/*
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   SLEPc - Scalable Library for Eigenvalue Problem Computations
   Copyright (c) 2002-2019, Universitat Politecnica de Valencia, Spain

   This file is part of SLEPc.
   SLEPc is distributed under a 2-clause BSD license (see LICENSE).
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*/

static char help[] = "Computes the smallest nonzero eigenvalue of the Laplacian of a graph.\n\n"
  "This example illustrates EPSSetDeflationSpace(). The example graph corresponds to a "
  "2-D regular mesh. 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>

int main (int argc,char **argv)
{
  EPS            eps;             /* eigenproblem solver context */
  Mat            A;               /* operator matrix */
  Vec            x;
  PetscInt       N,n=10,m,i,j,II,Istart,Iend,nev;
  PetscScalar    w;
  PetscBool      flag;
  PetscErrorCode ierr;

  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 = PetscPrintf(PETSC_COMM_WORLD,"\nFiedler vector of a 2-D regular mesh, N=%D (%Dx%D grid)\n\n",N,n,m);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Compute the operator matrix that defines the eigensystem, Ax=kx
     In this example, A = L(G), where L is the Laplacian of graph G, i.e.
     Lii = degree of node i, Lij = -1 if edge (i,j) exists in G
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  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 = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
  for (II=Istart;II<Iend;II++) {
    i = II/n; j = II-i*n;
    w = 0.0;
    if (i>0) { ierr = MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; }
    if (i<m-1) { ierr = MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; }
    if (j>0) { ierr = MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; }
    if (j<n-1) { ierr = MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; }
    ierr = MatSetValue(A,II,II,w,INSERT_VALUES);CHKERRQ(ierr);
  }

  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                Create the eigensolver and set various options
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  /*
     Create eigensolver context
  */
  ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr);

  /*
     Set operators. In this case, it is a standard eigenvalue problem
  */
  ierr = EPSSetOperators(eps,A,NULL);CHKERRQ(ierr);
  ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr);

  /*
     Select portion of spectrum
  */
  ierr = EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);CHKERRQ(ierr);

  /*
     Set solver parameters at runtime
  */
  ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);

  /*
     Attach deflation space: in this case, the matrix has a constant
     nullspace, [1 1 ... 1]^T is the eigenvector of the zero eigenvalue
  */
  ierr = MatCreateVecs(A,&x,NULL);CHKERRQ(ierr);
  ierr = VecSet(x,1.0);CHKERRQ(ierr);
  ierr = EPSSetDeflationSpace(eps,1,&x);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve the eigensystem
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  ierr = EPSSolve(eps);CHKERRQ(ierr);
  ierr = EPSGetDimensions(eps,&nev,NULL,NULL);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                    Display solution and clean up
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  ierr = EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);CHKERRQ(ierr);
  ierr = EPSDestroy(&eps);CHKERRQ(ierr);
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return ierr;
}

/*TEST

   testset:
      args: -eps_nev 4 -m 11 -eps_max_it 500
      requires: !single
      output_file: output/test10_1.out
      test:
         suffix: 1
         args: -eps_type {{krylovschur arnoldi lanczos gd jd rqcg lobpcg}}
      test:
         suffix: 1_gd2
         args: -eps_type gd -eps_gd_double_expansion

TEST*/
