/*
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   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).
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*/
/*
   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.
   This example solves the loaded_string problem by first transforming
   it to a quadratic eigenvalue problem.
*/

static char help[] = "Finite element model of a loaded vibrating string.\n\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 <slepcpep.h>

#define NMAT 3

int main(int argc,char **argv)
{
  Mat            A[3],M;      /* problem matrices */
  PEP            pep;         /* polynomial eigenproblem solver context */
  PetscInt       n=100,Istart,Iend,i;
  PetscBool      terse;
  PetscReal      kappa=1.0,m=1.0;
  PetscScalar    sigma;
  PetscErrorCode ierr;

  ierr = SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

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

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
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  /* initialize matrices */
  for (i=0;i<NMAT;i++) {
    ierr = MatCreate(PETSC_COMM_WORLD,&A[i]);CHKERRQ(ierr);
    ierr = MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
    ierr = MatSetFromOptions(A[i]);CHKERRQ(ierr);
    ierr = MatSetUp(A[i]);CHKERRQ(ierr);
  }
  ierr = MatGetOwnershipRange(A[0],&Istart,&Iend);CHKERRQ(ierr);

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

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

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

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

  /* build matrices for the QEP */
  ierr = MatAXPY(A[2],1.0,A[0],DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
  ierr = MatAXPY(A[2],sigma,A[1],SAME_NONZERO_PATTERN);CHKERRQ(ierr);
  ierr = MatScale(A[2],-1.0);CHKERRQ(ierr);
  ierr = MatScale(A[0],sigma);CHKERRQ(ierr);
  M = A[1];
  A[1] = A[2];
  A[2] = M;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                Create the eigensolver and solve the problem
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  ierr = PEPCreate(PETSC_COMM_WORLD,&pep);CHKERRQ(ierr);
  ierr = PEPSetOperators(pep,3,A);CHKERRQ(ierr);
  ierr = PEPSetFromOptions(pep);CHKERRQ(ierr);
  ierr = PEPSolve(pep);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                    Display solution and clean up
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  /* show detailed info unless -terse option is given by user */
  ierr = PetscOptionsHasName(NULL,NULL,"-terse",&terse);CHKERRQ(ierr);
  if (terse) {
    ierr = PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);CHKERRQ(ierr);
  } else {
    ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr);
    ierr = PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  ierr = PEPDestroy(&pep);CHKERRQ(ierr);
  for (i=0;i<NMAT;i++) {
    ierr = MatDestroy(&A[i]);CHKERRQ(ierr);
  }
  ierr = SlepcFinalize();
  return ierr;
}

/*TEST

   test:
      suffix: 1
      args: -pep_hyperbolic -pep_interval 4,900 -pep_type stoar -st_type sinvert -st_pc_type cholesky -terse
      requires: !single

TEST*/
