/*
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   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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*/

static char help[] = "Test the NEPProjectOperator() operator.\n\n"
  "This is based on ex22.\n"
  "The command line options are:\n"
  "  -n <n>, where <n> = number of grid subdivisions.\n"
  "  -tau <tau>, where <tau> is the delay parameter.\n";

/*
   Solve parabolic partial differential equation with time delay tau

            u_t = u_xx + a*u(t) + b*u(t-tau)
            u(0,t) = u(pi,t) = 0

   with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).

   Discretization leads to a DDE of dimension n

            -u' = A*u(t) + B*u(t-tau)

   which results in the nonlinear eigenproblem

            (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
*/

#include <slepcnep.h>

int main(int argc,char **argv)
{
  NEP            nep;
  Mat            Id,A,B,mats[3];
  FN             f1,f2,f3,funs[3];
  BV             V;
  DS             ds;
  Vec            v;
  PetscScalar    coeffs[2],b,*M;
  PetscInt       n=32,Istart,Iend,i,j,k,nc;
  PetscReal      tau=0.001,h,a=20,xi;
  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,"-tau",&tau,NULL);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n",n,(double)tau);CHKERRQ(ierr);
  h = PETSC_PI/(PetscReal)(n+1);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create nonlinear eigensolver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

  /* Identity matrix */
  ierr = MatCreate(PETSC_COMM_WORLD,&Id);CHKERRQ(ierr);
  ierr = MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetFromOptions(Id);CHKERRQ(ierr);
  ierr = MatSetUp(Id);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(Id,&Istart,&Iend);CHKERRQ(ierr);
  for (i=Istart;i<Iend;i++) {
    ierr = MatSetValue(Id,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);

  /* A = 1/h^2*tridiag(1,-2,1) + a*I */
  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A);CHKERRQ(ierr);
  ierr = MatSetUp(A);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
  for (i=Istart;i<Iend;i++) {
    if (i>0) { ierr = MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
    if (i<n-1) { ierr = MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
    ierr = MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);

  /* B = diag(b(xi)) */
  ierr = MatCreate(PETSC_COMM_WORLD,&B);CHKERRQ(ierr);
  ierr = MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetFromOptions(B);CHKERRQ(ierr);
  ierr = MatSetUp(B);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(B,&Istart,&Iend);CHKERRQ(ierr);
  for (i=Istart;i<Iend;i++) {
    xi = (i+1)*h;
    b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    ierr = MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);

  /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
  ierr = FNCreate(PETSC_COMM_WORLD,&f1);CHKERRQ(ierr);
  ierr = FNSetType(f1,FNRATIONAL);CHKERRQ(ierr);
  coeffs[0] = -1.0; coeffs[1] = 0.0;
  ierr = FNRationalSetNumerator(f1,2,coeffs);CHKERRQ(ierr);

  ierr = FNCreate(PETSC_COMM_WORLD,&f2);CHKERRQ(ierr);
  ierr = FNSetType(f2,FNRATIONAL);CHKERRQ(ierr);
  coeffs[0] = 1.0;
  ierr = FNRationalSetNumerator(f2,1,coeffs);CHKERRQ(ierr);

  ierr = FNCreate(PETSC_COMM_WORLD,&f3);CHKERRQ(ierr);
  ierr = FNSetType(f3,FNEXP);CHKERRQ(ierr);
  ierr = FNSetScale(f3,-tau,1.0);CHKERRQ(ierr);

  /* Set the split operator */
  mats[0] = A;  funs[0] = f2;
  mats[1] = Id; funs[1] = f1;
  mats[2] = B;  funs[2] = f3;
  ierr = NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);CHKERRQ(ierr);
  ierr = NEPSetType(nep,NEPNARNOLDI);CHKERRQ(ierr);
  ierr = NEPSetFromOptions(nep);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Project the NEP
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = NEPSetUp(nep);CHKERRQ(ierr);
  ierr = NEPGetBV(nep,&V);CHKERRQ(ierr);
  ierr = BVGetSizes(V,NULL,NULL,&nc);CHKERRQ(ierr);
  for (i=0;i<nc;i++) {
    ierr = BVGetColumn(V,i,&v);CHKERRQ(ierr);
    ierr = VecSetValue(v,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
    ierr = VecAssemblyBegin(v);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(v);CHKERRQ(ierr);
    ierr = BVRestoreColumn(V,i,&v);CHKERRQ(ierr);
  }
  ierr = NEPGetDS(nep,&ds);CHKERRQ(ierr);
  ierr = DSSetType(ds,DSNEP);CHKERRQ(ierr);
  ierr = DSNEPSetFN(ds,3,funs);CHKERRQ(ierr);
  ierr = DSAllocate(ds,nc);CHKERRQ(ierr);
  ierr = DSSetDimensions(ds,nc,0,0,0);CHKERRQ(ierr);
  ierr = NEPProjectOperator(nep,0,nc);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                Display projected matrices and clean up
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  for (k=0;k<3;k++) {
    ierr = DSGetArray(ds,DSMatExtra[k],&M);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"\nMatrix E%d = \n",k);CHKERRQ(ierr);
    for (i=0;i<nc;i++) {
      for (j=0;j<nc;j++) {
        ierr = PetscPrintf(PETSC_COMM_WORLD,"  %.5g",(double)PetscRealPart(M[i+j*nc]));CHKERRQ(ierr);
      }
      ierr = PetscPrintf(PETSC_COMM_WORLD,"\n");CHKERRQ(ierr);
    }
    ierr = DSRestoreArray(ds,DSMatExtra[k],&M);CHKERRQ(ierr);
  }

  ierr = NEPDestroy(&nep);CHKERRQ(ierr);
  ierr = MatDestroy(&Id);CHKERRQ(ierr);
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = MatDestroy(&B);CHKERRQ(ierr);
  ierr = FNDestroy(&f1);CHKERRQ(ierr);
  ierr = FNDestroy(&f2);CHKERRQ(ierr);
  ierr = FNDestroy(&f3);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return ierr;
}

/*TEST

   test:
      suffix: 1
      args: -nep_ncv 5

TEST*/
