/*
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   SLEPc - Scalable Library for Eigenvalue Problem Computations
   Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain

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

static char help[] = "Tests the case when both arguments of MFNSolve() are the same Vec.\n\n"
  "The command line options are:\n"
  "  -t <sval>, where <sval> = scalar value that multiplies the argument.\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 <slepcmfn.h>

int main(int argc,char **argv)
{
  Mat            A;           /* problem matrix */
  MFN            mfn;
  FN             f;
  PetscReal      norm;
  PetscScalar    t=0.3;
  PetscInt       N,n=25,m,Istart,Iend,II,i,j;
  PetscBool      flag;
  Vec            v,y;
  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 = PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nMatrix exponential y=exp(t*A)*e, of the 2-D Laplacian, N=%D (%Dx%D grid)\n\n",N,n,m);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                         Build the 2-D Laplacian
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

  /* set v = ones(n,1) */
  ierr = MatCreateVecs(A,NULL,&y);CHKERRQ(ierr);
  ierr = MatCreateVecs(A,NULL,&v);CHKERRQ(ierr);
  ierr = VecSet(v,1.0);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                Create the solver and set various options
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = FNCreate(PETSC_COMM_WORLD,&f);CHKERRQ(ierr);
  ierr = FNSetType(f,FNEXP);CHKERRQ(ierr);

  ierr = MFNCreate(PETSC_COMM_WORLD,&mfn);CHKERRQ(ierr);
  ierr = MFNSetOperator(mfn,A);CHKERRQ(ierr);
  ierr = MFNSetFN(mfn,f);CHKERRQ(ierr);
  ierr = MFNSetErrorIfNotConverged(mfn,PETSC_TRUE);CHKERRQ(ierr);
  ierr = MFNSetFromOptions(mfn);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve the problem, y=exp(t*A)*v
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = FNSetScale(f,t,1.0);CHKERRQ(ierr);
  ierr = MFNSolve(mfn,v,y);CHKERRQ(ierr);
  ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n\n",(double)PetscRealPart(t),(double)norm);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
           Repeat the computation in two steps, overwriting v:
              v=exp(0.5*t*A)*v,  v=exp(0.5*t*A)*v
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = FNSetScale(f,0.5*t,1.0);CHKERRQ(ierr);
  ierr = MFNSolve(mfn,v,v);CHKERRQ(ierr);
  ierr = MFNSolve(mfn,v,v);CHKERRQ(ierr);
  /* compute norm of difference */
  ierr = VecAXPY(y,-1.0,v);CHKERRQ(ierr);
  ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
  if (norm<100*PETSC_MACHINE_EPSILON) {
    ierr = PetscPrintf(PETSC_COMM_WORLD," The norm of the difference is <100*eps\n\n");CHKERRQ(ierr);
  } else {
    ierr = PetscPrintf(PETSC_COMM_WORLD," The norm of the difference is %g\n\n",(double)norm);CHKERRQ(ierr);
  }

  /*
     Free work space
  */
  ierr = MFNDestroy(&mfn);CHKERRQ(ierr);
  ierr = FNDestroy(&f);CHKERRQ(ierr);
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = VecDestroy(&v);CHKERRQ(ierr);
  ierr = VecDestroy(&y);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return ierr;
}

/*TEST

   testset:
      args: -mfn_type {{krylov expokit}}
      output_file: output/test2_1.out
      test:
         suffix: 1
      test:
         suffix: 1_cuda
         args: -mat_type aijcusparse
         requires: cuda

   test:
      suffix: 3
      args: -mfn_type expokit -t 0.6 -mfn_ncv 35
      requires: !__float128

TEST*/
