/* nag_lapackeig_dgees (f08pac) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.2, 2023.
 */

#include <math.h>
#include <nag.h>
#include <stdio.h>

#ifdef __cplusplus
extern "C" {
#endif
static Nag_Boolean NAG_CALL select_fun(const double wr, const double wi);
#ifdef __cplusplus
}
#endif

int main(void) {

  /* Scalars */
  double alpha, anorm, beta, eps, norm;
  Integer i, j, n, pda, pdc, pdd, pdvs, sdim;
  Integer exit_status = 0;

  /* Arrays */
  double *a = 0, *c = 0, *d = 0, *vs = 0, *wi = 0, *wr = 0;

  /* Nag Types */
  NagError fail;
  Nag_OrderType order;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
  order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_lapackeig_dgees (f08pac) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT "%*[^\n]", &n);
  if (n < 0) {
    printf("Invalid n\n");
    exit_status = 1;
    return exit_status;
  }

  pda = n;
  pdc = n;
  pdd = n;
  pdvs = n;
  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, double)) || !(c = NAG_ALLOC(n * n, double)) ||
      !(d = NAG_ALLOC(n * n, double)) || !(vs = NAG_ALLOC(n * n, double)) ||
      !(wi = NAG_ALLOC(n, double)) || !(wr = NAG_ALLOC(n, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read in the matrix A */
  for (i = 1; i <= n; ++i)
    for (j = 1; j <= n; ++j)
      scanf("%lf", &A(i, j));
  scanf("%*[^\n]");

  /* Copy A to D: nag_blast_dge_copy (f16qfc),
   * real valued general matrix copy.
   */
  nag_blast_dge_copy(order, Nag_NoTrans, n, n, a, pda, d, pdd, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dge_copy (f16qfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* nag_blast_dge_norm (f16rac): Find norm of matrix A for use later
   * in relative error test.
   */
  nag_blast_dge_norm(order, Nag_OneNorm, n, n, a, pda, &anorm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_file_print_matrix_real_gen (x04cac): Print Matrix A. */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 n, a, pda, "Matrix A", 0, &fail);
  printf("\n");
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Find the Schur factorization of A using nag_lapackeig_dgees (f08pac). */
  nag_lapackeig_dgees(order, Nag_Schur, Nag_SortEigVals, select_fun, n, a, pda,
                      &sdim, wr, wi, vs, pdvs, &fail);

  if (fail.code != NE_NOERROR && fail.code != NE_SCHUR_REORDER_SELECT) {
    printf("Error from nag_lapackeig_dgees (f08pac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Reconstruct A from Schur Factorization Z*T*Trans(Z) where T is upper
   * triangular and stored in A. This can be done using the following steps:
   * i.  C = Z*T (nag_blast_dgemm, f16yac),
   * ii. D = D-C*trans(Z) (nag_blast_dgemm, f16yac).
   */
  alpha = 1.0;
  beta = 0.0;
  nag_blast_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, vs, pdvs, a,
                  pda, beta, c, pdc, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dgemm (f16yac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_blast_dgemm (f16yac):
   * Compute D = A - C*Z^T.
   */
  alpha = -1.0;
  beta = 1.0;
  nag_blast_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, vs,
                  pdvs, beta, d, pdd, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dgemm (f16yac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_blast_dge_norm (f16rac): Find norm of difference matrix D and print
   * warning if it is too large relative to norm of A.
   */
  nag_blast_dge_norm(order, Nag_OneNorm, n, n, d, pdd, &norm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Get the machine precision, using nag_machine_precision (x02ajc) */
  eps = nag_machine_precision;
  if (norm > pow(eps, 0.8) * MAX(anorm, 1.0)) {
    printf("||A-(Z*T*Z^T)||/||A|| is larger than expected.\n"
           "Schur factorization has failed.\n");
    exit_status = 1;
    goto END;
  }

  /* Print details on eigenvalues */
  printf("Number of eigenvalues for which select is true = %4" NAG_IFMT "\n\n",
         sdim);
  if (fail.code == NE_SCHUR_REORDER_SELECT) {
    printf(" ** Note that rounding errors mean that leading eigenvalues in the"
           " Schur form\n    no longer satisfy select(lambda) = Nag_TRUE\n\n");
  } else {
    printf("The selected eigenvalues are:\n");
    for (i = 0; i < sdim; i++)
      printf("%3" NAG_IFMT " (%13.4e, %13.4e)\n", i + 1, wr[i], wi[i]);
  }

END:
  NAG_FREE(a);
  NAG_FREE(c);
  NAG_FREE(d);
  NAG_FREE(vs);
  NAG_FREE(wi);
  NAG_FREE(wr);

  return exit_status;
}

static Nag_Boolean NAG_CALL select_fun(const double ar, const double ai) {
  /* Boolean function select for use with nag_lapackeig_dgees (f08pac)
   * Returns the value Nag_TRUE if the eigenvalue is real and positive
   */

  return (ar > 0.0 && ai == 0.0 ? Nag_TRUE : Nag_FALSE);
}