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/*

      Implements the Cayley spectral transform.

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

   SLEPc - Scalable Library for Eigenvalue Problem Computations

   Copyright (c) 2002-2009, Universidad Politecnica de Valencia, Spain

   This file is part of SLEPc.

   SLEPc is free software: you can redistribute it and/or modify it under  the

   terms of version 3 of the GNU Lesser General Public License as published by

   the Free Software Foundation.

   SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY

   WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS

   FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for

   more details.

   You  should have received a copy of the GNU Lesser General  Public  License

   along with SLEPc. If not, see <http://www.gnu.org/licenses/>.

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*/

#include "private/stimpl.h"          /*I "slepcst.h" I*/

typedef struct {

  PetscScalar tau;

  PetscTruth  tau_set;

  Vec         w2;

} ST_CAYLEY;

#undef __FUNCT__  

#define __FUNCT__ "STApply_Cayley"

PetscErrorCode STApply_Cayley(ST st,Vec x,Vec y)

{

  PetscErrorCode ierr;

  ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;

  PetscScalar    tau = ctx->tau;

  PetscFunctionBegin;

  if (st->shift_matrix == STMATMODE_INPLACE) { tau = tau + st->sigma; };

  if (st->B) {

    /* generalized eigenproblem: y = (A - sB)^-1 (A + tB)x */

    ierr = MatMult(st->A,x,st->w);CHKERRQ(ierr);

    ierr = MatMult(st->B,x,ctx->w2);CHKERRQ(ierr);

    ierr = VecAXPY(st->w,tau,ctx->w2);CHKERRQ(ierr);    

    ierr = STAssociatedKSPSolve(st,st->w,y);CHKERRQ(ierr);

  }

  else {

    /* standard eigenproblem: y = (A - sI)^-1 (A + tI)x */

    ierr = MatMult(st->A,x,st->w);CHKERRQ(ierr);

    ierr = VecAXPY(st->w,tau,x);CHKERRQ(ierr);

    ierr = STAssociatedKSPSolve(st,st->w,y);CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STApplyTranspose_Cayley"

PetscErrorCode STApplyTranspose_Cayley(ST st,Vec x,Vec y)

{

  PetscErrorCode ierr;

  ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;

  PetscScalar    tau = ctx->tau;

  PetscFunctionBegin;

  if (st->shift_matrix == STMATMODE_INPLACE) { tau = tau + st->sigma; };

  if (st->B) {

    /* generalized eigenproblem: y = (A + tB)^T (A - sB)^-T x */

    ierr = STAssociatedKSPSolve(st,x,st->w);CHKERRQ(ierr);

    ierr = MatMult(st->A,st->w,y);CHKERRQ(ierr);

    ierr = MatMult(st->B,st->w,ctx->w2);CHKERRQ(ierr);

    ierr = VecAXPY(y,tau,ctx->w2);CHKERRQ(ierr);    

  }

  else {

    /* standard eigenproblem: y =  (A + tI)^T (A - sI)^-T x */

    ierr = STAssociatedKSPSolve(st,x,st->w);CHKERRQ(ierr);

    ierr = MatMult(st->A,st->w,y);CHKERRQ(ierr);

    ierr = VecAXPY(y,tau,st->w);CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STBilinearMatMult_Cayley"

PetscErrorCode STBilinearMatMult_Cayley(Mat B,Vec x,Vec y)

{

  PetscErrorCode ierr;

  ST             st;

  ST_CAYLEY      *ctx;

  PetscScalar    tau;

  PetscFunctionBegin;

  ierr = MatShellGetContext(B,(void**)&st);CHKERRQ(ierr);

  ctx = (ST_CAYLEY *) st->data;

  tau = ctx->tau;

  if (st->shift_matrix == STMATMODE_INPLACE) { tau = tau + st->sigma; };

  if (st->B) {

    /* generalized eigenproblem: y = (A + tB)x */

    ierr = MatMult(st->A,x,y);CHKERRQ(ierr);

    ierr = MatMult(st->B,x,ctx->w2);CHKERRQ(ierr);

    ierr = VecAXPY(y,tau,ctx->w2);CHKERRQ(ierr);    

  }

  else {

    /* standard eigenproblem: y = (A + tI)x */

    ierr = MatMult(st->A,x,y);CHKERRQ(ierr);

    ierr = VecAXPY(y,tau,x);CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STGetBilinearForm_Cayley"

PetscErrorCode STGetBilinearForm_Cayley(ST st,Mat *B)

{

  PetscErrorCode ierr;

  PetscInt       n,m;

  PetscFunctionBegin;

  ierr = MatGetLocalSize(st->B,&n,&m);CHKERRQ(ierr);

  ierr = MatCreateShell(((PetscObject)st)->comm,n,m,PETSC_DETERMINE,PETSC_DETERMINE,st,B);CHKERRQ(ierr);

  ierr = MatShellSetOperation(*B,MATOP_MULT,(void(*)(void))STBilinearMatMult_Cayley);CHKERRQ(ierr);  

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STBackTransform_Cayley"

PetscErrorCode STBackTransform_Cayley(ST st,PetscScalar *eigr,PetscScalar *eigi)

{

  ST_CAYLEY   *ctx = (ST_CAYLEY *) st->data;

#ifndef PETSC_USE_COMPLEX

  PetscScalar t,i,r;

  PetscFunctionBegin;

  PetscValidPointer(eigr,2);

  PetscValidPointer(eigi,3);

  if (*eigi == 0.0) *eigr = (ctx->tau + *eigr * st->sigma) / (*eigr - 1.0);

  else {

    r = *eigr;

    i = *eigi;

    r = st->sigma * (r * r + i * i - r) + ctx->tau * (r - 1);

    i = - st->sigma * i - ctx->tau * i;

    t = i * i + r * (r - 2.0) + 1.0;    

    *eigr = r / t;

    *eigi = i / t;    

  }

#else

  PetscFunctionBegin;

  PetscValidPointer(eigr,2);

  *eigr = (ctx->tau + *eigr * st->sigma) / (*eigr - 1.0);

#endif

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STPostSolve_Cayley"

PetscErrorCode STPostSolve_Cayley(ST st)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  if (st->shift_matrix == STMATMODE_INPLACE) {

    if (st->B) {

      ierr = MatAXPY(st->A,st->sigma,st->B,st->str);CHKERRQ(ierr);

    } else {

      ierr = MatShift(st->A,st->sigma); CHKERRQ(ierr);

    }

    st->setupcalled = 0;

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STSetUp_Cayley"

PetscErrorCode STSetUp_Cayley(ST st)

{

  PetscErrorCode ierr;

  ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;

  PetscFunctionBegin;

  if (st->mat) { ierr = MatDestroy(st->mat);CHKERRQ(ierr); }

  if (!ctx->tau_set) { ctx->tau = st->sigma; }

  if (ctx->tau == 0.0 &&  st->sigma == 0.0) {

    SETERRQ(1,"Values of shift and antishift cannot be zero simultaneously");

  }

  switch (st->shift_matrix) {

  case STMATMODE_INPLACE:

    st->mat = PETSC_NULL;

    if (st->sigma != 0.0) {

      if (st->B) {

        ierr = MatAXPY(st->A,-st->sigma,st->B,st->str);CHKERRQ(ierr);

      } else {

        ierr = MatShift(st->A,-st->sigma);CHKERRQ(ierr);

      }

    }

    ierr = KSPSetOperators(st->ksp,st->A,st->A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);

    break;

  case STMATMODE_SHELL:

    ierr = STMatShellCreate(st,&st->mat);CHKERRQ(ierr);

    ierr = KSPSetOperators(st->ksp,st->mat,st->mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);

    break;

  default:

    ierr = MatDuplicate(st->A,MAT_COPY_VALUES,&st->mat);CHKERRQ(ierr);

    if (st->sigma != 0.0) {

      if (st->B) {

        ierr = MatAXPY(st->mat,-st->sigma,st->B,st->str);CHKERRQ(ierr);

      } else {

        ierr = MatShift(st->mat,-st->sigma);CHKERRQ(ierr);

      }

    }

    ierr = KSPSetOperators(st->ksp,st->mat,st->mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);

  }

  if (st->B) {

   if (ctx->w2) { ierr = VecDestroy(ctx->w2);CHKERRQ(ierr); }

   ierr = MatGetVecs(st->B,&ctx->w2,PETSC_NULL);CHKERRQ(ierr);

  }

  ierr = KSPSetUp(st->ksp);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STSetShift_Cayley"

PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)

{

  PetscErrorCode ierr;

  ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;

  MatStructure   flg;

  PetscFunctionBegin;

  if (!ctx->tau_set) { ctx->tau = newshift; }

  if (ctx->tau == 0.0 &&  newshift == 0.0) {

    SETERRQ(1,"Values of shift and antishift cannot be zero simultaneously");

  }

  /* Nothing to be done if STSetUp has not been called yet */

  if (!st->setupcalled) PetscFunctionReturn(0);

  /* Check if the new KSP matrix has the same zero structure */

  if (st->B && st->str == DIFFERENT_NONZERO_PATTERN && (st->sigma == 0.0 || newshift == 0.0)) {

    flg = DIFFERENT_NONZERO_PATTERN;

  } else {

    flg = SAME_NONZERO_PATTERN;

  }

  switch (st->shift_matrix) {

  case STMATMODE_INPLACE:

    /* Undo previous operations */

    if (st->sigma != 0.0) {

      if (st->B) {

        ierr = MatAXPY(st->A,st->sigma,st->B,st->str);CHKERRQ(ierr);

      } else {

        ierr = MatShift(st->A,st->sigma);CHKERRQ(ierr);

      }

    }

    /* Apply new shift */

    if (newshift != 0.0) {

      if (st->B) {

        ierr = MatAXPY(st->A,-newshift,st->B,st->str);CHKERRQ(ierr);

      } else {

        ierr = MatShift(st->A,-newshift);CHKERRQ(ierr);

      }

    }

    ierr = KSPSetOperators(st->ksp,st->A,st->A,flg);CHKERRQ(ierr);

    break;

  case STMATMODE_SHELL:

    ierr = KSPSetOperators(st->ksp,st->mat,st->mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);    

    break;

  default:

    ierr = MatCopy(st->A, st->mat,SUBSET_NONZERO_PATTERN); CHKERRQ(ierr);

    if (newshift != 0.0) {  

      if (st->B) { ierr = MatAXPY(st->mat,-newshift,st->B,st->str);CHKERRQ(ierr); }

      else { ierr = MatShift(st->mat,-newshift);CHKERRQ(ierr); }

    }

    ierr = KSPSetOperators(st->ksp,st->mat,st->mat,flg);CHKERRQ(ierr);    

  }

  st->sigma = newshift;

  ierr = KSPSetUp(st->ksp);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STSetFromOptions_Cayley"

PetscErrorCode STSetFromOptions_Cayley(ST st)

{

  PetscErrorCode ierr;

  PetscScalar    tau;

  PetscTruth     flg;

  ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;

  PetscFunctionBegin;

  ierr = PetscOptionsHead("ST Cayley Options");CHKERRQ(ierr);

  ierr = PetscOptionsScalar("-st_antishift","Value of the antishift","STSetAntishift",ctx->tau,&tau,&flg); CHKERRQ(ierr);

  if (flg) {

    ierr = STCayleySetAntishift(st,tau);CHKERRQ(ierr);

  }

  ierr = PetscOptionsTail();CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "STCayleySetAntishift_Cayley"

PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)

{

  ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;

  PetscFunctionBegin;

  ctx->tau = newshift;

  ctx->tau_set = PETSC_TRUE;

  PetscFunctionReturn(0);

}

EXTERN_C_END

#undef __FUNCT__  

#define __FUNCT__ "STCayleySetAntishift"

/*@

   STCayleySetAntishift - Sets the value of the anti-shift for the Cayley

   spectral transformation.

   Collective on ST

   Input Parameters:

+  st  - the spectral transformation context

-  tau - the anti-shift

   Options Database Key:

.  -st_antishift - Sets the value of the anti-shift

   Level: intermediate

   Note:

   In the generalized Cayley transform, the operator can be expressed as

   OP = inv(A - sigma B)*(A + tau B). This function sets the value of tau.

   Use STSetShift() for setting sigma.

.seealso: STSetShift()

@*/

PetscErrorCode STCayleySetAntishift(ST st,PetscScalar tau)

{

  PetscErrorCode ierr, (*f)(ST,PetscScalar);

  PetscFunctionBegin;

  PetscValidHeaderSpecific(st,ST_COOKIE,1);

  ierr = PetscObjectQueryFunction((PetscObject)st,"STCayleySetAntishift_C",(void (**)(void))&f);CHKERRQ(ierr);

  if (f) {

    ierr = (*f)(st,tau);CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STView_Cayley"

PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)

{

  PetscErrorCode ierr;

  ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;

  PetscFunctionBegin;

#if !defined(PETSC_USE_COMPLEX)

  ierr = PetscViewerASCIIPrintf(viewer,"  antishift: %g\n",ctx->tau);CHKERRQ(ierr);

#else

  ierr = PetscViewerASCIIPrintf(viewer,"  antishift: %g+%g i\n",PetscRealPart(ctx->tau),PetscImaginaryPart(ctx->tau));CHKERRQ(ierr);

#endif

  ierr = STView_Default(st,viewer);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STDestroy_Cayley"

PetscErrorCode STDestroy_Cayley(ST st)

{

  PetscErrorCode ierr;

  ST_CAYLEY      *ctx = (ST_CAYLEY *) st->data;

  PetscFunctionBegin;

  if (ctx->w2) { ierr = VecDestroy(ctx->w2);CHKERRQ(ierr); }

  ierr = PetscFree(ctx);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "STCreate_Cayley"

PetscErrorCode STCreate_Cayley(ST st)

{

  PetscErrorCode ierr;

  ST_CAYLEY      *ctx;

  PetscFunctionBegin;

  ierr = PetscNew(ST_CAYLEY,&ctx); CHKERRQ(ierr);

  PetscLogObjectMemory(st,sizeof(ST_CAYLEY));

  st->data                 = (void *) ctx;

  st->ops->apply           = STApply_Cayley;

  st->ops->getbilinearform = STGetBilinearForm_Cayley;

  st->ops->applytrans      = STApplyTranspose_Cayley;

  st->ops->postsolve       = STPostSolve_Cayley;

  st->ops->backtr          = STBackTransform_Cayley;

  st->ops->setfromoptions  = STSetFromOptions_Cayley;

  st->ops->setup           = STSetUp_Cayley;

  st->ops->setshift        = STSetShift_Cayley;

  st->ops->destroy         = STDestroy_Cayley;

  st->ops->view            = STView_Cayley;

  st->checknullspace      = STCheckNullSpace_Default;

  ctx->tau                = 0.0;

  ctx->tau_set            = PETSC_FALSE;

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)st,"STCayleySetAntishift_C","STCayleySetAntishift_Cayley",

                    STCayleySetAntishift_Cayley);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_END