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1902     if (snes->domainerror) {
1903       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1904       PetscFunctionReturn(0);
1905     }
1906     if (snes->ops->solve != SNESSolveVI_SS) {
1907       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1908     } else {
1909       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1910     }
1911     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1912     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1913       if (vi->lsmonitor) {
1914         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line Search: Quadratically determined step, lambda=%G\n",lambda);CHKERRQ(ierr);
1915       }
1916       break;
1917     }
1918     count++;
1919   }
1920   theend2:
1921   /* Optional user-defined check for line search step validity */
1922   if (vi->postcheckstep) {
1923     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1924     if (changed_y) {
1925       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1926       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1927     }
1928     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1929       ierr = SNESComputeFunction(snes,w,g);
1930       if (snes->domainerror) {
1931         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1932         PetscFunctionReturn(0);
1933       }
1934       if (snes->ops->solve != SNESSolveVI_SS) {
1935         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1936       } else {
1937         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1938       }
1939 
1940       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1941       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1942       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1943     }
1944   }
1945   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1946   PetscFunctionReturn(0);
1947 }
1948 
1949 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*/
1950 /* -------------------------------------------------------------------------- */
1951 EXTERN_C_BEGIN
1952 #undef __FUNCT__
1953 #define __FUNCT__ "SNESLineSearchSet_VI"
1954 PetscErrorCode  SNESLineSearchSet_VI(SNES snes,FCN2 func,void *lsctx)
1955 {
1956   PetscFunctionBegin;
1957   ((SNES_VI *)(snes->data))->LineSearch = func;
1958   ((SNES_VI *)(snes->data))->lsP        = lsctx;
1959   PetscFunctionReturn(0);
1960 }
1961 EXTERN_C_END
1962 
1963 /* -------------------------------------------------------------------------- */
1964 EXTERN_C_BEGIN
1965 #undef __FUNCT__
1966 #define __FUNCT__ "SNESLineSearchSetMonitor_VI"
1967 PetscErrorCode  SNESLineSearchSetMonitor_VI(SNES snes,PetscBool flg)
1968 {
1969   SNES_VI        *vi = (SNES_VI*)snes->data;
1970   PetscErrorCode ierr;
1971 
1972   PetscFunctionBegin;
1973   if (flg && !vi->lsmonitor) {
1974     ierr = PetscViewerASCIIMonitorCreate(((PetscObject)snes)->comm,"stdout",((PetscObject)snes)->tablevel,&vi->lsmonitor);CHKERRQ(ierr);
1975   } else if (!flg && vi->lsmonitor) {
1976     ierr = PetscViewerASCIIMonitorDestroy(&vi->lsmonitor);CHKERRQ(ierr);
1977   }
1978   PetscFunctionReturn(0);
1979 }
1980 EXTERN_C_END
1981 
1982 /*
1983    SNESView_VI - Prints info from the SNESVI data structure.
1984 
1985    Input Parameters:
1986 .  SNES - the SNES context
1987 .  viewer - visualization context
1988 
1989    Application Interface Routine: SNESView()
1990 */
1991 #undef __FUNCT__
1992 #define __FUNCT__ "SNESView_VI"
1993 static PetscErrorCode SNESView_VI(SNES snes,PetscViewer viewer)
1994 {
1995   SNES_VI        *vi = (SNES_VI *)snes->data;
1996   const char     *cstr,*tstr;
1997   PetscErrorCode ierr;
1998   PetscBool     iascii;
1999 
2000   PetscFunctionBegin;
2001   ierr = PetscTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
2002   if (iascii) {
2003     if (vi->LineSearch == SNESLineSearchNo_VI)             cstr = "SNESLineSearchNo";
2004     else if (vi->LineSearch == SNESLineSearchQuadratic_VI) cstr = "SNESLineSearchQuadratic";
2005     else if (vi->LineSearch == SNESLineSearchCubic_VI)     cstr = "SNESLineSearchCubic";
2006     else                                                             cstr = "unknown";
2007     if (snes->ops->solve == SNESSolveVI_SS)      tstr = "Semismooth";
2008     else if (snes->ops->solve == SNESSolveVI_RS) tstr = "Reduced Space";
2009     else if (snes->ops->solve == SNESSolveVI_RS2) tstr = "Augmented Space";
2010     else                                         tstr = "unknown";
2011     ierr = PetscViewerASCIIPrintf(viewer,"  VI algorithm: %s\n",tstr);CHKERRQ(ierr);
2012     ierr = PetscViewerASCIIPrintf(viewer,"  line search variant: %s\n",cstr);CHKERRQ(ierr);
2013     ierr = PetscViewerASCIIPrintf(viewer,"  alpha=%G, maxstep=%G, minlambda=%G\n",vi->alpha,vi->maxstep,vi->minlambda);CHKERRQ(ierr);
2014   } else {
2015     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Viewer type %s not supported for SNES EQ VI",((PetscObject)viewer)->type_name);
2016   }
2017   PetscFunctionReturn(0);
2018 }
2019 
2020 #undef __FUNCT__
2021 #define __FUNCT__ "SNESVISetVariableBounds"
2022 /*@
2023    SNESVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu.
2024 
2025    Input Parameters:
2026 .  snes - the SNES context.
2027 .  xl   - lower bound.
2028 .  xu   - upper bound.
2029 
2030    Notes:
2031    If this routine is not called then the lower and upper bounds are set to
2032    PETSC_VI_INF and PETSC_VI_NINF respectively during SNESSetUp().
2033 
2034 @*/
2035 PetscErrorCode SNESVISetVariableBounds(SNES snes, Vec xl, Vec xu)
2036 {
2037   SNES_VI  *vi = (SNES_VI*)snes->data;
2038 
2039   PetscFunctionBegin;
2040   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
2041   PetscValidHeaderSpecific(xl,VEC_CLASSID,2);
2042   PetscValidHeaderSpecific(xu,VEC_CLASSID,3);
2043   if (!snes->vec_func) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call SNESSetFunction() first");
2044   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);
2045   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);
2046 
2047   vi->usersetxbounds = PETSC_TRUE;
2048   vi->xl = xl;
2049   vi->xu = xu;
2050   PetscFunctionReturn(0);
2051 }
2052 
2053 /* -------------------------------------------------------------------------- */
2054 /*
2055    SNESSetFromOptions_VI - Sets various parameters for the SNESVI method.
2056 
2057    Input Parameter:
2058 .  snes - the SNES context
2059 
2060    Application Interface Routine: SNESSetFromOptions()
2061 */
2062 #undef __FUNCT__
2063 #define __FUNCT__ "SNESSetFromOptions_VI"
2064 static PetscErrorCode SNESSetFromOptions_VI(SNES snes)
2065 {
2066   SNES_VI        *vi = (SNES_VI *)snes->data;
2067   const char     *lses[] = {"basic","basicnonorms","quadratic","cubic"};
2068   const char     *vies[] = {"ss","rs","rs2"};
2069   PetscErrorCode ierr;
2070   PetscInt       indx;
2071   PetscBool      flg,set,flg2;
2072 
2073   PetscFunctionBegin;
2074   ierr = PetscOptionsHead("SNES semismooth method options");CHKERRQ(ierr);
2075   ierr = PetscOptionsBool("-snes_vi_monitor","Monitor all non-active variables","None",PETSC_FALSE,&flg,0);CHKERRQ(ierr);
2076   if (flg) {
2077     ierr = SNESMonitorSet(snes,SNESMonitorVI,0,0);CHKERRQ(ierr);
2078   }
2079   ierr = PetscOptionsReal("-snes_ls_alpha","Function norm must decrease by","None",vi->alpha,&vi->alpha,0);CHKERRQ(ierr);
2080   ierr = PetscOptionsReal("-snes_ls_maxstep","Step must be less than","None",vi->maxstep,&vi->maxstep,0);CHKERRQ(ierr);
2081   ierr = PetscOptionsReal("-snes_ls_minlambda","Minimum lambda allowed","None",vi->minlambda,&vi->minlambda,0);CHKERRQ(ierr);
2082   ierr = PetscOptionsReal("-snes_vi_const_tol","constraint tolerance","None",vi->const_tol,&vi->const_tol,0);CHKERRQ(ierr);
2083   ierr = PetscOptionsBool("-snes_ls_monitor","Print progress of line searches","SNESLineSearchSetMonitor",vi->lsmonitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);CHKERRQ(ierr);
2084   if (set) {ierr = SNESLineSearchSetMonitor(snes,flg);CHKERRQ(ierr);}
2085   ierr = PetscOptionsEList("-snes_vi_type","Semismooth algorithm used","",vies,3,"ss",&indx,&flg2);CHKERRQ(ierr);
2086   if (flg2) {
2087     switch (indx) {
2088     case 0:
2089       snes->ops->solve = SNESSolveVI_SS;
2090       break;
2091     case 1:
2092       snes->ops->solve = SNESSolveVI_RS;
2093       break;
2094     case 2:
2095       snes->ops->solve = SNESSolveVI_RS2;
2096     }
2097   }
2098   ierr = PetscOptionsEList("-snes_ls","Line search used","SNESLineSearchSet",lses,4,"basic",&indx,&flg);CHKERRQ(ierr);
2099   if (flg) {
2100     switch (indx) {
2101     case 0:
2102       ierr = SNESLineSearchSet(snes,SNESLineSearchNo_VI,PETSC_NULL);CHKERRQ(ierr);
2103       break;
2104     case 1:
2105       ierr = SNESLineSearchSet(snes,SNESLineSearchNoNorms_VI,PETSC_NULL);CHKERRQ(ierr);
2106       break;
2107     case 2:
2108       ierr = SNESLineSearchSet(snes,SNESLineSearchQuadratic_VI,PETSC_NULL);CHKERRQ(ierr);
2109       break;
2110     case 3:
2111       ierr = SNESLineSearchSet(snes,SNESLineSearchCubic_VI,PETSC_NULL);CHKERRQ(ierr);
2112       break;
2113     }
2114   }
2115   ierr = PetscOptionsTail();CHKERRQ(ierr);
2116   PetscFunctionReturn(0);
2117 }
2118 /* -------------------------------------------------------------------------- */
2119 /*MC
2120       SNESVI - Semismooth newton method based nonlinear solver that uses a line search
2121 
2122    Options Database:
2123 +   -snes_ls [cubic,quadratic,basic,basicnonorms] - Selects line search
2124 .   -snes_ls_alpha <alpha> - Sets alpha
2125 .   -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)
2126 .   -snes_ls_minlambda <minlambda>  - Sets the minimum lambda the line search will use  minlambda / max_i ( y[i]/x[i] )
2127 -   -snes_ls_monitor - print information about progress of line searches
2128 
2129 
2130    Level: beginner
2131 
2132 .seealso:  SNESCreate(), SNES, SNESSetType(), SNESTR, SNESLineSearchSet(),
2133            SNESLineSearchSetPostCheck(), SNESLineSearchNo(), SNESLineSearchCubic(), SNESLineSearchQuadratic(),
2134            SNESLineSearchSet(), SNESLineSearchNoNorms(), SNESLineSearchSetPreCheck(), SNESLineSearchSetParams(), SNESLineSearchGetParams()
2135 
2136 M*/
2137 EXTERN_C_BEGIN
2138 #undef __FUNCT__
2139 #define __FUNCT__ "SNESCreate_VI"
2140 PetscErrorCode  SNESCreate_VI(SNES snes)
2141 {
2142   PetscErrorCode ierr;
2143   SNES_VI      *vi;
2144 
2145   PetscFunctionBegin;
2146   snes->ops->setup           = SNESSetUp_VI;
2147   snes->ops->solve           = SNESSolveVI_SS;
2148   snes->ops->destroy         = SNESDestroy_VI;
2149   snes->ops->setfromoptions  = SNESSetFromOptions_VI;
2150   snes->ops->view            = SNESView_VI;
2151   snes->ops->reset           = 0; /* XXX Implement!!! */
2152   snes->ops->converged       = SNESDefaultConverged_VI;
2153 
2154   ierr                  = PetscNewLog(snes,SNES_VI,&vi);CHKERRQ(ierr);
2155   snes->data            = (void*)vi;
2156   vi->alpha             = 1.e-4;
2157   vi->maxstep           = 1.e8;
2158   vi->minlambda         = 1.e-12;
2159   vi->LineSearch        = SNESLineSearchNo_VI;
2160   vi->lsP               = PETSC_NULL;
2161   vi->postcheckstep     = PETSC_NULL;
2162   vi->postcheck         = PETSC_NULL;
2163   vi->precheckstep      = PETSC_NULL;
2164   vi->precheck          = PETSC_NULL;
2165   vi->const_tol         =  2.2204460492503131e-16;
2166   vi->checkredundancy   = PETSC_NULL;
2167 
2168   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","SNESLineSearchSetMonitor_VI",SNESLineSearchSetMonitor_VI);CHKERRQ(ierr);
2169   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","SNESLineSearchSet_VI",SNESLineSearchSet_VI);CHKERRQ(ierr);
2170 
2171   PetscFunctionReturn(0);
2172 }
2173 EXTERN_C_END
2174