/*
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   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).
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
/*
   Example based on spring problem in NLEVP collection [1]. See the parameters
   meaning at Example 2 in [2].

   [1] T. Betcke, N. J. Higham, V. Mehrmann, C. Schroder, and F. Tisseur,
       NLEVP: A Collection of Nonlinear Eigenvalue Problems, MIMS EPrint
       2010.98, November 2010.
   [2] F. Tisseur, Backward error and condition of polynomial eigenvalue
       problems, Linear Algebra and its Applications, 309 (2000), pp. 339--361,
       April 2000.
*/

static char help[] = "Tests multiple calls to PEPSolve with different matrix of different size.\n\n"
  "This is based on the spring problem from NLEVP collection.\n\n"
  "The command line options are:\n"
  "  -n <n> ... number of grid subdivisions.\n"
  "  -mu <value> ... mass (default 1).\n"
  "  -tau <value> ... damping constant of the dampers (default 10).\n"
  "  -kappa <value> ... damping constant of the springs (default 5).\n"
  "  -initv ... set an initial vector.\n\n";

#include <slepcpep.h>

int main(int argc,char **argv)
{
  Mat            M,C,K,A[3];      /* problem matrices */
  PEP            pep;             /* polynomial eigenproblem solver context */
  PetscInt       n=30,Istart,Iend,i,nev;
  PetscReal      mu=1.0,tau=10.0,kappa=5.0;
  PetscBool      terse=PETSC_FALSE;

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

  PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
  PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL));
  PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
  PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /* K is a tridiagonal */
  PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
  PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n));
  PetscCall(MatSetFromOptions(K));

  PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
  for (i=Istart;i<Iend;i++) {
    if (i>0) PetscCall(MatSetValue(K,i,i-1,-kappa,INSERT_VALUES));
    PetscCall(MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES));
    if (i<n-1) PetscCall(MatSetValue(K,i,i+1,-kappa,INSERT_VALUES));
  }

  PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

  /* C is a tridiagonal */
  PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
  PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n));
  PetscCall(MatSetFromOptions(C));

  PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
  for (i=Istart;i<Iend;i++) {
    if (i>0) PetscCall(MatSetValue(C,i,i-1,-tau,INSERT_VALUES));
    PetscCall(MatSetValue(C,i,i,tau*3.0,INSERT_VALUES));
    if (i<n-1) PetscCall(MatSetValue(C,i,i+1,-tau,INSERT_VALUES));
  }

  PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

  /* M is a diagonal matrix */
  PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
  PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n));
  PetscCall(MatSetFromOptions(M));
  PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
  for (i=Istart;i<Iend;i++) PetscCall(MatSetValue(M,i,i,mu,INSERT_VALUES));
  PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

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

  PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
  A[0] = K; A[1] = C; A[2] = M;
  PetscCall(PEPSetOperators(pep,3,A));
  PetscCall(PEPSetProblemType(pep,PEP_GENERAL));
  PetscCall(PEPSetTolerances(pep,PETSC_SMALL,PETSC_DEFAULT));
  PetscCall(PEPSetFromOptions(pep));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve the eigensystem
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  PetscCall(PEPSolve(pep));
  PetscCall(PEPGetDimensions(pep,&nev,NULL,NULL));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Display solution of first solve
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
  if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
  else {
    PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
  }
  PetscCall(MatDestroy(&M));
  PetscCall(MatDestroy(&C));
  PetscCall(MatDestroy(&K));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Compute the eigensystem, (k^2*M+k*C+K)x=0 for bigger n
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  n *= 2;
  /* K is a tridiagonal */
  PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
  PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n));
  PetscCall(MatSetFromOptions(K));

  PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
  for (i=Istart;i<Iend;i++) {
    if (i>0) PetscCall(MatSetValue(K,i,i-1,-kappa,INSERT_VALUES));
    PetscCall(MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES));
    if (i<n-1) PetscCall(MatSetValue(K,i,i+1,-kappa,INSERT_VALUES));
  }

  PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

  /* C is a tridiagonal */
  PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
  PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n));
  PetscCall(MatSetFromOptions(C));

  PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
  for (i=Istart;i<Iend;i++) {
    if (i>0) PetscCall(MatSetValue(C,i,i-1,-tau,INSERT_VALUES));
    PetscCall(MatSetValue(C,i,i,tau*3.0,INSERT_VALUES));
    if (i<n-1) PetscCall(MatSetValue(C,i,i+1,-tau,INSERT_VALUES));
  }

  PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

  /* M is a diagonal matrix */
  PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
  PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n));
  PetscCall(MatSetFromOptions(M));
  PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
  for (i=Istart;i<Iend;i++) PetscCall(MatSetValue(M,i,i,mu,INSERT_VALUES));
  PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
       Solve again, calling PEPReset() since matrix size has changed
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  /* PetscCall(PEPReset(pep)); */  /* not required, will be called in PEPSetOperators() */
  A[0] = K; A[1] = C; A[2] = M;
  PetscCall(PEPSetOperators(pep,3,A));
  PetscCall(PEPSolve(pep));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                    Display solution and clean up
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
  else {
    PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
  }
  PetscCall(PEPDestroy(&pep));
  PetscCall(MatDestroy(&M));
  PetscCall(MatDestroy(&C));
  PetscCall(MatDestroy(&K));
  PetscCall(SlepcFinalize());
  return 0;
}

/*TEST

   test:
      suffix: 1
      args: -pep_type {{toar qarnoldi linear}} -pep_nev 4 -terse
      requires: double

   test:
      suffix: 2
      args: -pep_type stoar -pep_hermitian -pep_nev 4 -terse
      requires: !single

TEST*/
