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

   This file is part of SLEPc.
   SLEPc is distributed under a 2-clause BSD license (see LICENSE).
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
/*
   This example implements one of the problems found at
       NLEVP: A Collection of Nonlinear Eigenvalue Problems,
       The University of Manchester.
   The details of the collection can be found at:
       [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
           Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

   The loaded_string problem is a rational eigenvalue problem for the
   finite element model of a loaded vibrating string.
*/

static char help[] = "Test the NLEIGS solver with FNCOMBINE.\n\n"
  "This is based on loaded_string from the NLEVP collection.\n"
  "The command line options are:\n"
  "  -n <n>, dimension of the matrices.\n"
  "  -kappa <kappa>, stiffness of elastic spring.\n"
  "  -mass <m>, mass of the attached load.\n\n";

#include <slepcnep.h>

#define NMAT 3

int main(int argc,char **argv)
{
  Mat            A[NMAT];         /* problem matrices */
  FN             f[NMAT],g;       /* functions to define the nonlinear operator */
  NEP            nep;             /* nonlinear eigensolver context */
  PetscInt       n=100,Istart,Iend,i;
  PetscReal      kappa=1.0,m=1.0;
  PetscScalar    sigma,numer[2],denom[2];
  PetscBool      terse;

  PetscFunctionBeginUser;
  PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

  PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
  PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
  PetscCall(PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL));
  sigma = kappa/m;
  PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Loaded vibrating string, n=%" PetscInt_FMT " kappa=%g m=%g\n\n",n,(double)kappa,(double)m));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                       Build the problem matrices
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /* initialize matrices */
  for (i=0;i<NMAT;i++) {
    PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
    PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
    PetscCall(MatSetFromOptions(A[i]));
  }
  PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));

  /* A0 */
  for (i=Istart;i<Iend;i++) {
    PetscCall(MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES));
    if (i>0) PetscCall(MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES));
    if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES));
  }

  /* A1 */
  for (i=Istart;i<Iend;i++) {
    PetscCall(MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES));
    if (i>0) PetscCall(MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES));
    if (i<n-1) PetscCall(MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES));
  }

  /* A2 */
  if (Istart<=n-1 && n-1<Iend) PetscCall(MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES));

  /* assemble matrices */
  for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
  for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                       Create the problem functions
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /* f1=1 */
  PetscCall(FNCreate(PETSC_COMM_WORLD,&f[0]));
  PetscCall(FNSetType(f[0],FNRATIONAL));
  numer[0] = 1.0;
  PetscCall(FNRationalSetNumerator(f[0],1,numer));

  /* f2=-lambda */
  PetscCall(FNCreate(PETSC_COMM_WORLD,&f[1]));
  PetscCall(FNSetType(f[1],FNRATIONAL));
  numer[0] = -1.0; numer[1] = 0.0;
  PetscCall(FNRationalSetNumerator(f[1],2,numer));

  /* f3=lambda/(lambda-sigma)=1+sigma/(lambda-sigma) */
  PetscCall(FNCreate(PETSC_COMM_WORLD,&g));
  PetscCall(FNSetType(g,FNRATIONAL));
  numer[0] = sigma;
  denom[0] = 1.0; denom[1] = -sigma;
  PetscCall(FNRationalSetNumerator(g,1,numer));
  PetscCall(FNRationalSetDenominator(g,2,denom));
  PetscCall(FNCreate(PETSC_COMM_WORLD,&f[2]));
  PetscCall(FNSetType(f[2],FNCOMBINE));
  PetscCall(FNCombineSetChildren(f[2],FN_COMBINE_ADD,f[0],g));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                Create the eigensolver and solve the problem
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
  PetscCall(NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN));
  PetscCall(NEPSetProblemType(nep,NEP_RATIONAL));
  PetscCall(NEPSetFromOptions(nep));
  PetscCall(NEPSolve(nep));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                    Display solution and clean up
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /* show detailed info unless -terse option is given by user */
  PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
  if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
  else {
    PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
  }
  PetscCall(NEPDestroy(&nep));
  for (i=0;i<NMAT;i++) {
    PetscCall(MatDestroy(&A[i]));
    PetscCall(FNDestroy(&f[i]));
  }
  PetscCall(FNDestroy(&g));
  PetscCall(SlepcFinalize());
  return 0;
}

/*TEST

   test:
      suffix: 1
      args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 4,700,-.1,.1 -nep_nev 8 -nep_target 5 -terse
      filter: sed -e "s/[+-]0\.0*i//g"
      requires: !single

TEST*/
