xref: /petsc/src/snes/impls/vi/vi.c (revision 493a4f3d33b3df8611aa00daceb10ef57e5a2ab9)
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*))
1010 {
1011   SNES_VI         *vi = (SNES_VI*)snes->data;
1012 
1013   PetscFunctionBegin;
1014   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
1015   vi->checkredundancy = func;
1016   PetscFunctionReturn(0);
1017 }
1018 
1019 #if defined(PETSC_HAVE_MATLAB_ENGINE)
1020 #include <engine.h>
1021 #include <mex.h>
1022 typedef struct {char *funcname; mxArray *ctx;} SNESVIMatlabContext;
1023 
1024 #undef __FUNCT__
1025 #define __FUNCT__ "SNESVIRedundancyCheck_Matlab"
1026 PetscErrorCode SNESVIRedundancyCheck_Matlab(SNES snes,IS is_act,IS* is_redact,void* ctx)
1027 {
1028   PetscErrorCode      ierr;
1029   SNESVIMatlabContext *sctx = (SNESVIMatlabContext*)ctx;
1030   int                 nlhs = 2, nrhs = 4;
1031   mxArray             *plhs[2], *prhs[4];
1032   long long int       l1 = 0,ls = 0;
1033 
1034   PetscFunctionBegin;
1035   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
1036   PetscValidHeaderSpecific(is_act,IS_CLASSID,2);
1037   PetscValidPointer(is_redact,3);
1038   PetscCheckSameComm(snes,1,is_act,2);
1039 
1040   /* call Matlab function in ctx with arguments is_act */
1041   ierr = PetscMemcpy(&ls,&snes,sizeof(snes));CHKERRQ(ierr);
1042   ierr = PetscMemcpy(&l1,&is_act,sizeof(is_act));CHKERRQ(ierr);
1043   prhs[0] = mxCreateDoubleScalar((double)ls);
1044   prhs[1] = mxCreateDoubleScalar((double)l1);
1045   prhs[2] = mxCreateString(sctx->funcname);
1046   prhs[3] = sctx->ctx;
1047   ierr    = mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscSNESVIRedundancyCheckInternal");CHKERRQ(ierr);
1048   ierr    = mxGetScalar(plhs[0]);CHKERRQ(ierr);
1049   *is_redact = (IS)mxGetPr(plhs[1]);
1050   mxDestroyArray(prhs[0]);
1051   mxDestroyArray(prhs[1]);
1052   mxDestroyArray(prhs[2]);
1053   mxDestroyArray(prhs[3]);
1054   mxDestroyArray(plhs[0]);
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 #undef __FUNCT__
1059 #define __FUNCT__ "SNESVISetRedundancyCheckMatlab"
1060 PetscErrorCode SNESVISetRedundancyCheckMatlab(SNES snes,const char* func,mxArray* ctx)
1061 {
1062   PetscErrorCode      ierr;
1063   SNESVIMatlabContext *sctx;
1064   SNES_VI             *vi = (SNES_VI*)snes->data;
1065 
1066   PetscFunctionBegin;
1067   /* currently sctx is memory bleed */
1068   ierr = PetscMalloc(sizeof(SNESVIMatlabContext),&sctx);CHKERRQ(ierr);
1069   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
1070 
1071   sctx->ctx = mxDuplicateArray(ctx);
1072   vi->checkredundancy = SNESVIRedundancyCheck_Matlab;
1073   PetscFunctionReturn(0);
1074 }
1075 
1076 #endif
1077 
1078 
1079 /* Variational Inequality solver using augmented space method. It does the opposite of the
1080    reduced space method i.e. it identifies the active set variables and instead of discarding
1081    them it augments the original system by introducing additional equality
1082    constraint equations for active set variables. The user can optionally provide an IS for
1083    a subset of 'redundant' active set variables which will treated as free variables.
1084    Specific implementation for Allen-Cahn problem
1085 */
1086 #undef __FUNCT__
1087 #define __FUNCT__ "SNESSolveVI_RS2"
1088 PetscErrorCode SNESSolveVI_RS2(SNES snes)
1089 {
1090   SNES_VI          *vi = (SNES_VI*)snes->data;
1091   PetscErrorCode    ierr;
1092   PetscInt          maxits,i,lits;
1093   PetscBool         lssucceed;
1094   MatStructure      flg = DIFFERENT_NONZERO_PATTERN;
1095   PetscReal         fnorm,gnorm,xnorm=0,ynorm;
1096   Vec                Y,X,F,G,W;
1097   KSPConvergedReason kspreason;
1098 
1099   PetscFunctionBegin;
1100   snes->numFailures            = 0;
1101   snes->numLinearSolveFailures = 0;
1102   snes->reason                 = SNES_CONVERGED_ITERATING;
1103 
1104   maxits	= snes->max_its;	/* maximum number of iterations */
1105   X		= snes->vec_sol;	/* solution vector */
1106   F		= snes->vec_func;	/* residual vector */
1107   Y		= snes->work[0];	/* work vectors */
1108   G		= snes->work[1];
1109   W		= snes->work[2];
1110 
1111   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1112   snes->iter = 0;
1113   snes->norm = 0.0;
1114   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1115 
1116   ierr = SNESVIProjectOntoBounds(snes,X);CHKERRQ(ierr);
1117   ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);
1118   if (snes->domainerror) {
1119     snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
1120     PetscFunctionReturn(0);
1121   }
1122   ierr = SNESVIComputeInactiveSetFnorm(snes,F,X,&fnorm);CHKERRQ(ierr);
1123   ierr = VecNormBegin(X,NORM_2,&xnorm);CHKERRQ(ierr);	/* xnorm <- ||x||  */
1124   ierr = VecNormEnd(X,NORM_2,&xnorm);CHKERRQ(ierr);
1125   if (PetscIsInfOrNanReal(fnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1126 
1127   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1128   snes->norm = fnorm;
1129   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1130   SNESLogConvHistory(snes,fnorm,0);
1131   SNESMonitor(snes,0,fnorm);
1132 
1133   /* set parameter for default relative tolerance convergence test */
1134   snes->ttol = fnorm*snes->rtol;
1135   /* test convergence */
1136   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
1137   if (snes->reason) PetscFunctionReturn(0);
1138 
1139   for (i=0; i<maxits; i++) {
1140     IS             IS_act,IS_inact; /* _act -> active set _inact -> inactive set */
1141     IS             IS_redact=PETSC_NULL; /* redundant active set */
1142     Mat            J_aug,Jpre_aug;
1143     Vec            F_aug,Y_aug;
1144     PetscInt       nis_redact,nis_act;
1145     const PetscInt *idx_redact,*idx_act;
1146     PetscInt       k;
1147     PetscInt       *idx_actkept=PETSC_NULL,nkept=0; /* list of kept active set */
1148     PetscScalar    *f,*f2;
1149     PetscBool      isequal;
1150     PetscInt       i1=0,j1=0;
1151 
1152     /* Call general purpose update function */
1153     if (snes->ops->update) {
1154       ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
1155     }
1156     ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr);
1157 
1158     /* Create active and inactive index sets */
1159     ierr = SNESVICreateIndexSets_RS(snes,X,F,&IS_act,&IS_inact);CHKERRQ(ierr);
1160 
1161     /* Get local active set size */
1162     ierr = ISGetLocalSize(IS_act,&nis_act);CHKERRQ(ierr);
1163     ierr = ISGetIndices(IS_act,&idx_act);CHKERRQ(ierr);
1164     if(nis_act) {
1165       if(vi->checkredundancy) {
1166 	(*vi->checkredundancy)(snes,IS_act,&IS_redact,snes->funP);
1167       }
1168 
1169       if(!IS_redact) {
1170 	/* User called checkredundancy function but didn't create IS_redact because
1171            there were no redundant active set variables */
1172 	/* Copy over all active set indices to the list */
1173 	ierr = PetscMalloc(nis_act*sizeof(PetscInt),&idx_actkept);CHKERRQ(ierr);
1174 	for(k=0;k < nis_act;k++) idx_actkept[k] = idx_act[k];
1175 	nkept = nis_act;
1176       } else {
1177 	ierr = ISGetLocalSize(IS_redact,&nis_redact);CHKERRQ(ierr);
1178 	ierr = PetscMalloc((nis_act-nis_redact)*sizeof(PetscInt),&idx_actkept);CHKERRQ(ierr);
1179 
1180 	/* Create reduced active set list */
1181 	ierr = ISGetIndices(IS_act,&idx_act);CHKERRQ(ierr);
1182 	ierr = ISGetIndices(IS_redact,&idx_redact);CHKERRQ(ierr);
1183 	j1 = 0;
1184 	for(k=0;k<nis_act;k++) {
1185 	  if(j1 < nis_redact && idx_act[k] == idx_redact[j1]) j1++;
1186 	  else idx_actkept[nkept++] = idx_act[k];
1187 	}
1188 	ierr = ISRestoreIndices(IS_act,&idx_act);CHKERRQ(ierr);
1189 	ierr = ISRestoreIndices(IS_redact,&idx_redact);CHKERRQ(ierr);
1190       }
1191 
1192       /* Create augmented F and Y */
1193       ierr = VecCreate(((PetscObject)snes)->comm,&F_aug);CHKERRQ(ierr);
1194       ierr = VecSetSizes(F_aug,F->map->n+nkept,PETSC_DECIDE);CHKERRQ(ierr);
1195       ierr = VecSetFromOptions(F_aug);CHKERRQ(ierr);
1196       ierr = VecDuplicate(F_aug,&Y_aug);CHKERRQ(ierr);
1197 
1198       /* Copy over F to F_aug in the first n locations */
1199       ierr = VecGetArray(F,&f);CHKERRQ(ierr);
1200       ierr = VecGetArray(F_aug,&f2);CHKERRQ(ierr);
1201       ierr = PetscMemcpy(f2,f,F->map->n*sizeof(PetscScalar));CHKERRQ(ierr);
1202       ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
1203       ierr = VecRestoreArray(F_aug,&f2);CHKERRQ(ierr);
1204 
1205       /* Create the augmented jacobian matrix */
1206       ierr = MatCreate(((PetscObject)snes)->comm,&J_aug);CHKERRQ(ierr);
1207       ierr = MatSetSizes(J_aug,X->map->n+nkept,X->map->n+nkept,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
1208       ierr = MatSetFromOptions(J_aug);CHKERRQ(ierr);
1209 
1210 
1211       /* Preallocate augmented matrix and set values in it...Doing only sequential case first*/
1212       PetscInt          ncols;
1213       const PetscInt    *cols;
1214       const PetscScalar *vals;
1215       PetscScalar        value=1.0;
1216       PetscInt           row,col;
1217       PetscInt           *d_nnz;
1218 
1219       ierr = PetscMalloc((X->map->n+nkept)*sizeof(PetscInt),&d_nnz);CHKERRQ(ierr);
1220       ierr = PetscMemzero(d_nnz,(X->map->n+nkept)*sizeof(PetscInt));CHKERRQ(ierr);
1221       for(row=0;row<snes->jacobian->rmap->n;row++) {
1222         ierr = MatGetRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1223         d_nnz[row] += ncols;
1224         ierr = MatRestoreRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1225       }
1226 
1227       for(k=0;k<nkept;k++) {
1228         d_nnz[idx_actkept[k]] += 1;
1229         d_nnz[snes->jacobian->rmap->n+k] += 1;
1230       }
1231       ierr = MatSeqAIJSetPreallocation(J_aug,PETSC_NULL,d_nnz);CHKERRQ(ierr);
1232 
1233       ierr = PetscFree(d_nnz);CHKERRQ(ierr);
1234 
1235       /* Set the original jacobian matrix in J_aug */
1236       for(row=0;row<snes->jacobian->rmap->n;row++) {
1237 	ierr = MatGetRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1238 	ierr = MatSetValues(J_aug,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
1239 	ierr = MatRestoreRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1240       }
1241       /* Add the augmented part */
1242       for(k=0;k<nkept;k++) {
1243 	row = idx_actkept[k];
1244 	col = snes->jacobian->rmap->n+k;
1245 	ierr = MatSetValues(J_aug,1,&row,1,&col,&value,INSERT_VALUES);CHKERRQ(ierr);
1246 	ierr = MatSetValues(J_aug,1,&col,1,&row,&value,INSERT_VALUES);CHKERRQ(ierr);
1247       }
1248       ierr = MatAssemblyBegin(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1249       ierr = MatAssemblyEnd(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1250       /* Only considering prejac = jac for now */
1251       Jpre_aug = J_aug;
1252 
1253     } else {
1254       F_aug = F; J_aug = snes->jacobian; Y_aug = Y; Jpre_aug = snes->jacobian_pre;
1255     }
1256 
1257     ierr = ISEqual(vi->IS_inact_prev,IS_inact,&isequal);CHKERRQ(ierr);
1258     if (!isequal) {
1259       ierr = SNESVIResetPCandKSP(snes,J_aug,Jpre_aug);CHKERRQ(ierr);
1260     }
1261     ierr = KSPSetOperators(snes->ksp,J_aug,Jpre_aug,flg);CHKERRQ(ierr);
1262     ierr = KSPSetUp(snes->ksp);CHKERRQ(ierr);
1263     /*  {
1264       PC        pc;
1265       PetscBool flg;
1266       ierr = KSPGetPC(snes->ksp,&pc);CHKERRQ(ierr);
1267       ierr = PetscTypeCompare((PetscObject)pc,PCFIELDSPLIT,&flg);CHKERRQ(ierr);
1268       if (flg) {
1269         KSP      *subksps;
1270         ierr = PCFieldSplitGetSubKSP(pc,PETSC_NULL,&subksps);CHKERRQ(ierr);
1271         ierr = KSPGetPC(subksps[0],&pc);CHKERRQ(ierr);
1272         ierr = PetscFree(subksps);CHKERRQ(ierr);
1273         ierr = PetscTypeCompare((PetscObject)pc,PCBJACOBI,&flg);CHKERRQ(ierr);
1274         if (flg) {
1275           PetscInt       n,N = 101*101,j,cnts[3] = {0,0,0};
1276           const PetscInt *ii;
1277 
1278           ierr = ISGetSize(IS_inact,&n);CHKERRQ(ierr);
1279           ierr = ISGetIndices(IS_inact,&ii);CHKERRQ(ierr);
1280           for (j=0; j<n; j++) {
1281             if (ii[j] < N) cnts[0]++;
1282             else if (ii[j] < 2*N) cnts[1]++;
1283             else if (ii[j] < 3*N) cnts[2]++;
1284           }
1285           ierr = ISRestoreIndices(IS_inact,&ii);CHKERRQ(ierr);
1286 
1287           ierr = PCBJacobiSetTotalBlocks(pc,3,cnts);CHKERRQ(ierr);
1288         }
1289       }
1290     }
1291     */
1292     ierr = SNES_KSPSolve(snes,snes->ksp,F_aug,Y_aug);CHKERRQ(ierr);
1293     ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr);
1294     if (kspreason < 0) {
1295       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
1296         ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr);
1297         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
1298         break;
1299       }
1300     }
1301 
1302     if(nis_act) {
1303       PetscScalar *y1,*y2;
1304       ierr = VecGetArray(Y,&y1);CHKERRQ(ierr);
1305       ierr = VecGetArray(Y_aug,&y2);CHKERRQ(ierr);
1306       /* Copy over inactive Y_aug to Y */
1307       j1 = 0;
1308       for(i1=Y->map->rstart;i1 < Y->map->rend;i1++) {
1309 	if(j1 < nkept && idx_actkept[j1] == i1) j1++;
1310 	else y1[i1-Y->map->rstart] = y2[i1-Y->map->rstart];
1311       }
1312       ierr = VecRestoreArray(Y,&y1);CHKERRQ(ierr);
1313       ierr = VecRestoreArray(Y_aug,&y2);CHKERRQ(ierr);
1314 
1315       ierr = VecDestroy(F_aug);CHKERRQ(ierr);
1316       ierr = VecDestroy(Y_aug);CHKERRQ(ierr);
1317       ierr = MatDestroy(J_aug);CHKERRQ(ierr);
1318       ierr = PetscFree(idx_actkept);CHKERRQ(ierr);
1319     }
1320 
1321     if (!isequal) {
1322       ierr = ISDestroy(vi->IS_inact_prev);CHKERRQ(ierr);
1323       ierr = ISDuplicate(IS_inact,&vi->IS_inact_prev);CHKERRQ(ierr);
1324     }
1325     ierr = ISDestroy(IS_inact);CHKERRQ(ierr);
1326 
1327     ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr);
1328     snes->linear_its += lits;
1329     ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr);
1330     /*
1331     if (vi->precheckstep) {
1332       PetscBool changed_y = PETSC_FALSE;
1333       ierr = (*vi->precheckstep)(snes,X,Y,vi->precheck,&changed_y);CHKERRQ(ierr);
1334     }
1335 
1336     if (PetscLogPrintInfo){
1337       ierr = SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr);
1338     }
1339     */
1340     /* Compute a (scaled) negative update in the line search routine:
1341          Y <- X - lambda*Y
1342        and evaluate G = function(Y) (depends on the line search).
1343     */
1344     ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr);
1345     ynorm = 1; gnorm = fnorm;
1346     ierr = (*vi->LineSearch)(snes,vi->lsP,X,F,G,Y,W,fnorm,xnorm,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
1347     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",fnorm,gnorm,ynorm,(int)lssucceed);CHKERRQ(ierr);
1348     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
1349     if (snes->domainerror) {
1350       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
1351       PetscFunctionReturn(0);
1352     }
1353     if (!lssucceed) {
1354       if (++snes->numFailures >= snes->maxFailures) {
1355 	PetscBool ismin;
1356         snes->reason = SNES_DIVERGED_LINE_SEARCH;
1357         ierr = SNESVICheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr);
1358         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
1359         break;
1360       }
1361     }
1362     /* Update function and solution vectors */
1363     fnorm = gnorm;
1364     ierr = VecCopy(G,F);CHKERRQ(ierr);
1365     ierr = VecCopy(W,X);CHKERRQ(ierr);
1366     /* Monitor convergence */
1367     ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1368     snes->iter = i+1;
1369     snes->norm = fnorm;
1370     ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1371     SNESLogConvHistory(snes,snes->norm,lits);
1372     SNESMonitor(snes,snes->iter,snes->norm);
1373     /* Test for convergence, xnorm = || X || */
1374     if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); }
1375     ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
1376     if (snes->reason) break;
1377   }
1378   if (i == maxits) {
1379     ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr);
1380     if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
1381   }
1382   PetscFunctionReturn(0);
1383 }
1384 
1385 /* -------------------------------------------------------------------------- */
1386 /*
1387    SNESSetUp_VI - Sets up the internal data structures for the later use
1388    of the SNESVI nonlinear solver.
1389 
1390    Input Parameter:
1391 .  snes - the SNES context
1392 .  x - the solution vector
1393 
1394    Application Interface Routine: SNESSetUp()
1395 
1396    Notes:
1397    For basic use of the SNES solvers, the user need not explicitly call
1398    SNESSetUp(), since these actions will automatically occur during
1399    the call to SNESSolve().
1400  */
1401 #undef __FUNCT__
1402 #define __FUNCT__ "SNESSetUp_VI"
1403 PetscErrorCode SNESSetUp_VI(SNES snes)
1404 {
1405   PetscErrorCode ierr;
1406   SNES_VI        *vi = (SNES_VI*) snes->data;
1407   PetscInt       i_start[3],i_end[3];
1408 
1409   PetscFunctionBegin;
1410   if (!snes->vec_sol_update) {
1411     ierr = VecDuplicate(snes->vec_sol,&snes->vec_sol_update);CHKERRQ(ierr);
1412     ierr = PetscLogObjectParent(snes,snes->vec_sol_update);CHKERRQ(ierr);
1413   }
1414   if (!snes->work) {
1415     snes->nwork = 3;
1416     ierr = VecDuplicateVecs(snes->vec_sol,snes->nwork,&snes->work);CHKERRQ(ierr);
1417     ierr = PetscLogObjectParents(snes,snes->nwork,snes->work);CHKERRQ(ierr);
1418   }
1419 
1420   /* If the lower and upper bound on variables are not set, set it to
1421      -Inf and Inf */
1422   if (!vi->xl && !vi->xu) {
1423     vi->usersetxbounds = PETSC_FALSE;
1424     ierr = VecDuplicate(snes->vec_sol, &vi->xl); CHKERRQ(ierr);
1425     ierr = VecSet(vi->xl,PETSC_VI_NINF);CHKERRQ(ierr);
1426     ierr = VecDuplicate(snes->vec_sol, &vi->xu); CHKERRQ(ierr);
1427     ierr = VecSet(vi->xu,PETSC_VI_INF);CHKERRQ(ierr);
1428   } else {
1429     /* Check if lower bound, upper bound and solution vector distribution across the processors is identical */
1430     ierr = VecGetOwnershipRange(snes->vec_sol,i_start,i_end);CHKERRQ(ierr);
1431     ierr = VecGetOwnershipRange(vi->xl,i_start+1,i_end+1);CHKERRQ(ierr);
1432     ierr = VecGetOwnershipRange(vi->xu,i_start+2,i_end+2);CHKERRQ(ierr);
1433     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]))
1434       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.");
1435   }
1436   if (snes->ops->solve != SNESSolveVI_SS) {
1437     /* Set up previous active index set for the first snes solve
1438        vi->IS_inact_prev = 0,1,2,....N */
1439     PetscInt *indices;
1440     PetscInt  i,n,rstart,rend;
1441 
1442     ierr = VecGetOwnershipRange(snes->vec_sol,&rstart,&rend);CHKERRQ(ierr);
1443     ierr = VecGetLocalSize(snes->vec_sol,&n);CHKERRQ(ierr);
1444     ierr = PetscMalloc(n*sizeof(PetscInt),&indices);CHKERRQ(ierr);
1445     for(i=0;i < n; i++) indices[i] = rstart + i;
1446     ierr = ISCreateGeneral(((PetscObject)snes)->comm,n,indices,PETSC_OWN_POINTER,&vi->IS_inact_prev);
1447   }
1448 
1449   if (snes->ops->solve == SNESSolveVI_SS) {
1450     ierr = VecDuplicate(snes->vec_sol, &vi->dpsi);CHKERRQ(ierr);
1451     ierr = VecDuplicate(snes->vec_sol, &vi->phi); CHKERRQ(ierr);
1452     ierr = VecDuplicate(snes->vec_sol, &vi->Da); CHKERRQ(ierr);
1453     ierr = VecDuplicate(snes->vec_sol, &vi->Db); CHKERRQ(ierr);
1454     ierr = VecDuplicate(snes->vec_sol, &vi->z);CHKERRQ(ierr);
1455     ierr = VecDuplicate(snes->vec_sol, &vi->t); CHKERRQ(ierr);
1456   }
1457   PetscFunctionReturn(0);
1458 }
1459 /* -------------------------------------------------------------------------- */
1460 /*
1461    SNESDestroy_VI - Destroys the private SNES_VI context that was created
1462    with SNESCreate_VI().
1463 
1464    Input Parameter:
1465 .  snes - the SNES context
1466 
1467    Application Interface Routine: SNESDestroy()
1468  */
1469 #undef __FUNCT__
1470 #define __FUNCT__ "SNESDestroy_VI"
1471 PetscErrorCode SNESDestroy_VI(SNES snes)
1472 {
1473   SNES_VI        *vi = (SNES_VI*) snes->data;
1474   PetscErrorCode ierr;
1475 
1476   PetscFunctionBegin;
1477   if (snes->vec_sol_update) {
1478     ierr = VecDestroy(snes->vec_sol_update);CHKERRQ(ierr);
1479     snes->vec_sol_update = PETSC_NULL;
1480   }
1481   if (snes->work) {
1482     ierr = VecDestroyVecs(snes->nwork,&snes->work);CHKERRQ(ierr);
1483   }
1484   if (snes->ops->solve != SNESSolveVI_SS) {
1485     ierr = ISDestroy(vi->IS_inact_prev);
1486   }
1487 
1488   if (snes->ops->solve == SNESSolveVI_SS) {
1489     /* clear vectors */
1490     ierr = VecDestroy(vi->dpsi);CHKERRQ(ierr);
1491     ierr = VecDestroy(vi->phi); CHKERRQ(ierr);
1492     ierr = VecDestroy(vi->Da); CHKERRQ(ierr);
1493     ierr = VecDestroy(vi->Db); CHKERRQ(ierr);
1494     ierr = VecDestroy(vi->z); CHKERRQ(ierr);
1495     ierr = VecDestroy(vi->t); CHKERRQ(ierr);
1496   }
1497 
1498   if (!vi->usersetxbounds) {
1499     ierr = VecDestroy(vi->xl); CHKERRQ(ierr);
1500     ierr = VecDestroy(vi->xu); CHKERRQ(ierr);
1501   }
1502 
1503   if (vi->lsmonitor) {
1504     ierr = PetscViewerASCIIMonitorDestroy(vi->lsmonitor);CHKERRQ(ierr);
1505   }
1506   ierr = PetscFree(snes->data);CHKERRQ(ierr);
1507 
1508   /* clear composed functions */
1509   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","",PETSC_NULL);CHKERRQ(ierr);
1510   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","",PETSC_NULL);CHKERRQ(ierr);
1511   PetscFunctionReturn(0);
1512 }
1513 
1514 /* -------------------------------------------------------------------------- */
1515 #undef __FUNCT__
1516 #define __FUNCT__ "SNESLineSearchNo_VI"
1517 
1518 /*
1519   This routine does not actually do a line search but it takes a full newton
1520   step while ensuring that the new iterates remain within the constraints.
1521 
1522 */
1523 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)
1524 {
1525   PetscErrorCode ierr;
1526   SNES_VI        *vi = (SNES_VI*)snes->data;
1527   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1528 
1529   PetscFunctionBegin;
1530   *flag = PETSC_TRUE;
1531   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1532   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);         /* ynorm = || y || */
1533   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1534   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1535   if (vi->postcheckstep) {
1536    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1537   }
1538   if (changed_y) {
1539     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1540     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1541   }
1542   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1543   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1544   if (!snes->domainerror) {
1545     if (snes->ops->solve != SNESSolveVI_SS) {
1546        ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1547     } else {
1548       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);  /* gnorm = || g || */
1549     }
1550     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1551   }
1552   if (vi->lsmonitor) {
1553     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1554   }
1555   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1556   PetscFunctionReturn(0);
1557 }
1558 
1559 /* -------------------------------------------------------------------------- */
1560 #undef __FUNCT__
1561 #define __FUNCT__ "SNESLineSearchNoNorms_VI"
1562 
1563 /*
1564   This routine is a copy of SNESLineSearchNoNorms in snes/impls/ls/ls.c
1565 */
1566 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)
1567 {
1568   PetscErrorCode ierr;
1569   SNES_VI        *vi = (SNES_VI*)snes->data;
1570   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1571 
1572   PetscFunctionBegin;
1573   *flag = PETSC_TRUE;
1574   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1575   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y      */
1576   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1577   if (vi->postcheckstep) {
1578    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1579   }
1580   if (changed_y) {
1581     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1582     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1583   }
1584 
1585   /* don't evaluate function the last time through */
1586   if (snes->iter < snes->max_its-1) {
1587     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1588   }
1589   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1590   PetscFunctionReturn(0);
1591 }
1592 
1593 /* -------------------------------------------------------------------------- */
1594 #undef __FUNCT__
1595 #define __FUNCT__ "SNESLineSearchCubic_VI"
1596 /*
1597   This routine implements a cubic line search while doing a projection on the variable bounds
1598 */
1599 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)
1600 {
1601   PetscReal      initslope,lambdaprev,gnormprev,a,b,d,t1,t2,rellength;
1602   PetscReal      minlambda,lambda,lambdatemp;
1603 #if defined(PETSC_USE_COMPLEX)
1604   PetscScalar    cinitslope;
1605 #endif
1606   PetscErrorCode ierr;
1607   PetscInt       count;
1608   SNES_VI        *vi = (SNES_VI*)snes->data;
1609   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1610   MPI_Comm       comm;
1611 
1612   PetscFunctionBegin;
1613   ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr);
1614   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1615   *flag   = PETSC_TRUE;
1616 
1617   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1618   if (*ynorm == 0.0) {
1619     if (vi->lsmonitor) {
1620       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Initial direction and size is 0\n");CHKERRQ(ierr);
1621     }
1622     *gnorm = fnorm;
1623     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1624     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1625     *flag  = PETSC_FALSE;
1626     goto theend1;
1627   }
1628   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1629     if (vi->lsmonitor) {
1630       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Scaling step by %G old ynorm %G\n",vi->maxstep/(*ynorm),*ynorm);CHKERRQ(ierr);
1631     }
1632     ierr = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1633     *ynorm = vi->maxstep;
1634   }
1635   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1636   minlambda = vi->minlambda/rellength;
1637   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1638 #if defined(PETSC_USE_COMPLEX)
1639   ierr = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1640   initslope = PetscRealPart(cinitslope);
1641 #else
1642   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1643 #endif
1644   if (initslope > 0.0)  initslope = -initslope;
1645   if (initslope == 0.0) initslope = -1.0;
1646 
1647   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1648   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1649   if (snes->nfuncs >= snes->max_funcs) {
1650     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1651     *flag = PETSC_FALSE;
1652     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1653     goto theend1;
1654   }
1655   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1656   if (snes->ops->solve != SNESSolveVI_SS) {
1657     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1658   } else {
1659     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1660   }
1661   if (snes->domainerror) {
1662     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1663     PetscFunctionReturn(0);
1664   }
1665   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1666   ierr = PetscInfo2(snes,"Initial fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1667   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1668     if (vi->lsmonitor) {
1669       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1670     }
1671     goto theend1;
1672   }
1673 
1674   /* Fit points with quadratic */
1675   lambda     = 1.0;
1676   lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1677   lambdaprev = lambda;
1678   gnormprev  = *gnorm;
1679   if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1680   if (lambdatemp <= .1*lambda) lambda = .1*lambda;
1681   else                         lambda = lambdatemp;
1682 
1683   ierr  = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1684   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1685   if (snes->nfuncs >= snes->max_funcs) {
1686     ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while attempting quadratic backtracking! %D \n",snes->nfuncs);CHKERRQ(ierr);
1687     *flag = PETSC_FALSE;
1688     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1689     goto theend1;
1690   }
1691   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1692   if (snes->ops->solve != SNESSolveVI_SS) {
1693     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1694   } else {
1695     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1696   }
1697   if (snes->domainerror) {
1698     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1699     PetscFunctionReturn(0);
1700   }
1701   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1702   if (vi->lsmonitor) {
1703     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: gnorm after quadratic fit %G\n",*gnorm);CHKERRQ(ierr);
1704   }
1705   if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1706     if (vi->lsmonitor) {
1707       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Quadratically determined step, lambda=%18.16e\n",lambda);CHKERRQ(ierr);
1708     }
1709     goto theend1;
1710   }
1711 
1712   /* Fit points with cubic */
1713   count = 1;
1714   while (PETSC_TRUE) {
1715     if (lambda <= minlambda) {
1716       if (vi->lsmonitor) {
1717 	ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: unable to find good step length! After %D tries \n",count);CHKERRQ(ierr);
1718 	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);
1719       }
1720       *flag = PETSC_FALSE;
1721       break;
1722     }
1723     t1 = .5*((*gnorm)*(*gnorm) - fnorm*fnorm) - lambda*initslope;
1724     t2 = .5*(gnormprev*gnormprev  - fnorm*fnorm) - lambdaprev*initslope;
1725     a  = (t1/(lambda*lambda) - t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1726     b  = (-lambdaprev*t1/(lambda*lambda) + lambda*t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1727     d  = b*b - 3*a*initslope;
1728     if (d < 0.0) d = 0.0;
1729     if (a == 0.0) {
1730       lambdatemp = -initslope/(2.0*b);
1731     } else {
1732       lambdatemp = (-b + sqrt(d))/(3.0*a);
1733     }
1734     lambdaprev = lambda;
1735     gnormprev  = *gnorm;
1736     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1737     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1738     else                         lambda     = lambdatemp;
1739     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1740     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1741     if (snes->nfuncs >= snes->max_funcs) {
1742       ierr = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1743       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);
1744       *flag = PETSC_FALSE;
1745       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1746       break;
1747     }
1748     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1749     if (snes->ops->solve != SNESSolveVI_SS) {
1750       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1751     } else {
1752       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1753     }
1754     if (snes->domainerror) {
1755       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1756       PetscFunctionReturn(0);
1757     }
1758     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1759     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* is reduction enough? */
1760       if (vi->lsmonitor) {
1761 	ierr = PetscPrintf(comm,"    Line search: Cubically determined step, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1762       }
1763       break;
1764     } else {
1765       if (vi->lsmonitor) {
1766         ierr = PetscPrintf(comm,"    Line search: Cubic step no good, shrinking lambda, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1767       }
1768     }
1769     count++;
1770   }
1771   theend1:
1772   /* Optional user-defined check for line search step validity */
1773   if (vi->postcheckstep && *flag) {
1774     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1775     if (changed_y) {
1776       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1777       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1778     }
1779     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1780       ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1781       if (snes->ops->solve != SNESSolveVI_SS) {
1782         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1783       } else {
1784         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1785       }
1786       if (snes->domainerror) {
1787         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1788         PetscFunctionReturn(0);
1789       }
1790       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1791       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1792       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1793     }
1794   }
1795   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1796   PetscFunctionReturn(0);
1797 }
1798 
1799 #undef __FUNCT__
1800 #define __FUNCT__ "SNESLineSearchQuadratic_VI"
1801 /*
1802   This routine does a quadratic line search while keeping the iterates within the variable bounds
1803 */
1804 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)
1805 {
1806   /*
1807      Note that for line search purposes we work with with the related
1808      minimization problem:
1809         min  z(x):  R^n -> R,
1810      where z(x) = .5 * fnorm*fnorm,and fnorm = || f ||_2.
1811    */
1812   PetscReal      initslope,minlambda,lambda,lambdatemp,rellength;
1813 #if defined(PETSC_USE_COMPLEX)
1814   PetscScalar    cinitslope;
1815 #endif
1816   PetscErrorCode ierr;
1817   PetscInt       count;
1818   SNES_VI        *vi = (SNES_VI*)snes->data;
1819   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1820 
1821   PetscFunctionBegin;
1822   ierr    = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1823   *flag   = PETSC_TRUE;
1824 
1825   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1826   if (*ynorm == 0.0) {
1827     if (vi->lsmonitor) {
1828       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Direction and size is 0\n");CHKERRQ(ierr);
1829     }
1830     *gnorm = fnorm;
1831     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1832     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1833     *flag  = PETSC_FALSE;
1834     goto theend2;
1835   }
1836   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1837     ierr   = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1838     *ynorm = vi->maxstep;
1839   }
1840   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1841   minlambda = vi->minlambda/rellength;
1842   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1843 #if defined(PETSC_USE_COMPLEX)
1844   ierr      = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1845   initslope = PetscRealPart(cinitslope);
1846 #else
1847   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1848 #endif
1849   if (initslope > 0.0)  initslope = -initslope;
1850   if (initslope == 0.0) initslope = -1.0;
1851   ierr = PetscInfo1(snes,"Initslope %G \n",initslope);CHKERRQ(ierr);
1852 
1853   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1854   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1855   if (snes->nfuncs >= snes->max_funcs) {
1856     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1857     *flag = PETSC_FALSE;
1858     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1859     goto theend2;
1860   }
1861   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1862   if (snes->ops->solve != SNESSolveVI_SS) {
1863     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1864   } else {
1865     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1866   }
1867   if (snes->domainerror) {
1868     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1869     PetscFunctionReturn(0);
1870   }
1871   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1872   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1873     if (vi->lsmonitor) {
1874       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1875     }
1876     goto theend2;
1877   }
1878 
1879   /* Fit points with quadratic */
1880   lambda = 1.0;
1881   count = 1;
1882   while (PETSC_TRUE) {
1883     if (lambda <= minlambda) { /* bad luck; use full step */
1884       if (vi->lsmonitor) {
1885         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Unable to find good step length! %D \n",count);CHKERRQ(ierr);
1886         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);
1887       }
1888       ierr = VecCopy(x,w);CHKERRQ(ierr);
1889       *flag = PETSC_FALSE;
1890       break;
1891     }
1892     lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1893     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1894     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1895     else                         lambda     = lambdatemp;
1896 
1897     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1898     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1899     if (snes->nfuncs >= snes->max_funcs) {
1900       ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1901       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);
1902       *flag = PETSC_FALSE;
1903       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1904       break;
1905     }
1906     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1907     if (snes->domainerror) {
1908       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1909       PetscFunctionReturn(0);
1910     }
1911     if (snes->ops->solve != SNESSolveVI_SS) {
1912       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1913     } else {
1914       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1915     }
1916     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1917     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1918       if (vi->lsmonitor) {
1919         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line Search: Quadratically determined step, lambda=%G\n",lambda);CHKERRQ(ierr);
1920       }
1921       break;
1922     }
1923     count++;
1924   }
1925   theend2:
1926   /* Optional user-defined check for line search step validity */
1927   if (vi->postcheckstep) {
1928     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1929     if (changed_y) {
1930       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1931       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1932     }
1933     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1934       ierr = SNESComputeFunction(snes,w,g);
1935       if (snes->domainerror) {
1936         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1937         PetscFunctionReturn(0);
1938       }
1939       if (snes->ops->solve != SNESSolveVI_SS) {
1940         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1941       } else {
1942         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1943       }
1944 
1945       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1946       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1947       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1948     }
1949   }
1950   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1951   PetscFunctionReturn(0);
1952 }
1953 
1954 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*/
1955 /* -------------------------------------------------------------------------- */
1956 EXTERN_C_BEGIN
1957 #undef __FUNCT__
1958 #define __FUNCT__ "SNESLineSearchSet_VI"
1959 PetscErrorCode  SNESLineSearchSet_VI(SNES snes,FCN2 func,void *lsctx)
1960 {
1961   PetscFunctionBegin;
1962   ((SNES_VI *)(snes->data))->LineSearch = func;
1963   ((SNES_VI *)(snes->data))->lsP        = lsctx;
1964   PetscFunctionReturn(0);
1965 }
1966 EXTERN_C_END
1967 
1968 /* -------------------------------------------------------------------------- */
1969 EXTERN_C_BEGIN
1970 #undef __FUNCT__
1971 #define __FUNCT__ "SNESLineSearchSetMonitor_VI"
1972 PetscErrorCode  SNESLineSearchSetMonitor_VI(SNES snes,PetscBool flg)
1973 {
1974   SNES_VI        *vi = (SNES_VI*)snes->data;
1975   PetscErrorCode ierr;
1976 
1977   PetscFunctionBegin;
1978   if (flg && !vi->lsmonitor) {
1979     ierr = PetscViewerASCIIMonitorCreate(((PetscObject)snes)->comm,"stdout",((PetscObject)snes)->tablevel,&vi->lsmonitor);CHKERRQ(ierr);
1980   } else if (!flg && vi->lsmonitor) {
1981     ierr = PetscViewerASCIIMonitorDestroy(vi->lsmonitor);CHKERRQ(ierr);
1982   }
1983   PetscFunctionReturn(0);
1984 }
1985 EXTERN_C_END
1986 
1987 /*
1988    SNESView_VI - Prints info from the SNESVI data structure.
1989 
1990    Input Parameters:
1991 .  SNES - the SNES context
1992 .  viewer - visualization context
1993 
1994    Application Interface Routine: SNESView()
1995 */
1996 #undef __FUNCT__
1997 #define __FUNCT__ "SNESView_VI"
1998 static PetscErrorCode SNESView_VI(SNES snes,PetscViewer viewer)
1999 {
2000   SNES_VI        *vi = (SNES_VI *)snes->data;
2001   const char     *cstr,*tstr;
2002   PetscErrorCode ierr;
2003   PetscBool     iascii;
2004 
2005   PetscFunctionBegin;
2006   ierr = PetscTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
2007   if (iascii) {
2008     if (vi->LineSearch == SNESLineSearchNo_VI)             cstr = "SNESLineSearchNo";
2009     else if (vi->LineSearch == SNESLineSearchQuadratic_VI) cstr = "SNESLineSearchQuadratic";
2010     else if (vi->LineSearch == SNESLineSearchCubic_VI)     cstr = "SNESLineSearchCubic";
2011     else                                                             cstr = "unknown";
2012     if (snes->ops->solve == SNESSolveVI_SS)      tstr = "Semismooth";
2013     else if (snes->ops->solve == SNESSolveVI_RS) tstr = "Reduced Space";
2014     else if (snes->ops->solve == SNESSolveVI_RS2) tstr = "Augmented Space";
2015     else                                         tstr = "unknown";
2016     ierr = PetscViewerASCIIPrintf(viewer,"  VI algorithm: %s\n",tstr);CHKERRQ(ierr);
2017     ierr = PetscViewerASCIIPrintf(viewer,"  line search variant: %s\n",cstr);CHKERRQ(ierr);
2018     ierr = PetscViewerASCIIPrintf(viewer,"  alpha=%G, maxstep=%G, minlambda=%G\n",vi->alpha,vi->maxstep,vi->minlambda);CHKERRQ(ierr);
2019   } else {
2020     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Viewer type %s not supported for SNES EQ VI",((PetscObject)viewer)->type_name);
2021   }
2022   PetscFunctionReturn(0);
2023 }
2024 
2025 #undef __FUNCT__
2026 #define __FUNCT__ "SNESVISetVariableBounds"
2027 /*@
2028    SNESVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu.
2029 
2030    Input Parameters:
2031 .  snes - the SNES context.
2032 .  xl   - lower bound.
2033 .  xu   - upper bound.
2034 
2035    Notes:
2036    If this routine is not called then the lower and upper bounds are set to
2037    PETSC_VI_INF and PETSC_VI_NINF respectively during SNESSetUp().
2038 
2039 @*/
2040 PetscErrorCode SNESVISetVariableBounds(SNES snes, Vec xl, Vec xu)
2041 {
2042   SNES_VI  *vi = (SNES_VI*)snes->data;
2043 
2044   PetscFunctionBegin;
2045   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
2046   PetscValidHeaderSpecific(xl,VEC_CLASSID,2);
2047   PetscValidHeaderSpecific(xu,VEC_CLASSID,3);
2048   if (!snes->vec_func) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call SNESSetFunction() first");
2049   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);
2050   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);
2051 
2052   vi->usersetxbounds = PETSC_TRUE;
2053   vi->xl = xl;
2054   vi->xu = xu;
2055   PetscFunctionReturn(0);
2056 }
2057 
2058 /* -------------------------------------------------------------------------- */
2059 /*
2060    SNESSetFromOptions_VI - Sets various parameters for the SNESVI method.
2061 
2062    Input Parameter:
2063 .  snes - the SNES context
2064 
2065    Application Interface Routine: SNESSetFromOptions()
2066 */
2067 #undef __FUNCT__
2068 #define __FUNCT__ "SNESSetFromOptions_VI"
2069 static PetscErrorCode SNESSetFromOptions_VI(SNES snes)
2070 {
2071   SNES_VI        *vi = (SNES_VI *)snes->data;
2072   const char     *lses[] = {"basic","basicnonorms","quadratic","cubic"};
2073   const char     *vies[] = {"ss","rs","rs2"};
2074   PetscErrorCode ierr;
2075   PetscInt       indx;
2076   PetscBool      flg,set,flg2;
2077 
2078   PetscFunctionBegin;
2079   ierr = PetscOptionsHead("SNES semismooth method options");CHKERRQ(ierr);
2080   ierr = PetscOptionsBool("-snes_vi_monitor","Monitor all non-active variables","None",PETSC_FALSE,&flg,0);CHKERRQ(ierr);
2081   if (flg) {
2082     ierr = SNESMonitorSet(snes,SNESMonitorVI,0,0);CHKERRQ(ierr);
2083   }
2084   ierr = PetscOptionsReal("-snes_ls_alpha","Function norm must decrease by","None",vi->alpha,&vi->alpha,0);CHKERRQ(ierr);
2085   ierr = PetscOptionsReal("-snes_ls_maxstep","Step must be less than","None",vi->maxstep,&vi->maxstep,0);CHKERRQ(ierr);
2086   ierr = PetscOptionsReal("-snes_ls_minlambda","Minimum lambda allowed","None",vi->minlambda,&vi->minlambda,0);CHKERRQ(ierr);
2087   ierr = PetscOptionsReal("-snes_vi_const_tol","constraint tolerance","None",vi->const_tol,&vi->const_tol,0);CHKERRQ(ierr);
2088   ierr = PetscOptionsBool("-snes_ls_monitor","Print progress of line searches","SNESLineSearchSetMonitor",vi->lsmonitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);CHKERRQ(ierr);
2089   if (set) {ierr = SNESLineSearchSetMonitor(snes,flg);CHKERRQ(ierr);}
2090   ierr = PetscOptionsEList("-snes_vi_type","Semismooth algorithm used","",vies,3,"ss",&indx,&flg2);CHKERRQ(ierr);
2091   if (flg2) {
2092     switch (indx) {
2093     case 0:
2094       snes->ops->solve = SNESSolveVI_SS;
2095       break;
2096     case 1:
2097       snes->ops->solve = SNESSolveVI_RS;
2098       break;
2099     case 2:
2100       snes->ops->solve = SNESSolveVI_RS2;
2101     }
2102   }
2103   ierr = PetscOptionsEList("-snes_ls","Line search used","SNESLineSearchSet",lses,4,"basic",&indx,&flg);CHKERRQ(ierr);
2104   if (flg) {
2105     switch (indx) {
2106     case 0:
2107       ierr = SNESLineSearchSet(snes,SNESLineSearchNo_VI,PETSC_NULL);CHKERRQ(ierr);
2108       break;
2109     case 1:
2110       ierr = SNESLineSearchSet(snes,SNESLineSearchNoNorms_VI,PETSC_NULL);CHKERRQ(ierr);
2111       break;
2112     case 2:
2113       ierr = SNESLineSearchSet(snes,SNESLineSearchQuadratic_VI,PETSC_NULL);CHKERRQ(ierr);
2114       break;
2115     case 3:
2116       ierr = SNESLineSearchSet(snes,SNESLineSearchCubic_VI,PETSC_NULL);CHKERRQ(ierr);
2117       break;
2118     }
2119   }
2120   ierr = PetscOptionsTail();CHKERRQ(ierr);
2121   PetscFunctionReturn(0);
2122 }
2123 /* -------------------------------------------------------------------------- */
2124 /*MC
2125       SNESVI - Semismooth newton method based nonlinear solver that uses a line search
2126 
2127    Options Database:
2128 +   -snes_ls [cubic,quadratic,basic,basicnonorms] - Selects line search
2129 .   -snes_ls_alpha <alpha> - Sets alpha
2130 .   -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)
2131 .   -snes_ls_minlambda <minlambda>  - Sets the minimum lambda the line search will use  minlambda / max_i ( y[i]/x[i] )
2132 -   -snes_ls_monitor - print information about progress of line searches
2133 
2134 
2135    Level: beginner
2136 
2137 .seealso:  SNESCreate(), SNES, SNESSetType(), SNESTR, SNESLineSearchSet(),
2138            SNESLineSearchSetPostCheck(), SNESLineSearchNo(), SNESLineSearchCubic(), SNESLineSearchQuadratic(),
2139            SNESLineSearchSet(), SNESLineSearchNoNorms(), SNESLineSearchSetPreCheck(), SNESLineSearchSetParams(), SNESLineSearchGetParams()
2140 
2141 M*/
2142 EXTERN_C_BEGIN
2143 #undef __FUNCT__
2144 #define __FUNCT__ "SNESCreate_VI"
2145 PetscErrorCode  SNESCreate_VI(SNES snes)
2146 {
2147   PetscErrorCode ierr;
2148   SNES_VI      *vi;
2149 
2150   PetscFunctionBegin;
2151   snes->ops->setup	     = SNESSetUp_VI;
2152   snes->ops->solve	     = SNESSolveVI_SS;
2153   snes->ops->destroy	     = SNESDestroy_VI;
2154   snes->ops->setfromoptions  = SNESSetFromOptions_VI;
2155   snes->ops->view            = SNESView_VI;
2156   snes->ops->converged       = SNESDefaultConverged_VI;
2157 
2158   ierr                   = PetscNewLog(snes,SNES_VI,&vi);CHKERRQ(ierr);
2159   snes->data    	 = (void*)vi;
2160   vi->alpha		 = 1.e-4;
2161   vi->maxstep		 = 1.e8;
2162   vi->minlambda         = 1.e-12;
2163   vi->LineSearch        = SNESLineSearchNo_VI;
2164   vi->lsP               = PETSC_NULL;
2165   vi->postcheckstep     = PETSC_NULL;
2166   vi->postcheck         = PETSC_NULL;
2167   vi->precheckstep      = PETSC_NULL;
2168   vi->precheck          = PETSC_NULL;
2169   vi->const_tol         =  2.2204460492503131e-16;
2170   vi->checkredundancy   = PETSC_NULL;
2171 
2172   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","SNESLineSearchSetMonitor_VI",SNESLineSearchSetMonitor_VI);CHKERRQ(ierr);
2173   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","SNESLineSearchSet_VI",SNESLineSearchSet_VI);CHKERRQ(ierr);
2174 
2175   PetscFunctionReturn(0);
2176 }
2177 EXTERN_C_END
2178