xref: /petsc/src/snes/impls/vi/vi.c (revision 3192c3e1bf96856519ae22ffd756f12fe2bc5489) !
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       { /* local vars */
1212       /* Preallocate augmented matrix and set values in it...Doing only sequential case first*/
1213       PetscInt          ncols;
1214       const PetscInt    *cols;
1215       const PetscScalar *vals;
1216       PetscScalar        value=1.0;
1217       PetscInt           row,col;
1218       PetscInt           *d_nnz;
1219 
1220       ierr = PetscMalloc((X->map->n+nkept)*sizeof(PetscInt),&d_nnz);CHKERRQ(ierr);
1221       ierr = PetscMemzero(d_nnz,(X->map->n+nkept)*sizeof(PetscInt));CHKERRQ(ierr);
1222       for(row=0;row<snes->jacobian->rmap->n;row++) {
1223         ierr = MatGetRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1224         d_nnz[row] += ncols;
1225         ierr = MatRestoreRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1226       }
1227 
1228       for(k=0;k<nkept;k++) {
1229         d_nnz[idx_actkept[k]] += 1;
1230         d_nnz[snes->jacobian->rmap->n+k] += 1;
1231       }
1232       ierr = MatSeqAIJSetPreallocation(J_aug,PETSC_NULL,d_nnz);CHKERRQ(ierr);
1233 
1234       ierr = PetscFree(d_nnz);CHKERRQ(ierr);
1235 
1236       /* Set the original jacobian matrix in J_aug */
1237       for(row=0;row<snes->jacobian->rmap->n;row++) {
1238 	ierr = MatGetRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1239 	ierr = MatSetValues(J_aug,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
1240 	ierr = MatRestoreRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1241       }
1242       /* Add the augmented part */
1243       for(k=0;k<nkept;k++) {
1244 	row = idx_actkept[k];
1245 	col = snes->jacobian->rmap->n+k;
1246 	ierr = MatSetValues(J_aug,1,&row,1,&col,&value,INSERT_VALUES);CHKERRQ(ierr);
1247 	ierr = MatSetValues(J_aug,1,&col,1,&row,&value,INSERT_VALUES);CHKERRQ(ierr);
1248       }
1249       ierr = MatAssemblyBegin(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1250       ierr = MatAssemblyEnd(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1251       /* Only considering prejac = jac for now */
1252       Jpre_aug = J_aug;
1253       } /* local vars*/
1254     } else {
1255       F_aug = F; J_aug = snes->jacobian; Y_aug = Y; Jpre_aug = snes->jacobian_pre;
1256     }
1257 
1258     ierr = ISEqual(vi->IS_inact_prev,IS_inact,&isequal);CHKERRQ(ierr);
1259     if (!isequal) {
1260       ierr = SNESVIResetPCandKSP(snes,J_aug,Jpre_aug);CHKERRQ(ierr);
1261     }
1262     ierr = KSPSetOperators(snes->ksp,J_aug,Jpre_aug,flg);CHKERRQ(ierr);
1263     ierr = KSPSetUp(snes->ksp);CHKERRQ(ierr);
1264     /*  {
1265       PC        pc;
1266       PetscBool flg;
1267       ierr = KSPGetPC(snes->ksp,&pc);CHKERRQ(ierr);
1268       ierr = PetscTypeCompare((PetscObject)pc,PCFIELDSPLIT,&flg);CHKERRQ(ierr);
1269       if (flg) {
1270         KSP      *subksps;
1271         ierr = PCFieldSplitGetSubKSP(pc,PETSC_NULL,&subksps);CHKERRQ(ierr);
1272         ierr = KSPGetPC(subksps[0],&pc);CHKERRQ(ierr);
1273         ierr = PetscFree(subksps);CHKERRQ(ierr);
1274         ierr = PetscTypeCompare((PetscObject)pc,PCBJACOBI,&flg);CHKERRQ(ierr);
1275         if (flg) {
1276           PetscInt       n,N = 101*101,j,cnts[3] = {0,0,0};
1277           const PetscInt *ii;
1278 
1279           ierr = ISGetSize(IS_inact,&n);CHKERRQ(ierr);
1280           ierr = ISGetIndices(IS_inact,&ii);CHKERRQ(ierr);
1281           for (j=0; j<n; j++) {
1282             if (ii[j] < N) cnts[0]++;
1283             else if (ii[j] < 2*N) cnts[1]++;
1284             else if (ii[j] < 3*N) cnts[2]++;
1285           }
1286           ierr = ISRestoreIndices(IS_inact,&ii);CHKERRQ(ierr);
1287 
1288           ierr = PCBJacobiSetTotalBlocks(pc,3,cnts);CHKERRQ(ierr);
1289         }
1290       }
1291     }
1292     */
1293     ierr = SNES_KSPSolve(snes,snes->ksp,F_aug,Y_aug);CHKERRQ(ierr);
1294     ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr);
1295     if (kspreason < 0) {
1296       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
1297         ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr);
1298         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
1299         break;
1300       }
1301     }
1302 
1303     if(nis_act) {
1304       PetscScalar *y1,*y2;
1305       ierr = VecGetArray(Y,&y1);CHKERRQ(ierr);
1306       ierr = VecGetArray(Y_aug,&y2);CHKERRQ(ierr);
1307       /* Copy over inactive Y_aug to Y */
1308       j1 = 0;
1309       for(i1=Y->map->rstart;i1 < Y->map->rend;i1++) {
1310 	if(j1 < nkept && idx_actkept[j1] == i1) j1++;
1311 	else y1[i1-Y->map->rstart] = y2[i1-Y->map->rstart];
1312       }
1313       ierr = VecRestoreArray(Y,&y1);CHKERRQ(ierr);
1314       ierr = VecRestoreArray(Y_aug,&y2);CHKERRQ(ierr);
1315 
1316       ierr = VecDestroy(F_aug);CHKERRQ(ierr);
1317       ierr = VecDestroy(Y_aug);CHKERRQ(ierr);
1318       ierr = MatDestroy(J_aug);CHKERRQ(ierr);
1319       ierr = PetscFree(idx_actkept);CHKERRQ(ierr);
1320     }
1321 
1322     if (!isequal) {
1323       ierr = ISDestroy(vi->IS_inact_prev);CHKERRQ(ierr);
1324       ierr = ISDuplicate(IS_inact,&vi->IS_inact_prev);CHKERRQ(ierr);
1325     }
1326     ierr = ISDestroy(IS_inact);CHKERRQ(ierr);
1327 
1328     ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr);
1329     snes->linear_its += lits;
1330     ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr);
1331     /*
1332     if (vi->precheckstep) {
1333       PetscBool changed_y = PETSC_FALSE;
1334       ierr = (*vi->precheckstep)(snes,X,Y,vi->precheck,&changed_y);CHKERRQ(ierr);
1335     }
1336 
1337     if (PetscLogPrintInfo){
1338       ierr = SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr);
1339     }
1340     */
1341     /* Compute a (scaled) negative update in the line search routine:
1342          Y <- X - lambda*Y
1343        and evaluate G = function(Y) (depends on the line search).
1344     */
1345     ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr);
1346     ynorm = 1; gnorm = fnorm;
1347     ierr = (*vi->LineSearch)(snes,vi->lsP,X,F,G,Y,W,fnorm,xnorm,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
1348     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",fnorm,gnorm,ynorm,(int)lssucceed);CHKERRQ(ierr);
1349     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
1350     if (snes->domainerror) {
1351       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
1352       PetscFunctionReturn(0);
1353     }
1354     if (!lssucceed) {
1355       if (++snes->numFailures >= snes->maxFailures) {
1356 	PetscBool ismin;
1357         snes->reason = SNES_DIVERGED_LINE_SEARCH;
1358         ierr = SNESVICheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr);
1359         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
1360         break;
1361       }
1362     }
1363     /* Update function and solution vectors */
1364     fnorm = gnorm;
1365     ierr = VecCopy(G,F);CHKERRQ(ierr);
1366     ierr = VecCopy(W,X);CHKERRQ(ierr);
1367     /* Monitor convergence */
1368     ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1369     snes->iter = i+1;
1370     snes->norm = fnorm;
1371     ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1372     SNESLogConvHistory(snes,snes->norm,lits);
1373     SNESMonitor(snes,snes->iter,snes->norm);
1374     /* Test for convergence, xnorm = || X || */
1375     if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); }
1376     ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
1377     if (snes->reason) break;
1378   }
1379   if (i == maxits) {
1380     ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr);
1381     if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
1382   }
1383   PetscFunctionReturn(0);
1384 }
1385 
1386 /* -------------------------------------------------------------------------- */
1387 /*
1388    SNESSetUp_VI - Sets up the internal data structures for the later use
1389    of the SNESVI nonlinear solver.
1390 
1391    Input Parameter:
1392 .  snes - the SNES context
1393 .  x - the solution vector
1394 
1395    Application Interface Routine: SNESSetUp()
1396 
1397    Notes:
1398    For basic use of the SNES solvers, the user need not explicitly call
1399    SNESSetUp(), since these actions will automatically occur during
1400    the call to SNESSolve().
1401  */
1402 #undef __FUNCT__
1403 #define __FUNCT__ "SNESSetUp_VI"
1404 PetscErrorCode SNESSetUp_VI(SNES snes)
1405 {
1406   PetscErrorCode ierr;
1407   SNES_VI        *vi = (SNES_VI*) snes->data;
1408   PetscInt       i_start[3],i_end[3];
1409 
1410   PetscFunctionBegin;
1411 
1412   ierr = SNESDefaultGetWork(snes,3);CHKERRQ(ierr);
1413 
1414   /* If the lower and upper bound on variables are not set, set it to
1415      -Inf and Inf */
1416   if (!vi->xl && !vi->xu) {
1417     vi->usersetxbounds = PETSC_FALSE;
1418     ierr = VecDuplicate(snes->vec_sol, &vi->xl); CHKERRQ(ierr);
1419     ierr = VecSet(vi->xl,PETSC_VI_NINF);CHKERRQ(ierr);
1420     ierr = VecDuplicate(snes->vec_sol, &vi->xu); CHKERRQ(ierr);
1421     ierr = VecSet(vi->xu,PETSC_VI_INF);CHKERRQ(ierr);
1422   } else {
1423     /* Check if lower bound, upper bound and solution vector distribution across the processors is identical */
1424     ierr = VecGetOwnershipRange(snes->vec_sol,i_start,i_end);CHKERRQ(ierr);
1425     ierr = VecGetOwnershipRange(vi->xl,i_start+1,i_end+1);CHKERRQ(ierr);
1426     ierr = VecGetOwnershipRange(vi->xu,i_start+2,i_end+2);CHKERRQ(ierr);
1427     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]))
1428       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.");
1429   }
1430   if (snes->ops->solve != SNESSolveVI_SS) {
1431     /* Set up previous active index set for the first snes solve
1432        vi->IS_inact_prev = 0,1,2,....N */
1433     PetscInt *indices;
1434     PetscInt  i,n,rstart,rend;
1435 
1436     ierr = VecGetOwnershipRange(snes->vec_sol,&rstart,&rend);CHKERRQ(ierr);
1437     ierr = VecGetLocalSize(snes->vec_sol,&n);CHKERRQ(ierr);
1438     ierr = PetscMalloc(n*sizeof(PetscInt),&indices);CHKERRQ(ierr);
1439     for(i=0;i < n; i++) indices[i] = rstart + i;
1440     ierr = ISCreateGeneral(((PetscObject)snes)->comm,n,indices,PETSC_OWN_POINTER,&vi->IS_inact_prev);
1441   }
1442 
1443   if (snes->ops->solve == SNESSolveVI_SS) {
1444     ierr = VecDuplicate(snes->vec_sol, &vi->dpsi);CHKERRQ(ierr);
1445     ierr = VecDuplicate(snes->vec_sol, &vi->phi); CHKERRQ(ierr);
1446     ierr = VecDuplicate(snes->vec_sol, &vi->Da); CHKERRQ(ierr);
1447     ierr = VecDuplicate(snes->vec_sol, &vi->Db); CHKERRQ(ierr);
1448     ierr = VecDuplicate(snes->vec_sol, &vi->z);CHKERRQ(ierr);
1449     ierr = VecDuplicate(snes->vec_sol, &vi->t); CHKERRQ(ierr);
1450   }
1451   PetscFunctionReturn(0);
1452 }
1453 /* -------------------------------------------------------------------------- */
1454 /*
1455    SNESDestroy_VI - Destroys the private SNES_VI context that was created
1456    with SNESCreate_VI().
1457 
1458    Input Parameter:
1459 .  snes - the SNES context
1460 
1461    Application Interface Routine: SNESDestroy()
1462  */
1463 #undef __FUNCT__
1464 #define __FUNCT__ "SNESDestroy_VI"
1465 PetscErrorCode SNESDestroy_VI(SNES snes)
1466 {
1467   SNES_VI        *vi = (SNES_VI*) snes->data;
1468   PetscErrorCode ierr;
1469 
1470   PetscFunctionBegin;
1471   if (snes->ops->solve != SNESSolveVI_SS) {
1472     ierr = ISDestroy(vi->IS_inact_prev);
1473   }
1474 
1475   if (snes->ops->solve == SNESSolveVI_SS) {
1476     /* clear vectors */
1477     ierr = VecDestroy(vi->dpsi);CHKERRQ(ierr);
1478     ierr = VecDestroy(vi->phi); CHKERRQ(ierr);
1479     ierr = VecDestroy(vi->Da); CHKERRQ(ierr);
1480     ierr = VecDestroy(vi->Db); CHKERRQ(ierr);
1481     ierr = VecDestroy(vi->z); CHKERRQ(ierr);
1482     ierr = VecDestroy(vi->t); CHKERRQ(ierr);
1483   }
1484 
1485   if (!vi->usersetxbounds) {
1486     ierr = VecDestroy(vi->xl); CHKERRQ(ierr);
1487     ierr = VecDestroy(vi->xu); CHKERRQ(ierr);
1488   }
1489 
1490   if (vi->lsmonitor) {
1491     ierr = PetscViewerASCIIMonitorDestroy(vi->lsmonitor);CHKERRQ(ierr);
1492   }
1493   ierr = PetscFree(snes->data);CHKERRQ(ierr);
1494 
1495   /* clear composed functions */
1496   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","",PETSC_NULL);CHKERRQ(ierr);
1497   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","",PETSC_NULL);CHKERRQ(ierr);
1498   PetscFunctionReturn(0);
1499 }
1500 
1501 /* -------------------------------------------------------------------------- */
1502 #undef __FUNCT__
1503 #define __FUNCT__ "SNESLineSearchNo_VI"
1504 
1505 /*
1506   This routine does not actually do a line search but it takes a full newton
1507   step while ensuring that the new iterates remain within the constraints.
1508 
1509 */
1510 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)
1511 {
1512   PetscErrorCode ierr;
1513   SNES_VI        *vi = (SNES_VI*)snes->data;
1514   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1515 
1516   PetscFunctionBegin;
1517   *flag = PETSC_TRUE;
1518   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1519   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);         /* ynorm = || y || */
1520   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1521   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1522   if (vi->postcheckstep) {
1523    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1524   }
1525   if (changed_y) {
1526     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1527     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1528   }
1529   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1530   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1531   if (!snes->domainerror) {
1532     if (snes->ops->solve != SNESSolveVI_SS) {
1533        ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1534     } else {
1535       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);  /* gnorm = || g || */
1536     }
1537     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1538   }
1539   if (vi->lsmonitor) {
1540     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1541   }
1542   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1543   PetscFunctionReturn(0);
1544 }
1545 
1546 /* -------------------------------------------------------------------------- */
1547 #undef __FUNCT__
1548 #define __FUNCT__ "SNESLineSearchNoNorms_VI"
1549 
1550 /*
1551   This routine is a copy of SNESLineSearchNoNorms in snes/impls/ls/ls.c
1552 */
1553 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)
1554 {
1555   PetscErrorCode ierr;
1556   SNES_VI        *vi = (SNES_VI*)snes->data;
1557   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1558 
1559   PetscFunctionBegin;
1560   *flag = PETSC_TRUE;
1561   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1562   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y      */
1563   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1564   if (vi->postcheckstep) {
1565    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1566   }
1567   if (changed_y) {
1568     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1569     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1570   }
1571 
1572   /* don't evaluate function the last time through */
1573   if (snes->iter < snes->max_its-1) {
1574     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1575   }
1576   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1577   PetscFunctionReturn(0);
1578 }
1579 
1580 /* -------------------------------------------------------------------------- */
1581 #undef __FUNCT__
1582 #define __FUNCT__ "SNESLineSearchCubic_VI"
1583 /*
1584   This routine implements a cubic line search while doing a projection on the variable bounds
1585 */
1586 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)
1587 {
1588   PetscReal      initslope,lambdaprev,gnormprev,a,b,d,t1,t2,rellength;
1589   PetscReal      minlambda,lambda,lambdatemp;
1590 #if defined(PETSC_USE_COMPLEX)
1591   PetscScalar    cinitslope;
1592 #endif
1593   PetscErrorCode ierr;
1594   PetscInt       count;
1595   SNES_VI        *vi = (SNES_VI*)snes->data;
1596   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1597   MPI_Comm       comm;
1598 
1599   PetscFunctionBegin;
1600   ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr);
1601   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1602   *flag   = PETSC_TRUE;
1603 
1604   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1605   if (*ynorm == 0.0) {
1606     if (vi->lsmonitor) {
1607       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Initial direction and size is 0\n");CHKERRQ(ierr);
1608     }
1609     *gnorm = fnorm;
1610     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1611     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1612     *flag  = PETSC_FALSE;
1613     goto theend1;
1614   }
1615   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1616     if (vi->lsmonitor) {
1617       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Scaling step by %G old ynorm %G\n",vi->maxstep/(*ynorm),*ynorm);CHKERRQ(ierr);
1618     }
1619     ierr = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1620     *ynorm = vi->maxstep;
1621   }
1622   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1623   minlambda = vi->minlambda/rellength;
1624   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1625 #if defined(PETSC_USE_COMPLEX)
1626   ierr = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1627   initslope = PetscRealPart(cinitslope);
1628 #else
1629   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1630 #endif
1631   if (initslope > 0.0)  initslope = -initslope;
1632   if (initslope == 0.0) initslope = -1.0;
1633 
1634   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1635   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1636   if (snes->nfuncs >= snes->max_funcs) {
1637     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1638     *flag = PETSC_FALSE;
1639     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1640     goto theend1;
1641   }
1642   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1643   if (snes->ops->solve != SNESSolveVI_SS) {
1644     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1645   } else {
1646     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1647   }
1648   if (snes->domainerror) {
1649     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1650     PetscFunctionReturn(0);
1651   }
1652   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1653   ierr = PetscInfo2(snes,"Initial fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1654   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1655     if (vi->lsmonitor) {
1656       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1657     }
1658     goto theend1;
1659   }
1660 
1661   /* Fit points with quadratic */
1662   lambda     = 1.0;
1663   lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1664   lambdaprev = lambda;
1665   gnormprev  = *gnorm;
1666   if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1667   if (lambdatemp <= .1*lambda) lambda = .1*lambda;
1668   else                         lambda = lambdatemp;
1669 
1670   ierr  = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1671   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1672   if (snes->nfuncs >= snes->max_funcs) {
1673     ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while attempting quadratic backtracking! %D \n",snes->nfuncs);CHKERRQ(ierr);
1674     *flag = PETSC_FALSE;
1675     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1676     goto theend1;
1677   }
1678   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1679   if (snes->ops->solve != SNESSolveVI_SS) {
1680     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1681   } else {
1682     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1683   }
1684   if (snes->domainerror) {
1685     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1686     PetscFunctionReturn(0);
1687   }
1688   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1689   if (vi->lsmonitor) {
1690     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: gnorm after quadratic fit %G\n",*gnorm);CHKERRQ(ierr);
1691   }
1692   if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1693     if (vi->lsmonitor) {
1694       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Quadratically determined step, lambda=%18.16e\n",lambda);CHKERRQ(ierr);
1695     }
1696     goto theend1;
1697   }
1698 
1699   /* Fit points with cubic */
1700   count = 1;
1701   while (PETSC_TRUE) {
1702     if (lambda <= minlambda) {
1703       if (vi->lsmonitor) {
1704 	ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: unable to find good step length! After %D tries \n",count);CHKERRQ(ierr);
1705 	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);
1706       }
1707       *flag = PETSC_FALSE;
1708       break;
1709     }
1710     t1 = .5*((*gnorm)*(*gnorm) - fnorm*fnorm) - lambda*initslope;
1711     t2 = .5*(gnormprev*gnormprev  - fnorm*fnorm) - lambdaprev*initslope;
1712     a  = (t1/(lambda*lambda) - t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1713     b  = (-lambdaprev*t1/(lambda*lambda) + lambda*t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1714     d  = b*b - 3*a*initslope;
1715     if (d < 0.0) d = 0.0;
1716     if (a == 0.0) {
1717       lambdatemp = -initslope/(2.0*b);
1718     } else {
1719       lambdatemp = (-b + sqrt(d))/(3.0*a);
1720     }
1721     lambdaprev = lambda;
1722     gnormprev  = *gnorm;
1723     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1724     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1725     else                         lambda     = lambdatemp;
1726     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1727     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1728     if (snes->nfuncs >= snes->max_funcs) {
1729       ierr = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1730       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);
1731       *flag = PETSC_FALSE;
1732       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1733       break;
1734     }
1735     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1736     if (snes->ops->solve != SNESSolveVI_SS) {
1737       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1738     } else {
1739       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1740     }
1741     if (snes->domainerror) {
1742       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1743       PetscFunctionReturn(0);
1744     }
1745     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1746     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* is reduction enough? */
1747       if (vi->lsmonitor) {
1748 	ierr = PetscPrintf(comm,"    Line search: Cubically determined step, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1749       }
1750       break;
1751     } else {
1752       if (vi->lsmonitor) {
1753         ierr = PetscPrintf(comm,"    Line search: Cubic step no good, shrinking lambda, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1754       }
1755     }
1756     count++;
1757   }
1758   theend1:
1759   /* Optional user-defined check for line search step validity */
1760   if (vi->postcheckstep && *flag) {
1761     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1762     if (changed_y) {
1763       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1764       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1765     }
1766     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1767       ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1768       if (snes->ops->solve != SNESSolveVI_SS) {
1769         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1770       } else {
1771         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1772       }
1773       if (snes->domainerror) {
1774         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1775         PetscFunctionReturn(0);
1776       }
1777       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1778       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1779       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1780     }
1781   }
1782   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1783   PetscFunctionReturn(0);
1784 }
1785 
1786 #undef __FUNCT__
1787 #define __FUNCT__ "SNESLineSearchQuadratic_VI"
1788 /*
1789   This routine does a quadratic line search while keeping the iterates within the variable bounds
1790 */
1791 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)
1792 {
1793   /*
1794      Note that for line search purposes we work with with the related
1795      minimization problem:
1796         min  z(x):  R^n -> R,
1797      where z(x) = .5 * fnorm*fnorm,and fnorm = || f ||_2.
1798    */
1799   PetscReal      initslope,minlambda,lambda,lambdatemp,rellength;
1800 #if defined(PETSC_USE_COMPLEX)
1801   PetscScalar    cinitslope;
1802 #endif
1803   PetscErrorCode ierr;
1804   PetscInt       count;
1805   SNES_VI        *vi = (SNES_VI*)snes->data;
1806   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1807 
1808   PetscFunctionBegin;
1809   ierr    = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1810   *flag   = PETSC_TRUE;
1811 
1812   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1813   if (*ynorm == 0.0) {
1814     if (vi->lsmonitor) {
1815       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Direction and size is 0\n");CHKERRQ(ierr);
1816     }
1817     *gnorm = fnorm;
1818     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1819     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1820     *flag  = PETSC_FALSE;
1821     goto theend2;
1822   }
1823   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1824     ierr   = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1825     *ynorm = vi->maxstep;
1826   }
1827   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1828   minlambda = vi->minlambda/rellength;
1829   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1830 #if defined(PETSC_USE_COMPLEX)
1831   ierr      = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1832   initslope = PetscRealPart(cinitslope);
1833 #else
1834   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1835 #endif
1836   if (initslope > 0.0)  initslope = -initslope;
1837   if (initslope == 0.0) initslope = -1.0;
1838   ierr = PetscInfo1(snes,"Initslope %G \n",initslope);CHKERRQ(ierr);
1839 
1840   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1841   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1842   if (snes->nfuncs >= snes->max_funcs) {
1843     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1844     *flag = PETSC_FALSE;
1845     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1846     goto theend2;
1847   }
1848   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1849   if (snes->ops->solve != SNESSolveVI_SS) {
1850     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1851   } else {
1852     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1853   }
1854   if (snes->domainerror) {
1855     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1856     PetscFunctionReturn(0);
1857   }
1858   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1859   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1860     if (vi->lsmonitor) {
1861       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1862     }
1863     goto theend2;
1864   }
1865 
1866   /* Fit points with quadratic */
1867   lambda = 1.0;
1868   count = 1;
1869   while (PETSC_TRUE) {
1870     if (lambda <= minlambda) { /* bad luck; use full step */
1871       if (vi->lsmonitor) {
1872         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Unable to find good step length! %D \n",count);CHKERRQ(ierr);
1873         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);
1874       }
1875       ierr = VecCopy(x,w);CHKERRQ(ierr);
1876       *flag = PETSC_FALSE;
1877       break;
1878     }
1879     lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1880     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1881     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1882     else                         lambda     = lambdatemp;
1883 
1884     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1885     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1886     if (snes->nfuncs >= snes->max_funcs) {
1887       ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1888       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);
1889       *flag = PETSC_FALSE;
1890       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1891       break;
1892     }
1893     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1894     if (snes->domainerror) {
1895       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1896       PetscFunctionReturn(0);
1897     }
1898     if (snes->ops->solve != SNESSolveVI_SS) {
1899       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1900     } else {
1901       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1902     }
1903     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1904     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1905       if (vi->lsmonitor) {
1906         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line Search: Quadratically determined step, lambda=%G\n",lambda);CHKERRQ(ierr);
1907       }
1908       break;
1909     }
1910     count++;
1911   }
1912   theend2:
1913   /* Optional user-defined check for line search step validity */
1914   if (vi->postcheckstep) {
1915     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1916     if (changed_y) {
1917       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1918       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1919     }
1920     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1921       ierr = SNESComputeFunction(snes,w,g);
1922       if (snes->domainerror) {
1923         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1924         PetscFunctionReturn(0);
1925       }
1926       if (snes->ops->solve != SNESSolveVI_SS) {
1927         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1928       } else {
1929         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1930       }
1931 
1932       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1933       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1934       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1935     }
1936   }
1937   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1938   PetscFunctionReturn(0);
1939 }
1940 
1941 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*/
1942 /* -------------------------------------------------------------------------- */
1943 EXTERN_C_BEGIN
1944 #undef __FUNCT__
1945 #define __FUNCT__ "SNESLineSearchSet_VI"
1946 PetscErrorCode  SNESLineSearchSet_VI(SNES snes,FCN2 func,void *lsctx)
1947 {
1948   PetscFunctionBegin;
1949   ((SNES_VI *)(snes->data))->LineSearch = func;
1950   ((SNES_VI *)(snes->data))->lsP        = lsctx;
1951   PetscFunctionReturn(0);
1952 }
1953 EXTERN_C_END
1954 
1955 /* -------------------------------------------------------------------------- */
1956 EXTERN_C_BEGIN
1957 #undef __FUNCT__
1958 #define __FUNCT__ "SNESLineSearchSetMonitor_VI"
1959 PetscErrorCode  SNESLineSearchSetMonitor_VI(SNES snes,PetscBool flg)
1960 {
1961   SNES_VI        *vi = (SNES_VI*)snes->data;
1962   PetscErrorCode ierr;
1963 
1964   PetscFunctionBegin;
1965   if (flg && !vi->lsmonitor) {
1966     ierr = PetscViewerASCIIMonitorCreate(((PetscObject)snes)->comm,"stdout",((PetscObject)snes)->tablevel,&vi->lsmonitor);CHKERRQ(ierr);
1967   } else if (!flg && vi->lsmonitor) {
1968     ierr = PetscViewerASCIIMonitorDestroy(vi->lsmonitor);CHKERRQ(ierr);
1969   }
1970   PetscFunctionReturn(0);
1971 }
1972 EXTERN_C_END
1973 
1974 /*
1975    SNESView_VI - Prints info from the SNESVI data structure.
1976 
1977    Input Parameters:
1978 .  SNES - the SNES context
1979 .  viewer - visualization context
1980 
1981    Application Interface Routine: SNESView()
1982 */
1983 #undef __FUNCT__
1984 #define __FUNCT__ "SNESView_VI"
1985 static PetscErrorCode SNESView_VI(SNES snes,PetscViewer viewer)
1986 {
1987   SNES_VI        *vi = (SNES_VI *)snes->data;
1988   const char     *cstr,*tstr;
1989   PetscErrorCode ierr;
1990   PetscBool     iascii;
1991 
1992   PetscFunctionBegin;
1993   ierr = PetscTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1994   if (iascii) {
1995     if (vi->LineSearch == SNESLineSearchNo_VI)             cstr = "SNESLineSearchNo";
1996     else if (vi->LineSearch == SNESLineSearchQuadratic_VI) cstr = "SNESLineSearchQuadratic";
1997     else if (vi->LineSearch == SNESLineSearchCubic_VI)     cstr = "SNESLineSearchCubic";
1998     else                                                             cstr = "unknown";
1999     if (snes->ops->solve == SNESSolveVI_SS)      tstr = "Semismooth";
2000     else if (snes->ops->solve == SNESSolveVI_RS) tstr = "Reduced Space";
2001     else if (snes->ops->solve == SNESSolveVI_RS2) tstr = "Augmented Space";
2002     else                                         tstr = "unknown";
2003     ierr = PetscViewerASCIIPrintf(viewer,"  VI algorithm: %s\n",tstr);CHKERRQ(ierr);
2004     ierr = PetscViewerASCIIPrintf(viewer,"  line search variant: %s\n",cstr);CHKERRQ(ierr);
2005     ierr = PetscViewerASCIIPrintf(viewer,"  alpha=%G, maxstep=%G, minlambda=%G\n",vi->alpha,vi->maxstep,vi->minlambda);CHKERRQ(ierr);
2006   } else {
2007     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Viewer type %s not supported for SNES EQ VI",((PetscObject)viewer)->type_name);
2008   }
2009   PetscFunctionReturn(0);
2010 }
2011 
2012 #undef __FUNCT__
2013 #define __FUNCT__ "SNESVISetVariableBounds"
2014 /*@
2015    SNESVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu.
2016 
2017    Input Parameters:
2018 .  snes - the SNES context.
2019 .  xl   - lower bound.
2020 .  xu   - upper bound.
2021 
2022    Notes:
2023    If this routine is not called then the lower and upper bounds are set to
2024    PETSC_VI_INF and PETSC_VI_NINF respectively during SNESSetUp().
2025 
2026 @*/
2027 PetscErrorCode SNESVISetVariableBounds(SNES snes, Vec xl, Vec xu)
2028 {
2029   SNES_VI  *vi = (SNES_VI*)snes->data;
2030 
2031   PetscFunctionBegin;
2032   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
2033   PetscValidHeaderSpecific(xl,VEC_CLASSID,2);
2034   PetscValidHeaderSpecific(xu,VEC_CLASSID,3);
2035   if (!snes->vec_func) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call SNESSetFunction() first");
2036   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);
2037   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);
2038 
2039   vi->usersetxbounds = PETSC_TRUE;
2040   vi->xl = xl;
2041   vi->xu = xu;
2042   PetscFunctionReturn(0);
2043 }
2044 
2045 /* -------------------------------------------------------------------------- */
2046 /*
2047    SNESSetFromOptions_VI - Sets various parameters for the SNESVI method.
2048 
2049    Input Parameter:
2050 .  snes - the SNES context
2051 
2052    Application Interface Routine: SNESSetFromOptions()
2053 */
2054 #undef __FUNCT__
2055 #define __FUNCT__ "SNESSetFromOptions_VI"
2056 static PetscErrorCode SNESSetFromOptions_VI(SNES snes)
2057 {
2058   SNES_VI        *vi = (SNES_VI *)snes->data;
2059   const char     *lses[] = {"basic","basicnonorms","quadratic","cubic"};
2060   const char     *vies[] = {"ss","rs","rs2"};
2061   PetscErrorCode ierr;
2062   PetscInt       indx;
2063   PetscBool      flg,set,flg2;
2064 
2065   PetscFunctionBegin;
2066   ierr = PetscOptionsHead("SNES semismooth method options");CHKERRQ(ierr);
2067   ierr = PetscOptionsBool("-snes_vi_monitor","Monitor all non-active variables","None",PETSC_FALSE,&flg,0);CHKERRQ(ierr);
2068   if (flg) {
2069     ierr = SNESMonitorSet(snes,SNESMonitorVI,0,0);CHKERRQ(ierr);
2070   }
2071   ierr = PetscOptionsReal("-snes_ls_alpha","Function norm must decrease by","None",vi->alpha,&vi->alpha,0);CHKERRQ(ierr);
2072   ierr = PetscOptionsReal("-snes_ls_maxstep","Step must be less than","None",vi->maxstep,&vi->maxstep,0);CHKERRQ(ierr);
2073   ierr = PetscOptionsReal("-snes_ls_minlambda","Minimum lambda allowed","None",vi->minlambda,&vi->minlambda,0);CHKERRQ(ierr);
2074   ierr = PetscOptionsReal("-snes_vi_const_tol","constraint tolerance","None",vi->const_tol,&vi->const_tol,0);CHKERRQ(ierr);
2075   ierr = PetscOptionsBool("-snes_ls_monitor","Print progress of line searches","SNESLineSearchSetMonitor",vi->lsmonitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);CHKERRQ(ierr);
2076   if (set) {ierr = SNESLineSearchSetMonitor(snes,flg);CHKERRQ(ierr);}
2077   ierr = PetscOptionsEList("-snes_vi_type","Semismooth algorithm used","",vies,3,"ss",&indx,&flg2);CHKERRQ(ierr);
2078   if (flg2) {
2079     switch (indx) {
2080     case 0:
2081       snes->ops->solve = SNESSolveVI_SS;
2082       break;
2083     case 1:
2084       snes->ops->solve = SNESSolveVI_RS;
2085       break;
2086     case 2:
2087       snes->ops->solve = SNESSolveVI_RS2;
2088     }
2089   }
2090   ierr = PetscOptionsEList("-snes_ls","Line search used","SNESLineSearchSet",lses,4,"basic",&indx,&flg);CHKERRQ(ierr);
2091   if (flg) {
2092     switch (indx) {
2093     case 0:
2094       ierr = SNESLineSearchSet(snes,SNESLineSearchNo_VI,PETSC_NULL);CHKERRQ(ierr);
2095       break;
2096     case 1:
2097       ierr = SNESLineSearchSet(snes,SNESLineSearchNoNorms_VI,PETSC_NULL);CHKERRQ(ierr);
2098       break;
2099     case 2:
2100       ierr = SNESLineSearchSet(snes,SNESLineSearchQuadratic_VI,PETSC_NULL);CHKERRQ(ierr);
2101       break;
2102     case 3:
2103       ierr = SNESLineSearchSet(snes,SNESLineSearchCubic_VI,PETSC_NULL);CHKERRQ(ierr);
2104       break;
2105     }
2106   }
2107   ierr = PetscOptionsTail();CHKERRQ(ierr);
2108   PetscFunctionReturn(0);
2109 }
2110 /* -------------------------------------------------------------------------- */
2111 /*MC
2112       SNESVI - Semismooth newton method based nonlinear solver that uses a line search
2113 
2114    Options Database:
2115 +   -snes_ls [cubic,quadratic,basic,basicnonorms] - Selects line search
2116 .   -snes_ls_alpha <alpha> - Sets alpha
2117 .   -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)
2118 .   -snes_ls_minlambda <minlambda>  - Sets the minimum lambda the line search will use  minlambda / max_i ( y[i]/x[i] )
2119 -   -snes_ls_monitor - print information about progress of line searches
2120 
2121 
2122    Level: beginner
2123 
2124 .seealso:  SNESCreate(), SNES, SNESSetType(), SNESTR, SNESLineSearchSet(),
2125            SNESLineSearchSetPostCheck(), SNESLineSearchNo(), SNESLineSearchCubic(), SNESLineSearchQuadratic(),
2126            SNESLineSearchSet(), SNESLineSearchNoNorms(), SNESLineSearchSetPreCheck(), SNESLineSearchSetParams(), SNESLineSearchGetParams()
2127 
2128 M*/
2129 EXTERN_C_BEGIN
2130 #undef __FUNCT__
2131 #define __FUNCT__ "SNESCreate_VI"
2132 PetscErrorCode  SNESCreate_VI(SNES snes)
2133 {
2134   PetscErrorCode ierr;
2135   SNES_VI      *vi;
2136 
2137   PetscFunctionBegin;
2138   snes->ops->setup	     = SNESSetUp_VI;
2139   snes->ops->solve	     = SNESSolveVI_SS;
2140   snes->ops->destroy	     = SNESDestroy_VI;
2141   snes->ops->setfromoptions  = SNESSetFromOptions_VI;
2142   snes->ops->view            = SNESView_VI;
2143   snes->ops->reset           = 0; /* XXX Implement!!! */
2144   snes->ops->converged       = SNESDefaultConverged_VI;
2145 
2146   ierr                   = PetscNewLog(snes,SNES_VI,&vi);CHKERRQ(ierr);
2147   snes->data    	 = (void*)vi;
2148   vi->alpha		 = 1.e-4;
2149   vi->maxstep		 = 1.e8;
2150   vi->minlambda         = 1.e-12;
2151   vi->LineSearch        = SNESLineSearchNo_VI;
2152   vi->lsP               = PETSC_NULL;
2153   vi->postcheckstep     = PETSC_NULL;
2154   vi->postcheck         = PETSC_NULL;
2155   vi->precheckstep      = PETSC_NULL;
2156   vi->precheck          = PETSC_NULL;
2157   vi->const_tol         =  2.2204460492503131e-16;
2158   vi->checkredundancy   = PETSC_NULL;
2159 
2160   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","SNESLineSearchSetMonitor_VI",SNESLineSearchSetMonitor_VI);CHKERRQ(ierr);
2161   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","SNESLineSearchSet_VI",SNESLineSearchSet_VI);CHKERRQ(ierr);
2162 
2163   PetscFunctionReturn(0);
2164 }
2165 EXTERN_C_END
2166