/*
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   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).
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/

static char help[] = "Test DSNHEP.\n\n";

#include <slepcds.h>

int main(int argc,char **argv)
{
  PetscErrorCode ierr;
  DS             ds;
  SlepcSC        sc;
  DSType         type;
  DSStateType    state;
  PetscScalar    *A,*X,*Q,*wr,*wi,d;
  PetscReal      re,im,rnorm,aux;
  PetscInt       i,j,n=10,ld,method;
  PetscViewer    viewer;
  PetscBool      verbose,extrarow;

  ierr = SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
  ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type NHEP - dimension %D.\n",n);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(NULL,NULL,"-extrarow",&extrarow);CHKERRQ(ierr);

  /* Create DS object */
  ierr = DSCreate(PETSC_COMM_WORLD,&ds);CHKERRQ(ierr);
  ierr = DSSetType(ds,DSNHEP);CHKERRQ(ierr);
  ierr = DSSetFromOptions(ds);CHKERRQ(ierr);
  ld = n+2;  /* test leading dimension larger than n */
  ierr = DSAllocate(ds,ld);CHKERRQ(ierr);
  ierr = DSSetDimensions(ds,n,0,0,0);CHKERRQ(ierr);
  ierr = DSSetExtraRow(ds,extrarow);CHKERRQ(ierr);

  /* Set up viewer */
  ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr);
  ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr);
  ierr = DSView(ds,viewer);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
  }

  /* Fill with Grcar matrix */
  ierr = DSGetArray(ds,DS_MAT_A,&A);CHKERRQ(ierr);
  for (i=1;i<n;i++) A[i+(i-1)*ld]=-1.0;
  for (j=0;j<4;j++) {
    for (i=0;i<n-j;i++) A[i+(i+j)*ld]=1.0;
  }
  if (extrarow) A[n+(n-1)*ld]=-1.0;
  ierr = DSRestoreArray(ds,DS_MAT_A,&A);CHKERRQ(ierr);
  ierr = DSSetState(ds,DS_STATE_INTERMEDIATE);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");CHKERRQ(ierr);
    ierr = DSView(ds,viewer);CHKERRQ(ierr);
  }

  /* Solve */
  ierr = PetscMalloc2(n,&wr,n,&wi);CHKERRQ(ierr);
  ierr = DSGetSlepcSC(ds,&sc);CHKERRQ(ierr);
  sc->comparison    = SlepcCompareLargestMagnitude;
  sc->comparisonctx = NULL;
  sc->map           = NULL;
  sc->mapobj        = NULL;
  ierr = DSSolve(ds,wr,wi);CHKERRQ(ierr);
  ierr = DSSort(ds,wr,wi,NULL,NULL,NULL);CHKERRQ(ierr);
  if (extrarow) { ierr = DSUpdateExtraRow(ds);CHKERRQ(ierr); }

  ierr = DSGetType(ds,&type);CHKERRQ(ierr);
  ierr = DSGetMethod(ds,&method);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"DS of type %s, method used=%d\n",type,method);CHKERRQ(ierr);
  ierr = DSGetState(ds,&state);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"State after solve: %s\n",DSStateTypes[state]);CHKERRQ(ierr);

  if (verbose) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");CHKERRQ(ierr);
    ierr = DSView(ds,viewer);CHKERRQ(ierr);
  }

  /* Print eigenvalues */
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalues =\n");CHKERRQ(ierr);
  for (i=0;i<n;i++) {
#if defined(PETSC_USE_COMPLEX)
    re = PetscRealPart(wr[i]);
    im = PetscImaginaryPart(wr[i]);
#else
    re = wr[i];
    im = wi[i];
#endif
    if (PetscAbs(im)<1e-10) {
      ierr = PetscViewerASCIIPrintf(viewer,"  %.5f\n",(double)re);CHKERRQ(ierr);
    } else {
      ierr = PetscViewerASCIIPrintf(viewer,"  %.5f%+.5fi\n",(double)re,(double)im);CHKERRQ(ierr);
    }
  }

  if (extrarow) {
    /* Check that extra row is correct */
    ierr = DSGetArray(ds,DS_MAT_A,&A);CHKERRQ(ierr);
    ierr = DSGetArray(ds,DS_MAT_Q,&Q);CHKERRQ(ierr);
    d = 0.0;
    for (i=0;i<n;i++) d += A[n+i*ld]+Q[n-1+i*ld];
    if (PetscAbsScalar(d)>10*PETSC_MACHINE_EPSILON) {
      ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in the extra row of %g\n",(double)PetscAbsScalar(d));CHKERRQ(ierr);
    }
    ierr = DSRestoreArray(ds,DS_MAT_A,&A);CHKERRQ(ierr);
    ierr = DSRestoreArray(ds,DS_MAT_Q,&Q);CHKERRQ(ierr);
  }

  /* Eigenvectors */
  j = 2;
  ierr = DSVectors(ds,DS_MAT_X,&j,&rnorm);CHKERRQ(ierr);  /* third eigenvector */
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Value of rnorm for 3rd vector = %.3f\n",(double)rnorm);CHKERRQ(ierr);
  ierr = DSVectors(ds,DS_MAT_X,NULL,NULL);CHKERRQ(ierr);  /* all eigenvectors */
  j = 0;
  rnorm = 0.0;
  ierr = DSGetArray(ds,DS_MAT_X,&X);CHKERRQ(ierr);
  for (i=0;i<n;i++) {
#if defined(PETSC_USE_COMPLEX)
    aux = PetscAbsScalar(X[i+j*ld]);
#else
    if (PetscAbs(wi[j])==0.0) aux = PetscAbsScalar(X[i+j*ld]);
    else aux = SlepcAbsEigenvalue(X[i+j*ld],X[i+(j+1)*ld]);
#endif
    rnorm += aux*aux;
  }
  ierr = DSRestoreArray(ds,DS_MAT_X,&X);CHKERRQ(ierr);
  rnorm = PetscSqrtReal(rnorm);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st vector = %.3f\n",(double)rnorm);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"After vectors - - - - - - - - -\n");CHKERRQ(ierr);
    ierr = DSView(ds,viewer);CHKERRQ(ierr);
  }

  ierr = PetscFree2(wr,wi);CHKERRQ(ierr);
  ierr = DSDestroy(&ds);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return ierr;
}

/*TEST

   testset:
      filter: sed -e "s/[+-]\([0-9]\.[0-9]*i\)/+-\\1/" | sed -e "s/extrarow//"
      output_file: output/test1_1.out
      requires: !single
      test:
         suffix: 1
      test:
         suffix: 2
         args: -extrarow

TEST*/
