/*
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   SLEPc - Scalable Library for Eigenvalue Problem Computations
   Copyright (c) 2002-2016, 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/>.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/

static char help[] = "Generalized Symmetric eigenproblem.\n\n"
  "The problem is Ax = lambda Bx, with:\n"
  "   A = Laplacian operator in 2-D\n"
  "   B = diagonal matrix\n\n"
  "The command line options are:\n"
  "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
  "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

#include <slepceps.h>

#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc,char **argv)
{
  Mat            A,B;         /* matrices */
  EPS            eps;         /* eigenproblem solver context */
  ST             st;          /* spectral transformation context */
  Vec            x,b;
  KSP            ksp;
  PC             pc;
  PetscInt       N,n=10,m,Istart,Iend,II,i,j;
  PetscReal      norm;
  PetscBool      flag,terse;
  PetscErrorCode ierr;
  PetscBool      destroy, empty;

  ierr = SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
  ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);CHKERRQ(ierr);
  if (!flag) m=n;
  N = n*m;
  ierr = PetscOptionsHasName(NULL,NULL,"-terse",&terse);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%D (%Dx%D grid)\n\n",N,n,m);CHKERRQ(ierr);

  /// Flags dealing with optional destruction of EPS object
  PetscOptionsHasName(NULL,NULL,"-destroy_eps",&destroy);
  PetscOptionsHasName(NULL,NULL,"-empty_ksp",&empty);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Compute the matrices that define the eigensystem, Ax=kBx
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A);CHKERRQ(ierr);
  ierr = MatSetUp(A);CHKERRQ(ierr);

  ierr = MatCreate(PETSC_COMM_WORLD,&B);CHKERRQ(ierr);
  ierr = MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
  ierr = MatSetFromOptions(B);CHKERRQ(ierr);
  ierr = MatSetUp(B);CHKERRQ(ierr);

  ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
  for (II=Istart;II<Iend;II++) {
    i = II/n; j = II-i*n;
    if (i>0) { ierr = MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    if (i<m-1) { ierr = MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    if (j>0) { ierr = MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    if (j<n-1) { ierr = MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    ierr = MatSetValue(A,II,II,4.0,INSERT_VALUES);CHKERRQ(ierr);
    ierr = MatSetValue(B,II,II,4.0,INSERT_VALUES);CHKERRQ(ierr);
  }

  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatCreateVecs(B,&x,&b);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                Create a KSP with coefficient matrix B
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
  ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
  ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
  ierr = PCSetType(pc,PCLU);CHKERRQ(ierr);
  ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve first linear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = VecSetRandom(b,NULL);CHKERRQ(ierr);
  ierr = KSPSetOperators(ksp,B,B);CHKERRQ(ierr);
  ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
  ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of x= %g\n",(double)norm);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                     Create the eigensolver
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr);
  ierr = EPSSetOperators(eps,A,B);CHKERRQ(ierr);
  ierr = EPSSetProblemType(eps,EPS_GHEP);CHKERRQ(ierr);
  ierr = EPSGetST(eps,&st);CHKERRQ(ierr);
  ierr = STSetKSP(st,ksp);CHKERRQ(ierr);
  ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve first eigensystem
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = EPSSolve(eps);CHKERRQ(ierr);
  if (terse) {
    ierr = EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);CHKERRQ(ierr);
  } else {
    ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr);
    ierr = EPSReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Optionally destroy EPS object
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  if (empty)
  {
    KSP empty;
    ierr = EPSGetST(eps,&st);CHKERRQ(ierr);
    ierr = STSetKSP(st,empty);CHKERRQ(ierr);
  }
  if (destroy || empty)
  {
    ierr = EPSDestroy(&eps);CHKERRQ(ierr);
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Modify B matrix
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  for (II=Istart;II<Iend;II++) {
    i = II/n; j = II-i*n;
    ierr = MatSetValue(B,II,II,2.0+i,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve second linear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = VecSetRandom(b,NULL);CHKERRQ(ierr);
  ierr = KSPSetOperators(ksp,B,B);CHKERRQ(ierr);
  ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
  ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of x= %g\n",(double)norm);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                     Optionally recreate the eigensolver
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  if (destroy || empty)
  {
    ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr);
  }
  ierr = EPSSetOperators(eps,A,B);CHKERRQ(ierr);
  if (destroy || empty)
  {
    ierr = EPSSetProblemType(eps,EPS_GHEP);CHKERRQ(ierr);
    ierr = EPSGetST(eps,&st);CHKERRQ(ierr);
    ierr = STSetKSP(st,ksp);CHKERRQ(ierr);
    ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve second eigensystem
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = EPSSolve(eps);CHKERRQ(ierr);
  if (terse) {
    ierr = EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);CHKERRQ(ierr);
  } else {
    ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr);
    ierr = EPSReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }

  ierr = EPSDestroy(&eps);CHKERRQ(ierr);
  ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = MatDestroy(&B);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);
  ierr = VecDestroy(&b);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return ierr;
}