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/*

      Implements the Cayley spectral transform.

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

   SLEPc - Scalable Library for Eigenvalue Problem Computations

   Copyright (c) 2002-2011, Universitat 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 nu;

  PetscBool   nu_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    nu = ctx->nu;

  PetscFunctionBegin;

  if (st->shift_matrix == ST_MATMODE_INPLACE) { nu = nu + 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,nu,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,nu,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    nu = ctx->nu;

  PetscFunctionBegin;

  if (st->shift_matrix == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };

  if (st->B) {

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

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

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

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

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

  }

  else {

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

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

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

    ierr = VecAXPY(y,nu,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    nu;

  PetscFunctionBegin;

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

  ctx = (ST_CAYLEY*)st->data;

  nu = ctx->nu;

  if (st->shift_matrix == ST_MATMODE_INPLACE) { nu = nu + 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,nu,ctx->w2);CHKERRQ(ierr);    

  }

  else {

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

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

    ierr = VecAXPY(y,nu,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,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)

{

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

  PetscInt    j;

#if !defined(PETSC_USE_COMPLEX)

  PetscScalar t,i,r;

#endif

  PetscFunctionBegin;

#if !defined(PETSC_USE_COMPLEX)

  for (j=0;j<n;j++) {

    if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);

    else {

      r = eigr[j];

      i = eigi[j];

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

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

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

      eigr[j] = r / t;

      eigi[j] = i / t;    

    }

  }

#else

  for (j=0;j<n;j++) {

    eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);

  }

#endif

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STPostSolve_Cayley"

PetscErrorCode STPostSolve_Cayley(ST st)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  if (st->shift_matrix == ST_MATMODE_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;

  ierr = MatDestroy(&st->mat);CHKERRQ(ierr);

  /* if the user did not set the shift, use the target value */

  if (!st->sigma_set) st->sigma = st->defsigma;

  if (!ctx->nu_set) { ctx->nu = st->sigma; }

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

    SETERRQ(((PetscObject)st)->comm,1,"Values of shift and antishift cannot be zero simultaneously");

  }

  if (!st->ksp) { ierr = STGetKSP(st,&st->ksp);CHKERRQ(ierr); }

  switch (st->shift_matrix) {

  case ST_MATMODE_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 ST_MATMODE_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) {

    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->nu_set) { ctx->nu = newshift; }

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

    SETERRQ(((PetscObject)st)->comm,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 ST_MATMODE_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 ST_MATMODE_SHELL:

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

    break;

  default:

    ierr = MatCopy(st->A,st->mat,DIFFERENT_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    nu;

  PetscBool      flg;

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

  PC             pc;

  const PCType   pctype;

  const KSPType  ksptype;

  PetscFunctionBegin;

  if (!st->ksp) { ierr = STGetKSP(st,&st->ksp);CHKERRQ(ierr); }

  ierr = KSPGetPC(st->ksp,&pc);CHKERRQ(ierr);

  ierr = KSPGetType(st->ksp,&ksptype);CHKERRQ(ierr);

  ierr = PCGetType(pc,&pctype);CHKERRQ(ierr);

  if (!pctype && !ksptype) {

    if (st->shift_matrix == ST_MATMODE_SHELL) {

      /* in shell mode use GMRES with Jacobi as the default */

      ierr = KSPSetType(st->ksp,KSPGMRES);CHKERRQ(ierr);

      ierr = PCSetType(pc,PCJACOBI);CHKERRQ(ierr);

    } else {

      /* use direct solver as default */

      ierr = KSPSetType(st->ksp,KSPPREONLY);CHKERRQ(ierr);

      ierr = PCSetType(pc,PCREDUNDANT);CHKERRQ(ierr);

    }

  }

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

  ierr = PetscOptionsScalar("-st_cayley_antishift","Value of the antishift","STCayleySetAntishift",ctx->nu,&nu,&flg);CHKERRQ(ierr);

  if (flg) {

    ierr = STCayleySetAntishift(st,nu);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->nu     = newshift;

  ctx->nu_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.

   Logically Collective on ST

   Input Parameters:

+  st  - the spectral transformation context

-  nu  - the anti-shift

   Options Database Key:

.  -st_cayley_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 + nu B). This function sets the value of nu.

   Use STSetShift() for setting sigma.

.seealso: STSetShift(), STCayleyGetAntishift()

@*/

PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(st,ST_CLASSID,1);

  PetscValidLogicalCollectiveScalar(st,nu,2);

  ierr = PetscTryMethod(st,"STCayleySetAntishift_C",(ST,PetscScalar),(st,nu));CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "STCayleyGetAntishift_Cayley"

PetscErrorCode STCayleyGetAntishift_Cayley(ST st,PetscScalar *nu)

{

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

  PetscFunctionBegin;

  *nu = ctx->nu;

  PetscFunctionReturn(0);

}

EXTERN_C_END

#undef __FUNCT__  

#define __FUNCT__ "STCayleyGetAntishift"

/*@

   STCayleyGetAntishift - Gets the value of the anti-shift used in the Cayley

   spectral transformation.

   Not Collective

   Input Parameter:

.  st  - the spectral transformation context

   Output Parameter:

.  nu  - the anti-shift

   Level: intermediate

.seealso: STGetShift(), STCayleySetAntishift()

@*/

PetscErrorCode STCayleyGetAntishift(ST st,PetscScalar *nu)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(st,ST_CLASSID,1);

  PetscValidScalarPointer(nu,2);

  ierr = PetscTryMethod(st,"STCayleyGetAntishift_C",(ST,PetscScalar*),(st,nu));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,"  Cayley: antishift: %G\n",ctx->nu);CHKERRQ(ierr);

#else

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

#endif

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STReset_Cayley"

PetscErrorCode STReset_Cayley(ST st)

{

  PetscErrorCode ierr;

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

  PetscFunctionBegin;

  ierr = VecDestroy(&ctx->w2);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "STDestroy_Cayley"

PetscErrorCode STDestroy_Cayley(ST st)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  ierr = PetscFree(st->data);CHKERRQ(ierr);

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)st,"STCayleySetAntishift_C","",PETSC_NULL);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "STCreate_Cayley"

PetscErrorCode STCreate_Cayley(ST st)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  ierr = PetscNewLog(st,ST_CAYLEY,&st->data);CHKERRQ(ierr);

  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->reset           = STReset_Cayley;

  st->ops->view            = STView_Cayley;

  st->ops->checknullspace  = STCheckNullSpace_Default;

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

  PetscFunctionReturn(0);

}

EXTERN_C_END