/*
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   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).
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/

static char help[] = "Tests a user-defined convergence test in NEP.\n\n"
  "The command line options are:\n"
  "  -n <n>, where <n> = matrix dimension.\n";

/*
   Solve T(lambda)x=0 with T(lambda) = -D+sqrt(lambda)*I
      where D is the Laplacian operator in 1 dimension
*/

#include <slepcnep.h>

/*
  MyConvergedRel - Convergence test relative to the norm of D (given in ctx).
*/
PetscErrorCode MyConvergedRel(NEP nep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
{
  PetscReal norm = *(PetscReal*)ctx;

  PetscFunctionBegin;
  *errest = res/norm;
  PetscFunctionReturn(0);
}

int main(int argc,char **argv)
{
  NEP            nep;             /* nonlinear eigensolver context */
  Mat            A[2];
  PetscInt       n=100,Istart,Iend,i;
  PetscErrorCode ierr;
  PetscBool      terse;
  PetscReal      norm;
  FN             f[2];
  PetscScalar    coeffs;

  ierr = SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
  ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%D\n\n",n);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create nonlinear eigensolver, define problem in split form
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = NEPCreate(PETSC_COMM_WORLD,&nep);CHKERRQ(ierr);

  /* Create matrices */
  ierr = MatCreate(PETSC_COMM_WORLD,&A[0]);CHKERRQ(ierr);
  ierr = MatSetSizes(A[0],PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A[0]);CHKERRQ(ierr);
  ierr = MatSetUp(A[0]);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(A[0],&Istart,&Iend);CHKERRQ(ierr);
  for (i=Istart;i<Iend;i++) {
    if (i>0) { ierr = MatSetValue(A[0],i,i-1,1.0,INSERT_VALUES);CHKERRQ(ierr); }
    if (i<n-1) { ierr = MatSetValue(A[0],i,i+1,1.0,INSERT_VALUES);CHKERRQ(ierr); }
    ierr = MatSetValue(A[0],i,i,-2.0,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(A[0],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A[0],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = MatCreate(PETSC_COMM_WORLD,&A[1]);CHKERRQ(ierr);
  ierr = MatSetSizes(A[1],PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A[1]);CHKERRQ(ierr);
  ierr = MatSetUp(A[1]);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(A[1],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A[1],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatShift(A[1],1.0);CHKERRQ(ierr);

  /* Define functions */
  ierr = FNCreate(PETSC_COMM_WORLD,&f[0]);CHKERRQ(ierr);
  ierr = FNSetType(f[0],FNRATIONAL);CHKERRQ(ierr);
  coeffs = 1.0;
  ierr = FNRationalSetNumerator(f[0],1,&coeffs);CHKERRQ(ierr);
  ierr = FNCreate(PETSC_COMM_WORLD,&f[1]);CHKERRQ(ierr);
  ierr = FNSetType(f[1],FNSQRT);CHKERRQ(ierr);
  ierr = NEPSetSplitOperator(nep,2,A,f,SUBSET_NONZERO_PATTERN);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                   Set some options and solve
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = NEPSetTarget(nep,1.1);CHKERRQ(ierr);

  /* setup convergence test relative to the norm of D */
  ierr = MatNorm(A[0],NORM_1,&norm);CHKERRQ(ierr);
  ierr = NEPSetConvergenceTestFunction(nep,MyConvergedRel,&norm,NULL);CHKERRQ(ierr);

  ierr = NEPSetFromOptions(nep);CHKERRQ(ierr);
  ierr = NEPSolve(nep);CHKERRQ(ierr);

  /* show detailed info unless -terse option is given by user */
  ierr = PetscOptionsHasName(NULL,NULL,"-terse",&terse);CHKERRQ(ierr);
  if (terse) {
    ierr = NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL);CHKERRQ(ierr);
  } else {
    ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr);
    ierr = NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  ierr = NEPDestroy(&nep);CHKERRQ(ierr);
  ierr = MatDestroy(&A[0]);CHKERRQ(ierr);
  ierr = MatDestroy(&A[1]);CHKERRQ(ierr);
  ierr = FNDestroy(&f[0]);CHKERRQ(ierr);
  ierr = FNDestroy(&f[1]);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return ierr;
}

/*TEST

   test:
      suffix: 1
      args: -nep_type slp -nep_nev 2 -terse
      requires: double

TEST*/
