/* nag_lapackeig_dgebal (f08nhc) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.2, 2024.
 */

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

int main(void) {
  /* Scalars */
  Integer firstnz, i, ihi, ilo, j, m, n, pda, pdh, pdvr;
  Integer scale_len, tau_len, wi_len, wr_len;
  Integer exit_status = 0;
  NagError fail;
  Nag_OrderType order;
  /* Arrays */
  double *a = 0, *h = 0, *scale = 0, *tau = 0, *vl = 0, *vr = 0;
  double *wi = 0, *wr = 0;
  Nag_Boolean *select = 0;

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

  INIT_FAIL(fail);

  printf("nag_lapackeig_dgebal (f08nhc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%*[^\n] ", &n);

  pda = n;
  pdh = n;
  pdvr = n;
  scale_len = n;
  tau_len = n;
  wi_len = n;
  wr_len = n;

  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, double)) || !(h = NAG_ALLOC(n * n, double)) ||
      !(scale = NAG_ALLOC(scale_len, double)) ||
      !(tau = NAG_ALLOC(tau_len, double)) || !(vl = NAG_ALLOC(1 * 1, double)) ||
      !(vr = NAG_ALLOC(n * n, double)) || !(wi = NAG_ALLOC(wi_len, double)) ||
      !(wr = NAG_ALLOC(wr_len, double)) ||
      !(select = NAG_ALLOC(1, Nag_Boolean))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read A from data file */
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= n; ++j)
      scanf("%lf", &A(i, j));
  }
  scanf("%*[^\n] ");

  /* Balance A */
  /* nag_lapackeig_dgebal (f08nhc).
   * Balance real general matrix
   */
  nag_lapackeig_dgebal(order, Nag_DoBoth, n, a, pda, &ilo, &ihi, scale, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgebal (f08nhc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Reduce A to upper Hessenberg form H = (Q^T)*A*Q */
  /* nag_lapackeig_dgehrd (f08nec).
   * Orthogonal reduction of real general matrix to upper
   * Hessenberg form
   */
  nag_lapackeig_dgehrd(order, n, ilo, ihi, a, pda, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgehrd (f08nec).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Copy A to H and VR */
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= n; ++j) {
      H(i, j) = A(i, j);
      VR(i, j) = A(i, j);
    }
  }

  /* Form Q explicitly, storing the result in VR */
  /* nag_lapackeig_dorghr (f08nfc).
   * Generate orthogonal transformation matrix from reduction
   * to Hessenberg form determined by nag_lapackeig_dgehrd (f08nec)
   */
  nag_lapackeig_dorghr(order, n, 1, n, vr, pdvr, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dorghr (f08nfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Calculate the eigenvalues and Schur factorization of A */
  /* nag_lapackeig_dhseqr (f08pec).
   * Eigenvalues and Schur factorization of real upper
   * Hessenberg matrix reduced from real general matrix
   */
  nag_lapackeig_dhseqr(order, Nag_Schur, Nag_UpdateZ, n, ilo, ihi, h, pdh, wr,
                       wi, vr, pdvr, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dhseqr (f08pec).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  printf(" Eigenvalues\n");
  for (i = 1; i <= n; ++i)
    printf("(%8.4f,%8.4f)\n", wr[i - 1], wi[i - 1]);
  /* Calculate the eigenvectors of A, storing the result in VR */
  /* nag_lapackeig_dtrevc (f08qkc).
   * Left and right eigenvectors of real upper
   * quasi-triangular matrix
   */
  nag_lapackeig_dtrevc(order, Nag_RightSide, Nag_BackTransform, select, n, h,
                       pdh, vl, 1, vr, pdvr, n, &m, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dtrevc (f08qkc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* nag_lapackeig_dgebak (f08njc).
   * Transform eigenvectors of real balanced matrix to those
   * of original matrix supplied to nag_lapackeig_dgebal (f08nhc)
   */
  nag_lapackeig_dgebak(order, Nag_DoBoth, Nag_RightSide, n, ilo, ihi, scale, m,
                       vr, pdvr, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgebak (f08njc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Normalize the left eigenvectors */
  for (j = 1; j <= n; j++) {
    firstnz = n;
    for (i = n; i >= 1; i--) {
      if (VR(i, j) != 0) {
        firstnz = i;
      }
    }
    for (i = n; i >= 1; i--) {
      VR(i, j) = VR(i, j) / VR(firstnz, j);
    }
  }

  /* Print eigenvectors */
  printf("\n");
  /* nag_file_print_matrix_real_gen (x04cac).
   * Print real general matrix (easy-to-use)
   */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 m, vr, pdvr, "Contents of array VR", 0, &fail);
  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;
  }
END:
  NAG_FREE(a);
  NAG_FREE(h);
  NAG_FREE(scale);
  NAG_FREE(tau);
  NAG_FREE(vl);
  NAG_FREE(vr);
  NAG_FREE(wi);
  NAG_FREE(wr);
  NAG_FREE(select);

  return exit_status;
}