xref: /petsc/src/snes/impls/vi/vi.c (revision c479af0a55cddd28eaa69fb043729d4427f60ea8)
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] <= SNES_VI_NINF) && (u[i] >= SNES_VI_INF)) { /* no constraints on variable */
230       phi_arr[i] = f_arr[i];
231     } else if (l[i] <= SNES_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] >= SNES_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] <= SNES_VI_NINF) && (u[i] >= SNES_VI_INF)) {/* no constraints on variable */
275       da[i] = 0;
276       db[i] = 1;
277     } else if (l[i] <= SNES_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] >= SNES_VI_INF) {                      /* lower bound on variable only */
281       da[i] = DPhi(x[i] - l[i], f[i]);
282       db[i] = DPhi(f[i],x[i] - l[i]);
283     } else if (l[i] == u[i]) {                              /* fixed variable */
284       da[i] = 1;
285       db[i] = 0;
286     } else {                                                /* upper and lower bounds on variable */
287       da1 = DPhi(x[i] - l[i], -Phi(u[i] - x[i], -f[i]));
288       db1 = DPhi(-Phi(u[i] - x[i], -f[i]),x[i] - l[i]);
289       da2 = DPhi(u[i] - x[i], -f[i]);
290       db2 = DPhi(-f[i],u[i] - x[i]);
291       da[i] = da1 + db1*da2;
292       db[i] = db1*db2;
293     }
294   }
295 
296   ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
297   ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
298   ierr = VecRestoreArray(vi->xl,&l);CHKERRQ(ierr);
299   ierr = VecRestoreArray(vi->xu,&u);CHKERRQ(ierr);
300   ierr = VecRestoreArray(Da,&da);CHKERRQ(ierr);
301   ierr = VecRestoreArray(Db,&db);CHKERRQ(ierr);
302   PetscFunctionReturn(0);
303 }
304 
305 /*
306    SNESVIComputeJacobian - Computes the jacobian of the semismooth function.The Jacobian for the semismooth function is an element of the B-subdifferential of the Fischer-Burmeister function for complementarity problems.
307 
308    Input Parameters:
309 .  Da       - Diagonal shift vector for the semismooth jacobian.
310 .  Db       - Row scaling vector for the semismooth jacobian.
311 
312    Output Parameters:
313 .  jac      - semismooth jacobian
314 .  jac_pre  - optional preconditioning matrix
315 
316    Notes:
317    The semismooth jacobian matrix is given by
318    jac = Da + Db*jacfun
319    where Db is the row scaling matrix stored as a vector,
320          Da is the diagonal perturbation matrix stored as a vector
321    and   jacfun is the jacobian of the original nonlinear function.
322 */
323 #undef __FUNCT__
324 #define __FUNCT__ "SNESVIComputeJacobian"
325 PetscErrorCode SNESVIComputeJacobian(Mat jac, Mat jac_pre,Vec Da, Vec Db)
326 {
327   PetscErrorCode ierr;
328 
329   /* Do row scaling  and add diagonal perturbation */
330   ierr = MatDiagonalScale(jac,Db,PETSC_NULL);CHKERRQ(ierr);
331   ierr = MatDiagonalSet(jac,Da,ADD_VALUES);CHKERRQ(ierr);
332   if (jac != jac_pre) { /* If jac and jac_pre are different */
333     ierr = MatDiagonalScale(jac_pre,Db,PETSC_NULL);
334     ierr = MatDiagonalSet(jac_pre,Da,ADD_VALUES);CHKERRQ(ierr);
335   }
336   PetscFunctionReturn(0);
337 }
338 
339 /*
340    SNESVIComputeMeritFunctionGradient - Computes the gradient of the merit function psi.
341 
342    Input Parameters:
343    phi - semismooth function.
344    H   - semismooth jacobian
345 
346    Output Parameters:
347    dpsi - merit function gradient
348 
349    Notes:
350   The merit function gradient is computed as follows
351         dpsi = H^T*phi
352 */
353 #undef __FUNCT__
354 #define __FUNCT__ "SNESVIComputeMeritFunctionGradient"
355 PetscErrorCode SNESVIComputeMeritFunctionGradient(Mat H, Vec phi, Vec dpsi)
356 {
357   PetscErrorCode ierr;
358 
359   PetscFunctionBegin;
360   ierr = MatMultTranspose(H,phi,dpsi);CHKERRQ(ierr);
361   PetscFunctionReturn(0);
362 }
363 
364 /* -------------------------------------------------------------------------- */
365 /*
366    SNESVIProjectOntoBounds - Projects X onto the feasible region so that Xl[i] <= X[i] <= Xu[i] for i = 1...n.
367 
368    Input Parameters:
369 .  SNES - nonlinear solver context
370 
371    Output Parameters:
372 .  X - Bound projected X
373 
374 */
375 
376 #undef __FUNCT__
377 #define __FUNCT__ "SNESVIProjectOntoBounds"
378 PetscErrorCode SNESVIProjectOntoBounds(SNES snes,Vec X)
379 {
380   PetscErrorCode    ierr;
381   SNES_VI           *vi = (SNES_VI*)snes->data;
382   const PetscScalar *xl,*xu;
383   PetscScalar       *x;
384   PetscInt          i,n;
385 
386   PetscFunctionBegin;
387   ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
388   ierr = VecGetArray(X,&x);CHKERRQ(ierr);
389   ierr = VecGetArrayRead(vi->xl,&xl);CHKERRQ(ierr);
390   ierr = VecGetArrayRead(vi->xu,&xu);CHKERRQ(ierr);
391 
392   for(i = 0;i<n;i++) {
393     if (x[i] < xl[i]) x[i] = xl[i];
394     else if (x[i] > xu[i]) x[i] = xu[i];
395   }
396   ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
397   ierr = VecRestoreArrayRead(vi->xl,&xl);CHKERRQ(ierr);
398   ierr = VecRestoreArrayRead(vi->xu,&xu);CHKERRQ(ierr);
399   PetscFunctionReturn(0);
400 }
401 
402 /*  --------------------------------------------------------------------
403 
404      This file implements a semismooth truncated Newton method with a line search,
405      for solving a system of nonlinear equations in complementarity form, using the KSP, Vec,
406      and Mat interfaces for linear solvers, vectors, and matrices,
407      respectively.
408 
409      The following basic routines are required for each nonlinear solver:
410           SNESCreate_XXX()          - Creates a nonlinear solver context
411           SNESSetFromOptions_XXX()  - Sets runtime options
412           SNESSolve_XXX()           - Solves the nonlinear system
413           SNESDestroy_XXX()         - Destroys the nonlinear solver context
414      The suffix "_XXX" denotes a particular implementation, in this case
415      we use _VI (e.g., SNESCreate_VI, SNESSolve_VI) for solving
416      systems of nonlinear equations with a line search (LS) method.
417      These routines are actually called via the common user interface
418      routines SNESCreate(), SNESSetFromOptions(), SNESSolve(), and
419      SNESDestroy(), so the application code interface remains identical
420      for all nonlinear solvers.
421 
422      Another key routine is:
423           SNESSetUp_XXX()           - Prepares for the use of a nonlinear solver
424      by setting data structures and options.   The interface routine SNESSetUp()
425      is not usually called directly by the user, but instead is called by
426      SNESSolve() if necessary.
427 
428      Additional basic routines are:
429           SNESView_XXX()            - Prints details of runtime options that
430                                       have actually been used.
431      These are called by application codes via the interface routines
432      SNESView().
433 
434      The various types of solvers (preconditioners, Krylov subspace methods,
435      nonlinear solvers, timesteppers) are all organized similarly, so the
436      above description applies to these categories also.
437 
438     -------------------------------------------------------------------- */
439 /*
440    SNESSolveVI_SS - Solves the complementarity problem with a semismooth Newton
441    method using a line search.
442 
443    Input Parameters:
444 .  snes - the SNES context
445 
446    Output Parameter:
447 .  outits - number of iterations until termination
448 
449    Application Interface Routine: SNESSolve()
450 
451    Notes:
452    This implements essentially a semismooth Newton method with a
453    line search. The default line search does not do any line seach
454    but rather takes a full newton step.
455 */
456 #undef __FUNCT__
457 #define __FUNCT__ "SNESSolveVI_SS"
458 PetscErrorCode SNESSolveVI_SS(SNES snes)
459 {
460   SNES_VI            *vi = (SNES_VI*)snes->data;
461   PetscErrorCode     ierr;
462   PetscInt           maxits,i,lits;
463   PetscBool          lssucceed;
464   MatStructure       flg = DIFFERENT_NONZERO_PATTERN;
465   PetscReal          gnorm,xnorm=0,ynorm;
466   Vec                Y,X,F,G,W;
467   KSPConvergedReason kspreason;
468 
469   PetscFunctionBegin;
470   vi->computeuserfunction    = snes->ops->computefunction;
471   snes->ops->computefunction = SNESVIComputeFunction;
472 
473   snes->numFailures            = 0;
474   snes->numLinearSolveFailures = 0;
475   snes->reason                 = SNES_CONVERGED_ITERATING;
476 
477   maxits	= snes->max_its;	/* maximum number of iterations */
478   X		= snes->vec_sol;	/* solution vector */
479   F		= snes->vec_func;	/* residual vector */
480   Y		= snes->work[0];	/* work vectors */
481   G		= snes->work[1];
482   W		= snes->work[2];
483 
484   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
485   snes->iter = 0;
486   snes->norm = 0.0;
487   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
488 
489   ierr = SNESVIProjectOntoBounds(snes,X);CHKERRQ(ierr);
490   ierr = SNESComputeFunction(snes,X,vi->phi);CHKERRQ(ierr);
491   if (snes->domainerror) {
492     snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
493     snes->ops->computefunction = vi->computeuserfunction;
494     PetscFunctionReturn(0);
495   }
496    /* Compute Merit function */
497   ierr = SNESVIComputeMeritFunction(vi->phi,&vi->merit,&vi->phinorm);CHKERRQ(ierr);
498 
499   ierr = VecNormBegin(X,NORM_2,&xnorm);CHKERRQ(ierr);	/* xnorm <- ||x||  */
500   ierr = VecNormEnd(X,NORM_2,&xnorm);CHKERRQ(ierr);
501   if (PetscIsInfOrNanReal(vi->merit)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
502 
503   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
504   snes->norm = vi->phinorm;
505   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
506   SNESLogConvHistory(snes,vi->phinorm,0);
507   ierr = SNESMonitor(snes,0,vi->phinorm);CHKERRQ(ierr);
508 
509   /* set parameter for default relative tolerance convergence test */
510   snes->ttol = vi->phinorm*snes->rtol;
511   /* test convergence */
512   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,vi->phinorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
513   if (snes->reason) {
514     snes->ops->computefunction = vi->computeuserfunction;
515     PetscFunctionReturn(0);
516   }
517 
518   for (i=0; i<maxits; i++) {
519 
520     /* Call general purpose update function */
521     if (snes->ops->update) {
522       ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
523     }
524 
525     /* Solve J Y = Phi, where J is the semismooth jacobian */
526     /* Get the nonlinear function jacobian */
527     ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr);
528     /* Get the diagonal shift and row scaling vectors */
529     ierr = SNESVIComputeBsubdifferentialVectors(snes,X,F,snes->jacobian,vi->Da,vi->Db);CHKERRQ(ierr);
530     /* Compute the semismooth jacobian */
531     ierr = SNESVIComputeJacobian(snes->jacobian,snes->jacobian_pre,vi->Da,vi->Db);CHKERRQ(ierr);
532     /* Compute the merit function gradient */
533     ierr = SNESVIComputeMeritFunctionGradient(snes->jacobian,vi->phi,vi->dpsi);CHKERRQ(ierr);
534     ierr = KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);CHKERRQ(ierr);
535     ierr = SNES_KSPSolve(snes,snes->ksp,vi->phi,Y);CHKERRQ(ierr);
536     ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr);
537 
538     if (kspreason < 0) {
539       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
540         ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr);
541         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
542         break;
543       }
544     }
545     ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr);
546     snes->linear_its += lits;
547     ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr);
548     /*
549     if (vi->precheckstep) {
550       PetscBool changed_y = PETSC_FALSE;
551       ierr = (*vi->precheckstep)(snes,X,Y,vi->precheck,&changed_y);CHKERRQ(ierr);
552     }
553 
554     if (PetscLogPrintInfo){
555       ierr = SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr);
556     }
557     */
558     /* Compute a (scaled) negative update in the line search routine:
559          Y <- X - lambda*Y
560        and evaluate G = function(Y) (depends on the line search).
561     */
562     ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr);
563     ynorm = 1; gnorm = vi->phinorm;
564     ierr = (*vi->LineSearch)(snes,vi->lsP,X,vi->phi,G,Y,W,vi->phinorm,xnorm,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
565     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",vi->phinorm,gnorm,ynorm,(int)lssucceed);CHKERRQ(ierr);
566     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
567     if (snes->domainerror) {
568       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
569       snes->ops->computefunction = vi->computeuserfunction;
570       PetscFunctionReturn(0);
571     }
572     if (!lssucceed) {
573       if (++snes->numFailures >= snes->maxFailures) {
574 	PetscBool ismin;
575         snes->reason = SNES_DIVERGED_LINE_SEARCH;
576         ierr = SNESVICheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr);
577         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
578         break;
579       }
580     }
581     /* Update function and solution vectors */
582     vi->phinorm = gnorm;
583     vi->merit = 0.5*vi->phinorm*vi->phinorm;
584     ierr = VecCopy(G,vi->phi);CHKERRQ(ierr);
585     ierr = VecCopy(W,X);CHKERRQ(ierr);
586     /* Monitor convergence */
587     ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
588     snes->iter = i+1;
589     snes->norm = vi->phinorm;
590     ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
591     SNESLogConvHistory(snes,snes->norm,lits);
592     ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr);
593     /* Test for convergence, xnorm = || X || */
594     if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); }
595     ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,vi->phinorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
596     if (snes->reason) break;
597   }
598   if (i == maxits) {
599     ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr);
600     if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
601   }
602   snes->ops->computefunction = vi->computeuserfunction;
603   PetscFunctionReturn(0);
604 }
605 
606 #undef __FUNCT__
607 #define __FUNCT__ "SNESVIGetActiveSetIS"
608 /*
609    SNESVIGetActiveSetIndices - Gets the global indices for the active set variables
610 
611    Input parameter
612 .  snes - the SNES context
613 .  X    - the snes solution vector
614 .  F    - the nonlinear function vector
615 
616    Output parameter
617 .  ISact - active set index set
618  */
619 PetscErrorCode SNESVIGetActiveSetIS(SNES snes,Vec X,Vec F,IS* ISact)
620 {
621   PetscErrorCode   ierr;
622   SNES_VI          *vi = (SNES_VI*)snes->data;
623   Vec               Xl=vi->xl,Xu=vi->xu;
624   const PetscScalar *x,*f,*xl,*xu;
625   PetscInt          *idx_act,i,nlocal,nloc_isact=0,ilow,ihigh,i1=0;
626 
627   PetscFunctionBegin;
628   ierr = VecGetLocalSize(X,&nlocal);CHKERRQ(ierr);
629   ierr = VecGetOwnershipRange(X,&ilow,&ihigh);CHKERRQ(ierr);
630   ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
631   ierr = VecGetArrayRead(Xl,&xl);CHKERRQ(ierr);
632   ierr = VecGetArrayRead(Xu,&xu);CHKERRQ(ierr);
633   ierr = VecGetArrayRead(F,&f);CHKERRQ(ierr);
634   /* Compute active set size */
635   for (i=0; i < nlocal;i++) {
636     if (!((x[i] > xl[i] + 1.e-8 || (f[i] < 0.0)) && ((x[i] < xu[i] - 1.e-8) || f[i] > 0.0))) nloc_isact++;
637   }
638 
639   ierr = PetscMalloc(nloc_isact*sizeof(PetscInt),&idx_act);CHKERRQ(ierr);
640 
641   /* Set active set indices */
642   for(i=0; i < nlocal; i++) {
643     if (!((x[i] > xl[i] + 1.e-8 || (f[i] < 0.0)) && ((x[i] < xu[i] - 1.e-8) || f[i] > 0.0))) idx_act[i1++] = ilow+i;
644   }
645 
646    /* Create active set IS */
647   ierr = ISCreateGeneral(((PetscObject)snes)->comm,nloc_isact,idx_act,PETSC_OWN_POINTER,ISact);CHKERRQ(ierr);
648 
649   ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
650   ierr = VecRestoreArrayRead(Xl,&xl);CHKERRQ(ierr);
651   ierr = VecRestoreArrayRead(Xu,&xu);CHKERRQ(ierr);
652   ierr = VecRestoreArrayRead(F,&f);CHKERRQ(ierr);
653   PetscFunctionReturn(0);
654 }
655 
656 #undef __FUNCT__
657 #define __FUNCT__ "SNESVICreateIndexSets_RS"
658 PetscErrorCode SNESVICreateIndexSets_RS(SNES snes,Vec X,Vec F,IS* ISact,IS* ISinact)
659 {
660   PetscErrorCode     ierr;
661 
662   PetscFunctionBegin;
663   ierr = SNESVIGetActiveSetIS(snes,X,F,ISact);CHKERRQ(ierr);
664   ierr = ISComplement(*ISact,X->map->rstart,X->map->rend,ISinact);CHKERRQ(ierr);
665   PetscFunctionReturn(0);
666 }
667 
668 /* Create active and inactive set vectors. The local size of this vector is set and petsc computes the global size */
669 #undef __FUNCT__
670 #define __FUNCT__ "SNESVICreateSubVectors"
671 PetscErrorCode SNESVICreateSubVectors(SNES snes,PetscInt n,Vec* newv)
672 {
673   PetscErrorCode ierr;
674   Vec            v;
675 
676   PetscFunctionBegin;
677   ierr = VecCreate(((PetscObject)snes)->comm,&v);CHKERRQ(ierr);
678   ierr = VecSetSizes(v,n,PETSC_DECIDE);CHKERRQ(ierr);
679   ierr = VecSetFromOptions(v);CHKERRQ(ierr);
680   *newv = v;
681 
682   PetscFunctionReturn(0);
683 }
684 
685 /* Resets the snes PC and KSP when the active set sizes change */
686 #undef __FUNCT__
687 #define __FUNCT__ "SNESVIResetPCandKSP"
688 PetscErrorCode SNESVIResetPCandKSP(SNES snes,Mat Amat,Mat Pmat)
689 {
690   PetscErrorCode         ierr;
691   KSP                    kspnew,snesksp;
692   PC                     pcnew;
693   const MatSolverPackage stype;
694 
695   PetscFunctionBegin;
696   /* The active and inactive set sizes have changed so need to create a new snes->ksp object */
697   ierr = SNESGetKSP(snes,&snesksp);CHKERRQ(ierr);
698   ierr = KSPCreate(((PetscObject)snes)->comm,&kspnew);CHKERRQ(ierr);
699   /* Copy over snes->ksp info */
700   kspnew->pc_side = snesksp->pc_side;
701   kspnew->rtol    = snesksp->rtol;
702   kspnew->abstol    = snesksp->abstol;
703   kspnew->max_it  = snesksp->max_it;
704   ierr = KSPSetType(kspnew,((PetscObject)snesksp)->type_name);CHKERRQ(ierr);
705   ierr = KSPGetPC(kspnew,&pcnew);CHKERRQ(ierr);
706   ierr = PCSetType(kspnew->pc,((PetscObject)snesksp->pc)->type_name);CHKERRQ(ierr);
707   ierr = PCSetOperators(kspnew->pc,Amat,Pmat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
708   ierr = PCFactorGetMatSolverPackage(snesksp->pc,&stype);CHKERRQ(ierr);
709   ierr = PCFactorSetMatSolverPackage(kspnew->pc,stype);CHKERRQ(ierr);
710   ierr = KSPDestroy(&snesksp);CHKERRQ(ierr);
711   snes->ksp = kspnew;
712   ierr = PetscLogObjectParent(snes,kspnew);CHKERRQ(ierr);
713   ierr = KSPSetFromOptions(kspnew);CHKERRQ(ierr);
714   PetscFunctionReturn(0);
715 }
716 
717 
718 #undef __FUNCT__
719 #define __FUNCT__ "SNESVIComputeInactiveSetFnorm"
720 PetscErrorCode SNESVIComputeInactiveSetFnorm(SNES snes,Vec F,Vec X,PetscScalar *fnorm)
721 {
722   PetscErrorCode    ierr;
723   SNES_VI           *vi = (SNES_VI*)snes->data;
724   const PetscScalar *x,*xl,*xu,*f;
725   PetscInt          i,n;
726   PetscReal         rnorm;
727 
728   PetscFunctionBegin;
729   ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
730   ierr = VecGetArrayRead(vi->xl,&xl);CHKERRQ(ierr);
731   ierr = VecGetArrayRead(vi->xu,&xu);CHKERRQ(ierr);
732   ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
733   ierr = VecGetArrayRead(F,&f);CHKERRQ(ierr);
734   rnorm = 0.0;
735   for (i=0; i<n; i++) {
736     if (((x[i] > xl[i] + 1.e-8 || (f[i] < 0.0)) && ((x[i] < xu[i] - 1.e-8) || f[i] > 0.0))) rnorm += f[i]*f[i];
737   }
738   ierr = VecRestoreArrayRead(F,&f);CHKERRQ(ierr);
739   ierr = VecRestoreArrayRead(vi->xl,&xl);CHKERRQ(ierr);
740   ierr = VecRestoreArrayRead(vi->xu,&xu);CHKERRQ(ierr);
741   ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
742   ierr = MPI_Allreduce(&rnorm,fnorm,1,MPIU_REAL,MPIU_SUM,((PetscObject)snes)->comm);CHKERRQ(ierr);
743   *fnorm = sqrt(*fnorm);
744   PetscFunctionReturn(0);
745 }
746 
747 /* Variational Inequality solver using reduce space method. No semismooth algorithm is
748    implemented in this algorithm. It basically identifies the active variables and does
749    a linear solve on the inactive variables. */
750 #undef __FUNCT__
751 #define __FUNCT__ "SNESSolveVI_RS"
752 PetscErrorCode SNESSolveVI_RS(SNES snes)
753 {
754   SNES_VI          *vi = (SNES_VI*)snes->data;
755   PetscErrorCode    ierr;
756   PetscInt          maxits,i,lits;
757   PetscBool         lssucceed;
758   MatStructure      flg = DIFFERENT_NONZERO_PATTERN;
759   PetscReal         fnorm,gnorm,xnorm=0,ynorm;
760   Vec                Y,X,F,G,W;
761   KSPConvergedReason kspreason;
762 
763   PetscFunctionBegin;
764   snes->numFailures            = 0;
765   snes->numLinearSolveFailures = 0;
766   snes->reason                 = SNES_CONVERGED_ITERATING;
767 
768   maxits	= snes->max_its;	/* maximum number of iterations */
769   X		= snes->vec_sol;	/* solution vector */
770   F		= snes->vec_func;	/* residual vector */
771   Y		= snes->work[0];	/* work vectors */
772   G		= snes->work[1];
773   W		= snes->work[2];
774 
775   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
776   snes->iter = 0;
777   snes->norm = 0.0;
778   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
779 
780   ierr = SNESVIProjectOntoBounds(snes,X);CHKERRQ(ierr);
781   ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);
782   if (snes->domainerror) {
783     snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
784     PetscFunctionReturn(0);
785   }
786   ierr = SNESVIComputeInactiveSetFnorm(snes,F,X,&fnorm);CHKERRQ(ierr);
787   ierr = VecNormBegin(X,NORM_2,&xnorm);CHKERRQ(ierr);	/* xnorm <- ||x||  */
788   ierr = VecNormEnd(X,NORM_2,&xnorm);CHKERRQ(ierr);
789   if (PetscIsInfOrNanReal(fnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
790 
791   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
792   snes->norm = fnorm;
793   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
794   SNESLogConvHistory(snes,fnorm,0);
795   ierr = SNESMonitor(snes,0,fnorm);CHKERRQ(ierr);
796 
797   /* set parameter for default relative tolerance convergence test */
798   snes->ttol = fnorm*snes->rtol;
799   /* test convergence */
800   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
801   if (snes->reason) PetscFunctionReturn(0);
802 
803   for (i=0; i<maxits; i++) {
804 
805     IS         IS_act,IS_inact; /* _act -> active set _inact -> inactive set */
806     VecScatter scat_act,scat_inact;
807     PetscInt   nis_act,nis_inact;
808     Vec        Y_act,Y_inact,F_inact;
809     Mat        jac_inact_inact,prejac_inact_inact;
810     IS         keptrows;
811     PetscBool  isequal;
812 
813     /* Call general purpose update function */
814     if (snes->ops->update) {
815       ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
816     }
817     ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr);
818 
819     /* Create active and inactive index sets */
820     ierr = SNESVICreateIndexSets_RS(snes,X,F,&IS_act,&IS_inact);CHKERRQ(ierr);
821 
822     /* Create inactive set submatrix */
823     ierr = MatGetSubMatrix(snes->jacobian,IS_inact,IS_inact,MAT_INITIAL_MATRIX,&jac_inact_inact);CHKERRQ(ierr);
824     ierr = MatFindNonzeroRows(jac_inact_inact,&keptrows);CHKERRQ(ierr);
825     if (keptrows) {
826       PetscInt       cnt,*nrows,k;
827       const PetscInt *krows,*inact;
828       PetscInt       rstart=jac_inact_inact->rmap->rstart;
829 
830       ierr = MatDestroy(&jac_inact_inact);CHKERRQ(ierr);
831       ierr = ISDestroy(&IS_act);CHKERRQ(ierr);
832 
833       ierr = ISGetLocalSize(keptrows,&cnt);CHKERRQ(ierr);
834       ierr = ISGetIndices(keptrows,&krows);CHKERRQ(ierr);
835       ierr = ISGetIndices(IS_inact,&inact);CHKERRQ(ierr);
836       ierr = PetscMalloc(cnt*sizeof(PetscInt),&nrows);CHKERRQ(ierr);
837       for (k=0; k<cnt; k++) {
838         nrows[k] = inact[krows[k]-rstart];
839       }
840       ierr = ISRestoreIndices(keptrows,&krows);CHKERRQ(ierr);
841       ierr = ISRestoreIndices(IS_inact,&inact);CHKERRQ(ierr);
842       ierr = ISDestroy(&keptrows);CHKERRQ(ierr);
843       ierr = ISDestroy(&IS_inact);CHKERRQ(ierr);
844 
845       ierr = ISCreateGeneral(PETSC_COMM_WORLD,cnt,nrows,PETSC_OWN_POINTER,&IS_inact);CHKERRQ(ierr);
846       ierr = ISComplement(IS_inact,F->map->rstart,F->map->rend,&IS_act);CHKERRQ(ierr);
847       ierr = MatGetSubMatrix(snes->jacobian,IS_inact,IS_inact,MAT_INITIAL_MATRIX,&jac_inact_inact);CHKERRQ(ierr);
848     }
849 
850     /* Get sizes of active and inactive sets */
851     ierr = ISGetLocalSize(IS_act,&nis_act);CHKERRQ(ierr);
852     ierr = ISGetLocalSize(IS_inact,&nis_inact);CHKERRQ(ierr);
853 
854     /* Create active and inactive set vectors */
855     ierr = SNESVICreateSubVectors(snes,nis_inact,&F_inact);CHKERRQ(ierr);
856     ierr = SNESVICreateSubVectors(snes,nis_act,&Y_act);CHKERRQ(ierr);
857     ierr = SNESVICreateSubVectors(snes,nis_inact,&Y_inact);CHKERRQ(ierr);
858 
859     /* Create scatter contexts */
860     ierr = VecScatterCreate(Y,IS_act,Y_act,PETSC_NULL,&scat_act);CHKERRQ(ierr);
861     ierr = VecScatterCreate(Y,IS_inact,Y_inact,PETSC_NULL,&scat_inact);CHKERRQ(ierr);
862 
863     /* Do a vec scatter to active and inactive set vectors */
864     ierr = VecScatterBegin(scat_inact,F,F_inact,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
865     ierr = VecScatterEnd(scat_inact,F,F_inact,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
866 
867     ierr = VecScatterBegin(scat_act,Y,Y_act,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
868     ierr = VecScatterEnd(scat_act,Y,Y_act,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
869 
870     ierr = VecScatterBegin(scat_inact,Y,Y_inact,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
871     ierr = VecScatterEnd(scat_inact,Y,Y_inact,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
872 
873     /* Active set direction = 0 */
874     ierr = VecSet(Y_act,0);CHKERRQ(ierr);
875     if (snes->jacobian != snes->jacobian_pre) {
876       ierr = MatGetSubMatrix(snes->jacobian_pre,IS_inact,IS_inact,MAT_INITIAL_MATRIX,&prejac_inact_inact);CHKERRQ(ierr);
877     } else prejac_inact_inact = jac_inact_inact;
878 
879     ierr = ISEqual(vi->IS_inact_prev,IS_inact,&isequal);CHKERRQ(ierr);
880     if (!isequal) {
881       ierr = SNESVIResetPCandKSP(snes,jac_inact_inact,prejac_inact_inact);CHKERRQ(ierr);
882     }
883 
884     /*      ierr = ISView(IS_inact,0);CHKERRQ(ierr); */
885     /*      ierr = ISView(IS_act,0);CHKERRQ(ierr);*/
886     /*      ierr = MatView(snes->jacobian_pre,0); */
887 
888     ierr = KSPSetOperators(snes->ksp,jac_inact_inact,prejac_inact_inact,flg);CHKERRQ(ierr);
889     ierr = KSPSetUp(snes->ksp);CHKERRQ(ierr);
890     {
891       PC        pc;
892       PetscBool flg;
893       ierr = KSPGetPC(snes->ksp,&pc);CHKERRQ(ierr);
894       ierr = PetscTypeCompare((PetscObject)pc,PCFIELDSPLIT,&flg);CHKERRQ(ierr);
895       if (flg) {
896         KSP      *subksps;
897         ierr = PCFieldSplitGetSubKSP(pc,PETSC_NULL,&subksps);CHKERRQ(ierr);
898         ierr = KSPGetPC(subksps[0],&pc);CHKERRQ(ierr);
899         ierr = PetscFree(subksps);CHKERRQ(ierr);
900         ierr = PetscTypeCompare((PetscObject)pc,PCBJACOBI,&flg);CHKERRQ(ierr);
901         if (flg) {
902           PetscInt       n,N = 101*101,j,cnts[3] = {0,0,0};
903           const PetscInt *ii;
904 
905           ierr = ISGetSize(IS_inact,&n);CHKERRQ(ierr);
906           ierr = ISGetIndices(IS_inact,&ii);CHKERRQ(ierr);
907           for (j=0; j<n; j++) {
908             if (ii[j] < N) cnts[0]++;
909             else if (ii[j] < 2*N) cnts[1]++;
910             else if (ii[j] < 3*N) cnts[2]++;
911           }
912           ierr = ISRestoreIndices(IS_inact,&ii);CHKERRQ(ierr);
913 
914           ierr = PCBJacobiSetTotalBlocks(pc,3,cnts);CHKERRQ(ierr);
915         }
916       }
917     }
918 
919     ierr = SNES_KSPSolve(snes,snes->ksp,F_inact,Y_inact);CHKERRQ(ierr);
920     ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr);
921     if (kspreason < 0) {
922       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
923         ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr);
924         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
925         break;
926       }
927      }
928 
929     ierr = VecScatterBegin(scat_act,Y_act,Y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
930     ierr = VecScatterEnd(scat_act,Y_act,Y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
931     ierr = VecScatterBegin(scat_inact,Y_inact,Y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
932     ierr = VecScatterEnd(scat_inact,Y_inact,Y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
933 
934     ierr = VecDestroy(&F_inact);CHKERRQ(ierr);
935     ierr = VecDestroy(&Y_act);CHKERRQ(ierr);
936     ierr = VecDestroy(&Y_inact);CHKERRQ(ierr);
937     ierr = VecScatterDestroy(&scat_act);CHKERRQ(ierr);
938     ierr = VecScatterDestroy(&scat_inact);CHKERRQ(ierr);
939     ierr = ISDestroy(&IS_act);CHKERRQ(ierr);
940     if (!isequal) {
941       ierr = ISDestroy(&vi->IS_inact_prev);CHKERRQ(ierr);
942       ierr = ISDuplicate(IS_inact,&vi->IS_inact_prev);CHKERRQ(ierr);
943     }
944     ierr = ISDestroy(&IS_inact);CHKERRQ(ierr);
945     ierr = MatDestroy(&jac_inact_inact);CHKERRQ(ierr);
946     if (snes->jacobian != snes->jacobian_pre) {
947       ierr = MatDestroy(&prejac_inact_inact);CHKERRQ(ierr);
948     }
949     ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr);
950     snes->linear_its += lits;
951     ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr);
952     /*
953     if (vi->precheckstep) {
954       PetscBool changed_y = PETSC_FALSE;
955       ierr = (*vi->precheckstep)(snes,X,Y,vi->precheck,&changed_y);CHKERRQ(ierr);
956     }
957 
958     if (PetscLogPrintInfo){
959       ierr = SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr);
960     }
961     */
962     /* Compute a (scaled) negative update in the line search routine:
963          Y <- X - lambda*Y
964        and evaluate G = function(Y) (depends on the line search).
965     */
966     ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr);
967     ynorm = 1; gnorm = fnorm;
968     ierr = (*vi->LineSearch)(snes,vi->lsP,X,F,G,Y,W,fnorm,xnorm,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
969     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",fnorm,gnorm,ynorm,(int)lssucceed);CHKERRQ(ierr);
970     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
971     if (snes->domainerror) {
972       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
973       PetscFunctionReturn(0);
974     }
975     if (!lssucceed) {
976       if (++snes->numFailures >= snes->maxFailures) {
977 	PetscBool ismin;
978         snes->reason = SNES_DIVERGED_LINE_SEARCH;
979         ierr = SNESVICheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr);
980         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
981         break;
982       }
983     }
984     /* Update function and solution vectors */
985     fnorm = gnorm;
986     ierr = VecCopy(G,F);CHKERRQ(ierr);
987     ierr = VecCopy(W,X);CHKERRQ(ierr);
988     /* Monitor convergence */
989     ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
990     snes->iter = i+1;
991     snes->norm = fnorm;
992     ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
993     SNESLogConvHistory(snes,snes->norm,lits);
994     ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr);
995     /* Test for convergence, xnorm = || X || */
996     if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); }
997     ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
998     if (snes->reason) break;
999   }
1000   if (i == maxits) {
1001     ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr);
1002     if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
1003   }
1004   PetscFunctionReturn(0);
1005 }
1006 
1007 #undef __FUNCT__
1008 #define __FUNCT__ "SNESVISetRedundancyCheck"
1009 PetscErrorCode SNESVISetRedundancyCheck(SNES snes,PetscErrorCode (*func)(SNES,IS,IS*,void*),void *ctx)
1010 {
1011   SNES_VI         *vi = (SNES_VI*)snes->data;
1012 
1013   PetscFunctionBegin;
1014   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
1015   vi->checkredundancy = func;
1016   vi->ctxP            = ctx;
1017   PetscFunctionReturn(0);
1018 }
1019 
1020 #if defined(PETSC_HAVE_MATLAB_ENGINE)
1021 #include <engine.h>
1022 #include <mex.h>
1023 typedef struct {char *funcname; mxArray *ctx;} SNESMatlabContext;
1024 
1025 #undef __FUNCT__
1026 #define __FUNCT__ "SNESVIRedundancyCheck_Matlab"
1027 PetscErrorCode SNESVIRedundancyCheck_Matlab(SNES snes,IS is_act,IS* is_redact,void* ctx)
1028 {
1029   PetscErrorCode      ierr;
1030   SNESMatlabContext   *sctx = (SNESMatlabContext*)ctx;
1031   int                 nlhs = 1, nrhs = 5;
1032   mxArray             *plhs[1], *prhs[5];
1033   long long int       l1 = 0, l2 = 0, ls = 0;
1034   PetscInt            *indices=PETSC_NULL;
1035 
1036   PetscFunctionBegin;
1037   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
1038   PetscValidHeaderSpecific(is_act,IS_CLASSID,2);
1039   PetscValidPointer(is_redact,3);
1040   PetscCheckSameComm(snes,1,is_act,2);
1041 
1042   /* Create IS for reduced active set of size 0, its size and indices will
1043    bet set by the Matlab function */
1044   ierr = ISCreateGeneral(((PetscObject)snes)->comm,0,indices,PETSC_OWN_POINTER,is_redact);CHKERRQ(ierr);
1045   /* call Matlab function in ctx */
1046   ierr = PetscMemcpy(&ls,&snes,sizeof(snes));CHKERRQ(ierr);
1047   ierr = PetscMemcpy(&l1,&is_act,sizeof(is_act));CHKERRQ(ierr);
1048   ierr = PetscMemcpy(&l2,is_redact,sizeof(is_act));CHKERRQ(ierr);
1049   prhs[0] = mxCreateDoubleScalar((double)ls);
1050   prhs[1] = mxCreateDoubleScalar((double)l1);
1051   prhs[2] = mxCreateDoubleScalar((double)l2);
1052   prhs[3] = mxCreateString(sctx->funcname);
1053   prhs[4] = sctx->ctx;
1054   ierr    = mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscSNESVIRedundancyCheckInternal");CHKERRQ(ierr);
1055   ierr    = mxGetScalar(plhs[0]);CHKERRQ(ierr);
1056   mxDestroyArray(prhs[0]);
1057   mxDestroyArray(prhs[1]);
1058   mxDestroyArray(prhs[2]);
1059   mxDestroyArray(prhs[3]);
1060   mxDestroyArray(plhs[0]);
1061   PetscFunctionReturn(0);
1062 }
1063 
1064 #undef __FUNCT__
1065 #define __FUNCT__ "SNESVISetRedundancyCheckMatlab"
1066 PetscErrorCode SNESVISetRedundancyCheckMatlab(SNES snes,const char* func,mxArray* ctx)
1067 {
1068   PetscErrorCode      ierr;
1069   SNESMatlabContext   *sctx;
1070 
1071   PetscFunctionBegin;
1072   /* currently sctx is memory bleed */
1073   ierr = PetscMalloc(sizeof(SNESMatlabContext),&sctx);CHKERRQ(ierr);
1074   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
1075   sctx->ctx = mxDuplicateArray(ctx);
1076   ierr = SNESVISetRedundancyCheck(snes,SNESVIRedundancyCheck_Matlab,sctx);CHKERRQ(ierr);
1077   PetscFunctionReturn(0);
1078 }
1079 
1080 #endif
1081 
1082 
1083 /* Variational Inequality solver using augmented space method. It does the opposite of the
1084    reduced space method i.e. it identifies the active set variables and instead of discarding
1085    them it augments the original system by introducing additional equality
1086    constraint equations for active set variables. The user can optionally provide an IS for
1087    a subset of 'redundant' active set variables which will treated as free variables.
1088    Specific implementation for Allen-Cahn problem
1089 */
1090 #undef __FUNCT__
1091 #define __FUNCT__ "SNESSolveVI_RS2"
1092 PetscErrorCode SNESSolveVI_RS2(SNES snes)
1093 {
1094   SNES_VI          *vi = (SNES_VI*)snes->data;
1095   PetscErrorCode    ierr;
1096   PetscInt          maxits,i,lits;
1097   PetscBool         lssucceed;
1098   MatStructure      flg = DIFFERENT_NONZERO_PATTERN;
1099   PetscReal         fnorm,gnorm,xnorm=0,ynorm;
1100   Vec                Y,X,F,G,W;
1101   KSPConvergedReason kspreason;
1102 
1103   PetscFunctionBegin;
1104   snes->numFailures            = 0;
1105   snes->numLinearSolveFailures = 0;
1106   snes->reason                 = SNES_CONVERGED_ITERATING;
1107 
1108   maxits	= snes->max_its;	/* maximum number of iterations */
1109   X		= snes->vec_sol;	/* solution vector */
1110   F		= snes->vec_func;	/* residual vector */
1111   Y		= snes->work[0];	/* work vectors */
1112   G		= snes->work[1];
1113   W		= snes->work[2];
1114 
1115   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1116   snes->iter = 0;
1117   snes->norm = 0.0;
1118   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1119 
1120   ierr = SNESVIProjectOntoBounds(snes,X);CHKERRQ(ierr);
1121   ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);
1122   if (snes->domainerror) {
1123     snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
1124     PetscFunctionReturn(0);
1125   }
1126   ierr = SNESVIComputeInactiveSetFnorm(snes,F,X,&fnorm);CHKERRQ(ierr);
1127   ierr = VecNormBegin(X,NORM_2,&xnorm);CHKERRQ(ierr);	/* xnorm <- ||x||  */
1128   ierr = VecNormEnd(X,NORM_2,&xnorm);CHKERRQ(ierr);
1129   if (PetscIsInfOrNanReal(fnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1130 
1131   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1132   snes->norm = fnorm;
1133   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1134   SNESLogConvHistory(snes,fnorm,0);
1135   ierr = SNESMonitor(snes,0,fnorm);CHKERRQ(ierr);
1136 
1137   /* set parameter for default relative tolerance convergence test */
1138   snes->ttol = fnorm*snes->rtol;
1139   /* test convergence */
1140   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
1141   if (snes->reason) PetscFunctionReturn(0);
1142 
1143   for (i=0; i<maxits; i++) {
1144     IS             IS_act,IS_inact; /* _act -> active set _inact -> inactive set */
1145     IS             IS_redact; /* redundant active set */
1146     Mat            J_aug,Jpre_aug;
1147     Vec            F_aug,Y_aug;
1148     PetscInt       nis_redact,nis_act;
1149     const PetscInt *idx_redact,*idx_act;
1150     PetscInt       k;
1151     PetscInt       *idx_actkept=PETSC_NULL,nkept=0; /* list of kept active set */
1152     PetscScalar    *f,*f2;
1153     PetscBool      isequal;
1154     PetscInt       i1=0,j1=0;
1155 
1156     /* Call general purpose update function */
1157     if (snes->ops->update) {
1158       ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
1159     }
1160     ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr);
1161 
1162     /* Create active and inactive index sets */
1163     ierr = SNESVICreateIndexSets_RS(snes,X,F,&IS_act,&IS_inact);CHKERRQ(ierr);
1164 
1165     /* Get local active set size */
1166     ierr = ISGetLocalSize(IS_act,&nis_act);CHKERRQ(ierr);
1167     ierr = ISGetIndices(IS_act,&idx_act);CHKERRQ(ierr);
1168     if(nis_act) {
1169       if(vi->checkredundancy) {
1170 	(*vi->checkredundancy)(snes,IS_act,&IS_redact,vi->ctxP);
1171       }
1172 
1173       if(!IS_redact) {
1174 	/* User called checkredundancy function but didn't create IS_redact because
1175            there were no redundant active set variables */
1176 	/* Copy over all active set indices to the list */
1177 	ierr = PetscMalloc(nis_act*sizeof(PetscInt),&idx_actkept);CHKERRQ(ierr);
1178 	for(k=0;k < nis_act;k++) idx_actkept[k] = idx_act[k];
1179 	nkept = nis_act;
1180       } else {
1181 	ierr = ISGetLocalSize(IS_redact,&nis_redact);CHKERRQ(ierr);
1182 	ierr = PetscMalloc((nis_act-nis_redact)*sizeof(PetscInt),&idx_actkept);CHKERRQ(ierr);
1183 
1184 	/* Create reduced active set list */
1185 	ierr = ISGetIndices(IS_act,&idx_act);CHKERRQ(ierr);
1186 	ierr = ISGetIndices(IS_redact,&idx_redact);CHKERRQ(ierr);
1187 	j1 = 0;nkept = 0;
1188 	for(k=0;k<nis_act;k++) {
1189 	  if(j1 < nis_redact && idx_act[k] == idx_redact[j1]) j1++;
1190 	  else idx_actkept[nkept++] = idx_act[k];
1191 	}
1192 	ierr = ISRestoreIndices(IS_act,&idx_act);CHKERRQ(ierr);
1193 	ierr = ISRestoreIndices(IS_redact,&idx_redact);CHKERRQ(ierr);
1194 
1195         ierr = ISDestroy(&IS_redact);CHKERRQ(ierr);
1196       }
1197 
1198       /* Create augmented F and Y */
1199       ierr = VecCreate(((PetscObject)snes)->comm,&F_aug);CHKERRQ(ierr);
1200       ierr = VecSetSizes(F_aug,F->map->n+nkept,PETSC_DECIDE);CHKERRQ(ierr);
1201       ierr = VecSetFromOptions(F_aug);CHKERRQ(ierr);
1202       ierr = VecDuplicate(F_aug,&Y_aug);CHKERRQ(ierr);
1203 
1204       /* Copy over F to F_aug in the first n locations */
1205       ierr = VecGetArray(F,&f);CHKERRQ(ierr);
1206       ierr = VecGetArray(F_aug,&f2);CHKERRQ(ierr);
1207       ierr = PetscMemcpy(f2,f,F->map->n*sizeof(PetscScalar));CHKERRQ(ierr);
1208       ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
1209       ierr = VecRestoreArray(F_aug,&f2);CHKERRQ(ierr);
1210 
1211       /* Create the augmented jacobian matrix */
1212       ierr = MatCreate(((PetscObject)snes)->comm,&J_aug);CHKERRQ(ierr);
1213       ierr = MatSetSizes(J_aug,X->map->n+nkept,X->map->n+nkept,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
1214       ierr = MatSetFromOptions(J_aug);CHKERRQ(ierr);
1215 
1216 
1217       { /* local vars */
1218       /* Preallocate augmented matrix and set values in it...Doing only sequential case first*/
1219       PetscInt          ncols;
1220       const PetscInt    *cols;
1221       const PetscScalar *vals;
1222       PetscScalar        value=1.0;
1223       PetscInt           row,col;
1224       PetscInt           *d_nnz;
1225 
1226       ierr = PetscMalloc((X->map->n+nkept)*sizeof(PetscInt),&d_nnz);CHKERRQ(ierr);
1227       ierr = PetscMemzero(d_nnz,(X->map->n+nkept)*sizeof(PetscInt));CHKERRQ(ierr);
1228       for(row=0;row<snes->jacobian->rmap->n;row++) {
1229         ierr = MatGetRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1230         d_nnz[row] += ncols;
1231         ierr = MatRestoreRow(snes->jacobian,row,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
1232       }
1233 
1234       for(k=0;k<nkept;k++) {
1235         d_nnz[idx_actkept[k]] += 1;
1236         d_nnz[snes->jacobian->rmap->n+k] += 1;
1237       }
1238       ierr = MatSeqAIJSetPreallocation(J_aug,PETSC_NULL,d_nnz);CHKERRQ(ierr);
1239 
1240       ierr = PetscFree(d_nnz);CHKERRQ(ierr);
1241 
1242       /* Set the original jacobian matrix in J_aug */
1243       for(row=0;row<snes->jacobian->rmap->n;row++) {
1244 	ierr = MatGetRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1245 	ierr = MatSetValues(J_aug,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
1246 	ierr = MatRestoreRow(snes->jacobian,row,&ncols,&cols,&vals);CHKERRQ(ierr);
1247       }
1248       /* Add the augmented part */
1249       for(k=0;k<nkept;k++) {
1250 	row = idx_actkept[k];
1251 	col = snes->jacobian->rmap->n+k;
1252 	ierr = MatSetValues(J_aug,1,&row,1,&col,&value,INSERT_VALUES);CHKERRQ(ierr);
1253 	ierr = MatSetValues(J_aug,1,&col,1,&row,&value,INSERT_VALUES);CHKERRQ(ierr);
1254       }
1255       ierr = MatAssemblyBegin(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1256       ierr = MatAssemblyEnd(J_aug,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1257       /* Only considering prejac = jac for now */
1258       Jpre_aug = J_aug;
1259       } /* local vars*/
1260     } else {
1261       F_aug = F; J_aug = snes->jacobian; Y_aug = Y; Jpre_aug = snes->jacobian_pre;
1262     }
1263 
1264     ierr = ISEqual(vi->IS_inact_prev,IS_inact,&isequal);CHKERRQ(ierr);
1265     if (!isequal) {
1266       ierr = SNESVIResetPCandKSP(snes,J_aug,Jpre_aug);CHKERRQ(ierr);
1267     }
1268     ierr = KSPSetOperators(snes->ksp,J_aug,Jpre_aug,flg);CHKERRQ(ierr);
1269     ierr = KSPSetUp(snes->ksp);CHKERRQ(ierr);
1270     /*  {
1271       PC        pc;
1272       PetscBool flg;
1273       ierr = KSPGetPC(snes->ksp,&pc);CHKERRQ(ierr);
1274       ierr = PetscTypeCompare((PetscObject)pc,PCFIELDSPLIT,&flg);CHKERRQ(ierr);
1275       if (flg) {
1276         KSP      *subksps;
1277         ierr = PCFieldSplitGetSubKSP(pc,PETSC_NULL,&subksps);CHKERRQ(ierr);
1278         ierr = KSPGetPC(subksps[0],&pc);CHKERRQ(ierr);
1279         ierr = PetscFree(subksps);CHKERRQ(ierr);
1280         ierr = PetscTypeCompare((PetscObject)pc,PCBJACOBI,&flg);CHKERRQ(ierr);
1281         if (flg) {
1282           PetscInt       n,N = 101*101,j,cnts[3] = {0,0,0};
1283           const PetscInt *ii;
1284 
1285           ierr = ISGetSize(IS_inact,&n);CHKERRQ(ierr);
1286           ierr = ISGetIndices(IS_inact,&ii);CHKERRQ(ierr);
1287           for (j=0; j<n; j++) {
1288             if (ii[j] < N) cnts[0]++;
1289             else if (ii[j] < 2*N) cnts[1]++;
1290             else if (ii[j] < 3*N) cnts[2]++;
1291           }
1292           ierr = ISRestoreIndices(IS_inact,&ii);CHKERRQ(ierr);
1293 
1294           ierr = PCBJacobiSetTotalBlocks(pc,3,cnts);CHKERRQ(ierr);
1295         }
1296       }
1297     }
1298     */
1299     ierr = SNES_KSPSolve(snes,snes->ksp,F_aug,Y_aug);CHKERRQ(ierr);
1300     ierr = KSPGetConvergedReason(snes->ksp,&kspreason);CHKERRQ(ierr);
1301     if (kspreason < 0) {
1302       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
1303         ierr = PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);CHKERRQ(ierr);
1304         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
1305         break;
1306       }
1307     }
1308 
1309     if(nis_act) {
1310       PetscScalar *y1,*y2;
1311       ierr = VecGetArray(Y,&y1);CHKERRQ(ierr);
1312       ierr = VecGetArray(Y_aug,&y2);CHKERRQ(ierr);
1313       /* Copy over inactive Y_aug to Y */
1314       j1 = 0;
1315       for(i1=Y->map->rstart;i1 < Y->map->rend;i1++) {
1316 	if(j1 < nkept && idx_actkept[j1] == i1) j1++;
1317 	else y1[i1-Y->map->rstart] = y2[i1-Y->map->rstart];
1318       }
1319       ierr = VecRestoreArray(Y,&y1);CHKERRQ(ierr);
1320       ierr = VecRestoreArray(Y_aug,&y2);CHKERRQ(ierr);
1321 
1322       ierr = VecDestroy(&F_aug);CHKERRQ(ierr);
1323       ierr = VecDestroy(&Y_aug);CHKERRQ(ierr);
1324       ierr = MatDestroy(&J_aug);CHKERRQ(ierr);
1325       ierr = PetscFree(idx_actkept);CHKERRQ(ierr);
1326     }
1327 
1328     if (!isequal) {
1329       ierr = ISDestroy(&vi->IS_inact_prev);CHKERRQ(ierr);
1330       ierr = ISDuplicate(IS_inact,&vi->IS_inact_prev);CHKERRQ(ierr);
1331     }
1332     ierr = ISDestroy(&IS_inact);CHKERRQ(ierr);
1333 
1334     ierr = KSPGetIterationNumber(snes->ksp,&lits);CHKERRQ(ierr);
1335     snes->linear_its += lits;
1336     ierr = PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);CHKERRQ(ierr);
1337     /*
1338     if (vi->precheckstep) {
1339       PetscBool changed_y = PETSC_FALSE;
1340       ierr = (*vi->precheckstep)(snes,X,Y,vi->precheck,&changed_y);CHKERRQ(ierr);
1341     }
1342 
1343     if (PetscLogPrintInfo){
1344       ierr = SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);CHKERRQ(ierr);
1345     }
1346     */
1347     /* Compute a (scaled) negative update in the line search routine:
1348          Y <- X - lambda*Y
1349        and evaluate G = function(Y) (depends on the line search).
1350     */
1351     ierr = VecCopy(Y,snes->vec_sol_update);CHKERRQ(ierr);
1352     ynorm = 1; gnorm = fnorm;
1353     ierr = (*vi->LineSearch)(snes,vi->lsP,X,F,G,Y,W,fnorm,xnorm,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
1354     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",fnorm,gnorm,ynorm,(int)lssucceed);CHKERRQ(ierr);
1355     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
1356     if (snes->domainerror) {
1357       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
1358       PetscFunctionReturn(0);
1359     }
1360     if (!lssucceed) {
1361       if (++snes->numFailures >= snes->maxFailures) {
1362 	PetscBool ismin;
1363         snes->reason = SNES_DIVERGED_LINE_SEARCH;
1364         ierr = SNESVICheckLocalMin_Private(snes,snes->jacobian,G,W,gnorm,&ismin);CHKERRQ(ierr);
1365         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
1366         break;
1367       }
1368     }
1369     /* Update function and solution vectors */
1370     fnorm = gnorm;
1371     ierr = VecCopy(G,F);CHKERRQ(ierr);
1372     ierr = VecCopy(W,X);CHKERRQ(ierr);
1373     /* Monitor convergence */
1374     ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
1375     snes->iter = i+1;
1376     snes->norm = fnorm;
1377     ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
1378     SNESLogConvHistory(snes,snes->norm,lits);
1379     ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr);
1380     /* Test for convergence, xnorm = || X || */
1381     if (snes->ops->converged != SNESSkipConverged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); }
1382     ierr = (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
1383     if (snes->reason) break;
1384   }
1385   if (i == maxits) {
1386     ierr = PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);CHKERRQ(ierr);
1387     if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
1388   }
1389   PetscFunctionReturn(0);
1390 }
1391 
1392 /* -------------------------------------------------------------------------- */
1393 /*
1394    SNESSetUp_VI - Sets up the internal data structures for the later use
1395    of the SNESVI nonlinear solver.
1396 
1397    Input Parameter:
1398 .  snes - the SNES context
1399 .  x - the solution vector
1400 
1401    Application Interface Routine: SNESSetUp()
1402 
1403    Notes:
1404    For basic use of the SNES solvers, the user need not explicitly call
1405    SNESSetUp(), since these actions will automatically occur during
1406    the call to SNESSolve().
1407  */
1408 #undef __FUNCT__
1409 #define __FUNCT__ "SNESSetUp_VI"
1410 PetscErrorCode SNESSetUp_VI(SNES snes)
1411 {
1412   PetscErrorCode ierr;
1413   SNES_VI        *vi = (SNES_VI*) snes->data;
1414   PetscInt       i_start[3],i_end[3];
1415 
1416   PetscFunctionBegin;
1417 
1418   ierr = SNESDefaultGetWork(snes,3);CHKERRQ(ierr);
1419 
1420   /* If the lower and upper bound on variables are not set, set it to
1421      -Inf and Inf */
1422   if (!vi->xl && !vi->xu) {
1423     vi->usersetxbounds = PETSC_FALSE;
1424     ierr = VecDuplicate(snes->vec_sol, &vi->xl); CHKERRQ(ierr);
1425     ierr = VecSet(vi->xl,SNES_VI_NINF);CHKERRQ(ierr);
1426     ierr = VecDuplicate(snes->vec_sol, &vi->xu); CHKERRQ(ierr);
1427     ierr = VecSet(vi->xu,SNES_VI_INF);CHKERRQ(ierr);
1428   } else {
1429     /* Check if lower bound, upper bound and solution vector distribution across the processors is identical */
1430     ierr = VecGetOwnershipRange(snes->vec_sol,i_start,i_end);CHKERRQ(ierr);
1431     ierr = VecGetOwnershipRange(vi->xl,i_start+1,i_end+1);CHKERRQ(ierr);
1432     ierr = VecGetOwnershipRange(vi->xu,i_start+2,i_end+2);CHKERRQ(ierr);
1433     if ((i_start[0] != i_start[1]) || (i_start[0] != i_start[2]) || (i_end[0] != i_end[1]) || (i_end[0] != i_end[2]))
1434       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Distribution of lower bound, upper bound and the solution vector should be identical across all the processors.");
1435   }
1436   if (snes->ops->solve != SNESSolveVI_SS) {
1437     /* Set up previous active index set for the first snes solve
1438        vi->IS_inact_prev = 0,1,2,....N */
1439     PetscInt *indices;
1440     PetscInt  i,n,rstart,rend;
1441 
1442     ierr = VecGetOwnershipRange(snes->vec_sol,&rstart,&rend);CHKERRQ(ierr);
1443     ierr = VecGetLocalSize(snes->vec_sol,&n);CHKERRQ(ierr);
1444     ierr = PetscMalloc(n*sizeof(PetscInt),&indices);CHKERRQ(ierr);
1445     for(i=0;i < n; i++) indices[i] = rstart + i;
1446     ierr = ISCreateGeneral(((PetscObject)snes)->comm,n,indices,PETSC_OWN_POINTER,&vi->IS_inact_prev);
1447   }
1448 
1449   if (snes->ops->solve == SNESSolveVI_SS) {
1450     ierr = VecDuplicate(snes->vec_sol, &vi->dpsi);CHKERRQ(ierr);
1451     ierr = VecDuplicate(snes->vec_sol, &vi->phi); CHKERRQ(ierr);
1452     ierr = VecDuplicate(snes->vec_sol, &vi->Da); CHKERRQ(ierr);
1453     ierr = VecDuplicate(snes->vec_sol, &vi->Db); CHKERRQ(ierr);
1454     ierr = VecDuplicate(snes->vec_sol, &vi->z);CHKERRQ(ierr);
1455     ierr = VecDuplicate(snes->vec_sol, &vi->t); CHKERRQ(ierr);
1456   }
1457   PetscFunctionReturn(0);
1458 }
1459 /* -------------------------------------------------------------------------- */
1460 /*
1461    SNESDestroy_VI - Destroys the private SNES_VI context that was created
1462    with SNESCreate_VI().
1463 
1464    Input Parameter:
1465 .  snes - the SNES context
1466 
1467    Application Interface Routine: SNESDestroy()
1468  */
1469 #undef __FUNCT__
1470 #define __FUNCT__ "SNESDestroy_VI"
1471 PetscErrorCode SNESDestroy_VI(SNES snes)
1472 {
1473   SNES_VI        *vi = (SNES_VI*) snes->data;
1474   PetscErrorCode ierr;
1475 
1476   PetscFunctionBegin;
1477   if (snes->ops->solve != SNESSolveVI_SS) {
1478     ierr = ISDestroy(&vi->IS_inact_prev);
1479   }
1480 
1481   if (snes->ops->solve == SNESSolveVI_SS) {
1482     /* clear vectors */
1483     ierr = VecDestroy(&vi->dpsi);CHKERRQ(ierr);
1484     ierr = VecDestroy(&vi->phi); CHKERRQ(ierr);
1485     ierr = VecDestroy(&vi->Da); CHKERRQ(ierr);
1486     ierr = VecDestroy(&vi->Db); CHKERRQ(ierr);
1487     ierr = VecDestroy(&vi->z); CHKERRQ(ierr);
1488     ierr = VecDestroy(&vi->t); CHKERRQ(ierr);
1489   }
1490 
1491   if (!vi->usersetxbounds) {
1492     ierr = VecDestroy(&vi->xl); CHKERRQ(ierr);
1493     ierr = VecDestroy(&vi->xu); CHKERRQ(ierr);
1494   }
1495 
1496   ierr = PetscViewerASCIIMonitorDestroy(&vi->lsmonitor);CHKERRQ(ierr);
1497   ierr = PetscFree(snes->data);CHKERRQ(ierr);
1498 
1499   /* clear composed functions */
1500   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","",PETSC_NULL);CHKERRQ(ierr);
1501   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","",PETSC_NULL);CHKERRQ(ierr);
1502   PetscFunctionReturn(0);
1503 }
1504 
1505 /* -------------------------------------------------------------------------- */
1506 #undef __FUNCT__
1507 #define __FUNCT__ "SNESLineSearchNo_VI"
1508 
1509 /*
1510   This routine does not actually do a line search but it takes a full newton
1511   step while ensuring that the new iterates remain within the constraints.
1512 
1513 */
1514 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)
1515 {
1516   PetscErrorCode ierr;
1517   SNES_VI        *vi = (SNES_VI*)snes->data;
1518   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1519 
1520   PetscFunctionBegin;
1521   *flag = PETSC_TRUE;
1522   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1523   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);         /* ynorm = || y || */
1524   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1525   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1526   if (vi->postcheckstep) {
1527    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1528   }
1529   if (changed_y) {
1530     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1531     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1532   }
1533   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1534   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1535   if (!snes->domainerror) {
1536     if (snes->ops->solve != SNESSolveVI_SS) {
1537        ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1538     } else {
1539       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);  /* gnorm = || g || */
1540     }
1541     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1542   }
1543   if (vi->lsmonitor) {
1544     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1545   }
1546   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1547   PetscFunctionReturn(0);
1548 }
1549 
1550 /* -------------------------------------------------------------------------- */
1551 #undef __FUNCT__
1552 #define __FUNCT__ "SNESLineSearchNoNorms_VI"
1553 
1554 /*
1555   This routine is a copy of SNESLineSearchNoNorms in snes/impls/ls/ls.c
1556 */
1557 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)
1558 {
1559   PetscErrorCode ierr;
1560   SNES_VI        *vi = (SNES_VI*)snes->data;
1561   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1562 
1563   PetscFunctionBegin;
1564   *flag = PETSC_TRUE;
1565   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1566   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y      */
1567   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1568   if (vi->postcheckstep) {
1569    ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1570   }
1571   if (changed_y) {
1572     ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
1573     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1574   }
1575 
1576   /* don't evaluate function the last time through */
1577   if (snes->iter < snes->max_its-1) {
1578     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1579   }
1580   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1581   PetscFunctionReturn(0);
1582 }
1583 
1584 /* -------------------------------------------------------------------------- */
1585 #undef __FUNCT__
1586 #define __FUNCT__ "SNESLineSearchCubic_VI"
1587 /*
1588   This routine implements a cubic line search while doing a projection on the variable bounds
1589 */
1590 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)
1591 {
1592   PetscReal      initslope,lambdaprev,gnormprev,a,b,d,t1,t2,rellength;
1593   PetscReal      minlambda,lambda,lambdatemp;
1594 #if defined(PETSC_USE_COMPLEX)
1595   PetscScalar    cinitslope;
1596 #endif
1597   PetscErrorCode ierr;
1598   PetscInt       count;
1599   SNES_VI        *vi = (SNES_VI*)snes->data;
1600   PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1601   MPI_Comm       comm;
1602 
1603   PetscFunctionBegin;
1604   ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr);
1605   ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1606   *flag   = PETSC_TRUE;
1607 
1608   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1609   if (*ynorm == 0.0) {
1610     if (vi->lsmonitor) {
1611       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Initial direction and size is 0\n");CHKERRQ(ierr);
1612     }
1613     *gnorm = fnorm;
1614     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1615     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1616     *flag  = PETSC_FALSE;
1617     goto theend1;
1618   }
1619   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1620     if (vi->lsmonitor) {
1621       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Scaling step by %G old ynorm %G\n",vi->maxstep/(*ynorm),*ynorm);CHKERRQ(ierr);
1622     }
1623     ierr = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1624     *ynorm = vi->maxstep;
1625   }
1626   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1627   minlambda = vi->minlambda/rellength;
1628   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1629 #if defined(PETSC_USE_COMPLEX)
1630   ierr = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1631   initslope = PetscRealPart(cinitslope);
1632 #else
1633   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1634 #endif
1635   if (initslope > 0.0)  initslope = -initslope;
1636   if (initslope == 0.0) initslope = -1.0;
1637 
1638   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1639   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1640   if (snes->nfuncs >= snes->max_funcs) {
1641     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1642     *flag = PETSC_FALSE;
1643     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1644     goto theend1;
1645   }
1646   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1647   if (snes->ops->solve != SNESSolveVI_SS) {
1648     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1649   } else {
1650     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1651   }
1652   if (snes->domainerror) {
1653     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1654     PetscFunctionReturn(0);
1655   }
1656   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1657   ierr = PetscInfo2(snes,"Initial fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1658   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1659     if (vi->lsmonitor) {
1660       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1661     }
1662     goto theend1;
1663   }
1664 
1665   /* Fit points with quadratic */
1666   lambda     = 1.0;
1667   lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1668   lambdaprev = lambda;
1669   gnormprev  = *gnorm;
1670   if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1671   if (lambdatemp <= .1*lambda) lambda = .1*lambda;
1672   else                         lambda = lambdatemp;
1673 
1674   ierr  = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1675   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1676   if (snes->nfuncs >= snes->max_funcs) {
1677     ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while attempting quadratic backtracking! %D \n",snes->nfuncs);CHKERRQ(ierr);
1678     *flag = PETSC_FALSE;
1679     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1680     goto theend1;
1681   }
1682   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1683   if (snes->ops->solve != SNESSolveVI_SS) {
1684     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1685   } else {
1686     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1687   }
1688   if (snes->domainerror) {
1689     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1690     PetscFunctionReturn(0);
1691   }
1692   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1693   if (vi->lsmonitor) {
1694     ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: gnorm after quadratic fit %G\n",*gnorm);CHKERRQ(ierr);
1695   }
1696   if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1697     if (vi->lsmonitor) {
1698       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Quadratically determined step, lambda=%18.16e\n",lambda);CHKERRQ(ierr);
1699     }
1700     goto theend1;
1701   }
1702 
1703   /* Fit points with cubic */
1704   count = 1;
1705   while (PETSC_TRUE) {
1706     if (lambda <= minlambda) {
1707       if (vi->lsmonitor) {
1708 	ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: unable to find good step length! After %D tries \n",count);CHKERRQ(ierr);
1709 	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);
1710       }
1711       *flag = PETSC_FALSE;
1712       break;
1713     }
1714     t1 = .5*((*gnorm)*(*gnorm) - fnorm*fnorm) - lambda*initslope;
1715     t2 = .5*(gnormprev*gnormprev  - fnorm*fnorm) - lambdaprev*initslope;
1716     a  = (t1/(lambda*lambda) - t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1717     b  = (-lambdaprev*t1/(lambda*lambda) + lambda*t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
1718     d  = b*b - 3*a*initslope;
1719     if (d < 0.0) d = 0.0;
1720     if (a == 0.0) {
1721       lambdatemp = -initslope/(2.0*b);
1722     } else {
1723       lambdatemp = (-b + sqrt(d))/(3.0*a);
1724     }
1725     lambdaprev = lambda;
1726     gnormprev  = *gnorm;
1727     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1728     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1729     else                         lambda     = lambdatemp;
1730     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1731     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1732     if (snes->nfuncs >= snes->max_funcs) {
1733       ierr = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1734       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);
1735       *flag = PETSC_FALSE;
1736       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1737       break;
1738     }
1739     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1740     if (snes->ops->solve != SNESSolveVI_SS) {
1741       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1742     } else {
1743       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1744     }
1745     if (snes->domainerror) {
1746       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1747       PetscFunctionReturn(0);
1748     }
1749     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1750     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* is reduction enough? */
1751       if (vi->lsmonitor) {
1752 	ierr = PetscPrintf(comm,"    Line search: Cubically determined step, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1753       }
1754       break;
1755     } else {
1756       if (vi->lsmonitor) {
1757         ierr = PetscPrintf(comm,"    Line search: Cubic step no good, shrinking lambda, current gnorm %G lambda=%18.16e\n",*gnorm,lambda);CHKERRQ(ierr);
1758       }
1759     }
1760     count++;
1761   }
1762   theend1:
1763   /* Optional user-defined check for line search step validity */
1764   if (vi->postcheckstep && *flag) {
1765     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1766     if (changed_y) {
1767       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1768       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1769     }
1770     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1771       ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1772       if (snes->ops->solve != SNESSolveVI_SS) {
1773         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1774       } else {
1775         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1776       }
1777       if (snes->domainerror) {
1778         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1779         PetscFunctionReturn(0);
1780       }
1781       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1782       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1783       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1784     }
1785   }
1786   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1787   PetscFunctionReturn(0);
1788 }
1789 
1790 #undef __FUNCT__
1791 #define __FUNCT__ "SNESLineSearchQuadratic_VI"
1792 /*
1793   This routine does a quadratic line search while keeping the iterates within the variable bounds
1794 */
1795 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)
1796 {
1797   /*
1798      Note that for line search purposes we work with with the related
1799      minimization problem:
1800         min  z(x):  R^n -> R,
1801      where z(x) = .5 * fnorm*fnorm,and fnorm = || f ||_2.
1802    */
1803   PetscReal      initslope,minlambda,lambda,lambdatemp,rellength;
1804 #if defined(PETSC_USE_COMPLEX)
1805   PetscScalar    cinitslope;
1806 #endif
1807   PetscErrorCode ierr;
1808   PetscInt       count;
1809   SNES_VI        *vi = (SNES_VI*)snes->data;
1810   PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
1811 
1812   PetscFunctionBegin;
1813   ierr    = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1814   *flag   = PETSC_TRUE;
1815 
1816   ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
1817   if (*ynorm == 0.0) {
1818     if (vi->lsmonitor) {
1819       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Direction and size is 0\n");CHKERRQ(ierr);
1820     }
1821     *gnorm = fnorm;
1822     ierr   = VecCopy(x,w);CHKERRQ(ierr);
1823     ierr   = VecCopy(f,g);CHKERRQ(ierr);
1824     *flag  = PETSC_FALSE;
1825     goto theend2;
1826   }
1827   if (*ynorm > vi->maxstep) {	/* Step too big, so scale back */
1828     ierr   = VecScale(y,vi->maxstep/(*ynorm));CHKERRQ(ierr);
1829     *ynorm = vi->maxstep;
1830   }
1831   ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
1832   minlambda = vi->minlambda/rellength;
1833   ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
1834 #if defined(PETSC_USE_COMPLEX)
1835   ierr      = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
1836   initslope = PetscRealPart(cinitslope);
1837 #else
1838   ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
1839 #endif
1840   if (initslope > 0.0)  initslope = -initslope;
1841   if (initslope == 0.0) initslope = -1.0;
1842   ierr = PetscInfo1(snes,"Initslope %G \n",initslope);CHKERRQ(ierr);
1843 
1844   ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1845   ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1846   if (snes->nfuncs >= snes->max_funcs) {
1847     ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
1848     *flag = PETSC_FALSE;
1849     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1850     goto theend2;
1851   }
1852   ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1853   if (snes->ops->solve != SNESSolveVI_SS) {
1854     ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1855   } else {
1856     ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1857   }
1858   if (snes->domainerror) {
1859     ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1860     PetscFunctionReturn(0);
1861   }
1862   if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1863   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + vi->alpha*initslope) { /* Sufficient reduction */
1864     if (vi->lsmonitor) {
1865       ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line search: Using full step: fnorm %G gnorm %G\n",fnorm,*gnorm);CHKERRQ(ierr);
1866     }
1867     goto theend2;
1868   }
1869 
1870   /* Fit points with quadratic */
1871   lambda = 1.0;
1872   count = 1;
1873   while (PETSC_TRUE) {
1874     if (lambda <= minlambda) { /* bad luck; use full step */
1875       if (vi->lsmonitor) {
1876         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"Line search: Unable to find good step length! %D \n",count);CHKERRQ(ierr);
1877         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);
1878       }
1879       ierr = VecCopy(x,w);CHKERRQ(ierr);
1880       *flag = PETSC_FALSE;
1881       break;
1882     }
1883     lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
1884     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
1885     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
1886     else                         lambda     = lambdatemp;
1887 
1888     ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
1889     ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1890     if (snes->nfuncs >= snes->max_funcs) {
1891       ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
1892       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);
1893       *flag = PETSC_FALSE;
1894       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
1895       break;
1896     }
1897     ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
1898     if (snes->domainerror) {
1899       ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1900       PetscFunctionReturn(0);
1901     }
1902     if (snes->ops->solve != SNESSolveVI_SS) {
1903       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1904     } else {
1905       ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1906     }
1907     if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1908     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*vi->alpha*initslope) { /* sufficient reduction */
1909       if (vi->lsmonitor) {
1910         ierr = PetscViewerASCIIMonitorPrintf(vi->lsmonitor,"    Line Search: Quadratically determined step, lambda=%G\n",lambda);CHKERRQ(ierr);
1911       }
1912       break;
1913     }
1914     count++;
1915   }
1916   theend2:
1917   /* Optional user-defined check for line search step validity */
1918   if (vi->postcheckstep) {
1919     ierr = (*vi->postcheckstep)(snes,x,y,w,vi->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
1920     if (changed_y) {
1921       ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
1922       ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
1923     }
1924     if (changed_y || changed_w) { /* recompute the function if the step has changed */
1925       ierr = SNESComputeFunction(snes,w,g);
1926       if (snes->domainerror) {
1927         ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1928         PetscFunctionReturn(0);
1929       }
1930       if (snes->ops->solve != SNESSolveVI_SS) {
1931         ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
1932       } else {
1933         ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
1934       }
1935 
1936       ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
1937       ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
1938       if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
1939     }
1940   }
1941   ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
1942   PetscFunctionReturn(0);
1943 }
1944 
1945 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*/
1946 /* -------------------------------------------------------------------------- */
1947 EXTERN_C_BEGIN
1948 #undef __FUNCT__
1949 #define __FUNCT__ "SNESLineSearchSet_VI"
1950 PetscErrorCode  SNESLineSearchSet_VI(SNES snes,FCN2 func,void *lsctx)
1951 {
1952   PetscFunctionBegin;
1953   ((SNES_VI *)(snes->data))->LineSearch = func;
1954   ((SNES_VI *)(snes->data))->lsP        = lsctx;
1955   PetscFunctionReturn(0);
1956 }
1957 EXTERN_C_END
1958 
1959 /* -------------------------------------------------------------------------- */
1960 EXTERN_C_BEGIN
1961 #undef __FUNCT__
1962 #define __FUNCT__ "SNESLineSearchSetMonitor_VI"
1963 PetscErrorCode  SNESLineSearchSetMonitor_VI(SNES snes,PetscBool flg)
1964 {
1965   SNES_VI        *vi = (SNES_VI*)snes->data;
1966   PetscErrorCode ierr;
1967 
1968   PetscFunctionBegin;
1969   if (flg && !vi->lsmonitor) {
1970     ierr = PetscViewerASCIIMonitorCreate(((PetscObject)snes)->comm,"stdout",((PetscObject)snes)->tablevel,&vi->lsmonitor);CHKERRQ(ierr);
1971   } else if (!flg && vi->lsmonitor) {
1972     ierr = PetscViewerASCIIMonitorDestroy(&vi->lsmonitor);CHKERRQ(ierr);
1973   }
1974   PetscFunctionReturn(0);
1975 }
1976 EXTERN_C_END
1977 
1978 /*
1979    SNESView_VI - Prints info from the SNESVI data structure.
1980 
1981    Input Parameters:
1982 .  SNES - the SNES context
1983 .  viewer - visualization context
1984 
1985    Application Interface Routine: SNESView()
1986 */
1987 #undef __FUNCT__
1988 #define __FUNCT__ "SNESView_VI"
1989 static PetscErrorCode SNESView_VI(SNES snes,PetscViewer viewer)
1990 {
1991   SNES_VI        *vi = (SNES_VI *)snes->data;
1992   const char     *cstr,*tstr;
1993   PetscErrorCode ierr;
1994   PetscBool     iascii;
1995 
1996   PetscFunctionBegin;
1997   ierr = PetscTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1998   if (iascii) {
1999     if (vi->LineSearch == SNESLineSearchNo_VI)             cstr = "SNESLineSearchNo";
2000     else if (vi->LineSearch == SNESLineSearchQuadratic_VI) cstr = "SNESLineSearchQuadratic";
2001     else if (vi->LineSearch == SNESLineSearchCubic_VI)     cstr = "SNESLineSearchCubic";
2002     else                                                             cstr = "unknown";
2003     if (snes->ops->solve == SNESSolveVI_SS)      tstr = "Semismooth";
2004     else if (snes->ops->solve == SNESSolveVI_RS) tstr = "Reduced Space";
2005     else if (snes->ops->solve == SNESSolveVI_RS2) tstr = "Augmented Space";
2006     else                                         tstr = "unknown";
2007     ierr = PetscViewerASCIIPrintf(viewer,"  VI algorithm: %s\n",tstr);CHKERRQ(ierr);
2008     ierr = PetscViewerASCIIPrintf(viewer,"  line search variant: %s\n",cstr);CHKERRQ(ierr);
2009     ierr = PetscViewerASCIIPrintf(viewer,"  alpha=%G, maxstep=%G, minlambda=%G\n",vi->alpha,vi->maxstep,vi->minlambda);CHKERRQ(ierr);
2010   } else {
2011     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Viewer type %s not supported for SNES EQ VI",((PetscObject)viewer)->type_name);
2012   }
2013   PetscFunctionReturn(0);
2014 }
2015 
2016 #undef __FUNCT__
2017 #define __FUNCT__ "SNESVISetVariableBounds"
2018 /*@
2019    SNESVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu.
2020 
2021    Input Parameters:
2022 .  snes - the SNES context.
2023 .  xl   - lower bound.
2024 .  xu   - upper bound.
2025 
2026    Notes:
2027    If this routine is not called then the lower and upper bounds are set to
2028    SNES_VI_INF and SNES_VI_NINF respectively during SNESSetUp().
2029 
2030 @*/
2031 PetscErrorCode SNESVISetVariableBounds(SNES snes, Vec xl, Vec xu)
2032 {
2033   SNES_VI        *vi;
2034   PetscErrorCode ierr;
2035 
2036   PetscFunctionBegin;
2037   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
2038   PetscValidHeaderSpecific(xl,VEC_CLASSID,2);
2039   PetscValidHeaderSpecific(xu,VEC_CLASSID,3);
2040   if (!snes->vec_func) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call SNESSetFunction() first");
2041   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);
2042   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);
2043   ierr = SNESSetType(snes,SNESVI);CHKERRQ(ierr);
2044   vi = (SNES_VI*)snes->data;
2045   vi->usersetxbounds = PETSC_TRUE;
2046   vi->xl = xl;
2047   vi->xu = xu;
2048   PetscFunctionReturn(0);
2049 }
2050 
2051 /* -------------------------------------------------------------------------- */
2052 /*
2053    SNESSetFromOptions_VI - Sets various parameters for the SNESVI method.
2054 
2055    Input Parameter:
2056 .  snes - the SNES context
2057 
2058    Application Interface Routine: SNESSetFromOptions()
2059 */
2060 #undef __FUNCT__
2061 #define __FUNCT__ "SNESSetFromOptions_VI"
2062 static PetscErrorCode SNESSetFromOptions_VI(SNES snes)
2063 {
2064   SNES_VI        *vi = (SNES_VI *)snes->data;
2065   const char     *lses[] = {"basic","basicnonorms","quadratic","cubic"};
2066   const char     *vies[] = {"ss","rs","rs2"};
2067   PetscErrorCode ierr;
2068   PetscInt       indx;
2069   PetscBool      flg,set,flg2;
2070 
2071   PetscFunctionBegin;
2072   ierr = PetscOptionsHead("SNES semismooth method options");CHKERRQ(ierr);
2073   ierr = PetscOptionsBool("-snes_vi_monitor","Monitor all non-active variables","None",PETSC_FALSE,&flg,0);CHKERRQ(ierr);
2074   if (flg) {
2075     ierr = SNESMonitorSet(snes,SNESMonitorVI,0,0);CHKERRQ(ierr);
2076   }
2077   ierr = PetscOptionsReal("-snes_ls_alpha","Function norm must decrease by","None",vi->alpha,&vi->alpha,0);CHKERRQ(ierr);
2078   ierr = PetscOptionsReal("-snes_ls_maxstep","Step must be less than","None",vi->maxstep,&vi->maxstep,0);CHKERRQ(ierr);
2079   ierr = PetscOptionsReal("-snes_ls_minlambda","Minimum lambda allowed","None",vi->minlambda,&vi->minlambda,0);CHKERRQ(ierr);
2080   ierr = PetscOptionsReal("-snes_vi_const_tol","constraint tolerance","None",vi->const_tol,&vi->const_tol,0);CHKERRQ(ierr);
2081   ierr = PetscOptionsBool("-snes_ls_monitor","Print progress of line searches","SNESLineSearchSetMonitor",vi->lsmonitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);CHKERRQ(ierr);
2082   if (set) {ierr = SNESLineSearchSetMonitor(snes,flg);CHKERRQ(ierr);}
2083   ierr = PetscOptionsEList("-snes_vi_type","Semismooth algorithm used","",vies,3,"ss",&indx,&flg2);CHKERRQ(ierr);
2084   if (flg2) {
2085     switch (indx) {
2086     case 0:
2087       snes->ops->solve = SNESSolveVI_SS;
2088       break;
2089     case 1:
2090       snes->ops->solve = SNESSolveVI_RS;
2091       break;
2092     case 2:
2093       snes->ops->solve = SNESSolveVI_RS2;
2094     }
2095   }
2096   ierr = PetscOptionsEList("-snes_ls","Line search used","SNESLineSearchSet",lses,4,"basic",&indx,&flg);CHKERRQ(ierr);
2097   if (flg) {
2098     switch (indx) {
2099     case 0:
2100       ierr = SNESLineSearchSet(snes,SNESLineSearchNo_VI,PETSC_NULL);CHKERRQ(ierr);
2101       break;
2102     case 1:
2103       ierr = SNESLineSearchSet(snes,SNESLineSearchNoNorms_VI,PETSC_NULL);CHKERRQ(ierr);
2104       break;
2105     case 2:
2106       ierr = SNESLineSearchSet(snes,SNESLineSearchQuadratic_VI,PETSC_NULL);CHKERRQ(ierr);
2107       break;
2108     case 3:
2109       ierr = SNESLineSearchSet(snes,SNESLineSearchCubic_VI,PETSC_NULL);CHKERRQ(ierr);
2110       break;
2111     }
2112   }
2113   ierr = PetscOptionsTail();CHKERRQ(ierr);
2114   PetscFunctionReturn(0);
2115 }
2116 /* -------------------------------------------------------------------------- */
2117 /*MC
2118       SNESVI - Semismooth newton method based nonlinear solver that uses a line search
2119 
2120    Options Database:
2121 +   -snes_ls [cubic,quadratic,basic,basicnonorms] - Selects line search
2122 .   -snes_ls_alpha <alpha> - Sets alpha
2123 .   -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)
2124 .   -snes_ls_minlambda <minlambda>  - Sets the minimum lambda the line search will use  minlambda / max_i ( y[i]/x[i] )
2125 -   -snes_ls_monitor - print information about progress of line searches
2126 
2127 
2128    Level: beginner
2129 
2130 .seealso:  SNESCreate(), SNES, SNESSetType(), SNESTR, SNESLineSearchSet(),
2131            SNESLineSearchSetPostCheck(), SNESLineSearchNo(), SNESLineSearchCubic(), SNESLineSearchQuadratic(),
2132            SNESLineSearchSet(), SNESLineSearchNoNorms(), SNESLineSearchSetPreCheck(), SNESLineSearchSetParams(), SNESLineSearchGetParams()
2133 
2134 M*/
2135 EXTERN_C_BEGIN
2136 #undef __FUNCT__
2137 #define __FUNCT__ "SNESCreate_VI"
2138 PetscErrorCode  SNESCreate_VI(SNES snes)
2139 {
2140   PetscErrorCode ierr;
2141   SNES_VI      *vi;
2142 
2143   PetscFunctionBegin;
2144   snes->ops->setup           = SNESSetUp_VI;
2145   snes->ops->solve           = SNESSolveVI_RS;
2146   snes->ops->destroy         = SNESDestroy_VI;
2147   snes->ops->setfromoptions  = SNESSetFromOptions_VI;
2148   snes->ops->view            = SNESView_VI;
2149   snes->ops->reset           = 0; /* XXX Implement!!! */
2150   snes->ops->converged       = SNESDefaultConverged_VI;
2151 
2152   ierr                  = PetscNewLog(snes,SNES_VI,&vi);CHKERRQ(ierr);
2153   snes->data            = (void*)vi;
2154   vi->alpha             = 1.e-4;
2155   vi->maxstep           = 1.e8;
2156   vi->minlambda         = 1.e-12;
2157   vi->LineSearch        = SNESLineSearchNo_VI;
2158   vi->lsP               = PETSC_NULL;
2159   vi->postcheckstep     = PETSC_NULL;
2160   vi->postcheck         = PETSC_NULL;
2161   vi->precheckstep      = PETSC_NULL;
2162   vi->precheck          = PETSC_NULL;
2163   vi->const_tol         =  2.2204460492503131e-16;
2164   vi->checkredundancy   = PETSC_NULL;
2165 
2166   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","SNESLineSearchSetMonitor_VI",SNESLineSearchSetMonitor_VI);CHKERRQ(ierr);
2167   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","SNESLineSearchSet_VI",SNESLineSearchSet_VI);CHKERRQ(ierr);
2168 
2169   PetscFunctionReturn(0);
2170 }
2171 EXTERN_C_END
2172