/*
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   SLEPc - Scalable Library for Eigenvalue Problem Computations
   Copyright (c) 2002-2021, 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[] = "Illustrates the use of a user-defined stopping test.\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\n";

#include <slepcpep.h>

/*
   User-defined routines
*/
PetscErrorCode MyStoppingTest(PEP,PetscInt,PetscInt,PetscInt,PetscInt,PEPConvergedReason*,void*);

typedef struct {
  PetscInt    lastnconv;      /* last value of nconv; used in stopping test */
  PetscInt    nreps;          /* number of repetitions of nconv; used in stopping test */
} CTX_SPRING;

int main(int argc,char **argv)
{
  Mat            M,C,K,A[3];      /* problem matrices */
  PEP            pep;             /* polynomial eigenproblem solver context */
  RG             rg;              /* region object */
  ST             st;
  CTX_SPRING     *ctx;
  PetscBool      terse;
  PetscErrorCode ierr;
  PetscViewer    viewer;
  PetscInt       n=30,Istart,Iend,i,mpd;
  PetscReal      mu=1.0,tau=10.0,kappa=5.0;

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

  ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nDamped mass-spring system, n=%D mu=%g tau=%g kappa=%g\n\n",n,(double)mu,(double)tau,(double)kappa);CHKERRQ(ierr);

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

  /* K is a tridiagonal */
  ierr = MatCreate(PETSC_COMM_WORLD,&K);CHKERRQ(ierr);
  ierr = MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetFromOptions(K);CHKERRQ(ierr);
  ierr = MatSetUp(K);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(K,&Istart,&Iend);CHKERRQ(ierr);
  for (i=Istart;i<Iend;i++) {
    if (i>0) {
      ierr = MatSetValue(K,i,i-1,-kappa,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES);CHKERRQ(ierr);
    if (i<n-1) {
      ierr = MatSetValue(K,i,i+1,-kappa,INSERT_VALUES);CHKERRQ(ierr);
    }
  }
  ierr = MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* C is a tridiagonal */
  ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
  ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetFromOptions(C);CHKERRQ(ierr);
  ierr = MatSetUp(C);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(C,&Istart,&Iend);CHKERRQ(ierr);
  for (i=Istart;i<Iend;i++) {
    if (i>0) {
      ierr = MatSetValue(C,i,i-1,-tau,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = MatSetValue(C,i,i,tau*3.0,INSERT_VALUES);CHKERRQ(ierr);
    if (i<n-1) {
      ierr = MatSetValue(C,i,i+1,-tau,INSERT_VALUES);CHKERRQ(ierr);
    }
  }
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

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

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

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

  /*
     Define the region containing the eigenvalues of interest
  */
  ierr = PEPGetRG(pep,&rg);CHKERRQ(ierr);
  ierr = RGSetType(rg,RGINTERVAL);CHKERRQ(ierr);
  ierr = RGIntervalSetEndpoints(rg,-0.5057,-0.5052,-0.001,0.001);CHKERRQ(ierr);
  ierr = PEPSetTarget(pep,-0.43);CHKERRQ(ierr);
  ierr = PEPSetWhichEigenpairs(pep,PEP_TARGET_MAGNITUDE);CHKERRQ(ierr);
  ierr = PEPGetST(pep,&st);CHKERRQ(ierr);
  ierr = STSetType(st,STSINVERT);CHKERRQ(ierr);

  /*
     Set solver options. In particular, we must allocate sufficient
     storage for all eigenpairs that may converge (ncv). This is
     application-dependent.
  */
  mpd = 40;
  ierr = PEPSetDimensions(pep,2*mpd,3*mpd,mpd);CHKERRQ(ierr);
  ierr = PEPSetTolerances(pep,PETSC_DEFAULT,2000);CHKERRQ(ierr);
  ierr = PetscNew(&ctx);CHKERRQ(ierr);
  ctx->lastnconv = 0;
  ctx->nreps     = 0;
  ierr = PEPSetStoppingTestFunction(pep,MyStoppingTest,(void*)ctx,NULL);CHKERRQ(ierr);

  ierr = PEPSetFromOptions(pep);CHKERRQ(ierr);

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

  ierr = PEPSolve(pep);CHKERRQ(ierr);

  /* show detailed info unless -terse option is given by user */
  ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr);
  ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr);
  ierr = PEPConvergedReasonView(pep,viewer);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(NULL,NULL,"-terse",&terse);CHKERRQ(ierr);
  if (!terse) {
    ierr = PEPErrorView(pep,PEP_ERROR_BACKWARD,viewer);CHKERRQ(ierr);
  }
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);

  ierr = PEPDestroy(&pep);CHKERRQ(ierr);
  ierr = MatDestroy(&M);CHKERRQ(ierr);
  ierr = MatDestroy(&C);CHKERRQ(ierr);
  ierr = MatDestroy(&K);CHKERRQ(ierr);
  ierr = PetscFree(ctx);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return ierr;
}

/*
    Function for user-defined stopping test.

    Ignores the value of nev. It only takes into account the number of
    eigenpairs that have converged in recent outer iterations (restarts);
    if no new eigenvalues have converged in the last few restarts,
    we stop the iteration, assuming that no more eigenvalues are present
    inside the region.
*/
PetscErrorCode MyStoppingTest(PEP pep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,PEPConvergedReason *reason,void *ptr)
{
  PetscErrorCode ierr;
  CTX_SPRING     *ctx = (CTX_SPRING*)ptr;

  PetscFunctionBeginUser;
  /* check usual termination conditions, but ignoring the case nconv>=nev */
  ierr = PEPStoppingBasic(pep,its,max_it,nconv,PETSC_MAX_INT,reason,NULL);CHKERRQ(ierr);
  if (*reason==PEP_CONVERGED_ITERATING) {
    /* check if nconv is the same as before */
    if (nconv==ctx->lastnconv) ctx->nreps++;
    else {
      ctx->lastnconv = nconv;
      ctx->nreps     = 0;
    }
    /* check if no eigenvalues converged in last 10 restarts */
    if (nconv && ctx->nreps>10) *reason = PEP_CONVERGED_USER;
  }
  PetscFunctionReturn(0);
}

/*TEST

   test:
      args: -terse
      suffix: 1

TEST*/
