/* nag_lapackeig_dgbbrd (f08lec) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.1, 2024.
 */

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

int main(void) {
  /* Scalars */
  double alpha, beta, norm;
  Integer i, j, kl, ku, m, n, ncc, pdab, pdaw, pdc, pdf, pdq;
  Integer pdpt, d_len, e_len;
  Integer exit_status = 0;
  NagError fail;
  Nag_OrderType order;
  /* Arrays */
  double *ab = 0, *aw = 0, *c = 0, *d = 0, *e = 0, *f = 0, *pt = 0, *q = 0;

#ifdef NAG_COLUMN_MAJOR
#define AB(I, J) ab[(J - 1) * pdab + ku + I - J]
#define AW(I, J) aw[(J - 1) * pdaw + I - 1]
#define F(I, J) f[(J - 1) * pdf + I - 1]
#define Q(I, J) q[(J - 1) * pdq + I - 1]
  order = Nag_ColMajor;
#else
#define AB(I, J) ab[(I - 1) * pdab + kl + J - I]
#define AW(I, J) aw[(I - 1) * pdaw + J - 1]
#define F(I, J) f[(I - 1) * pdf + J - 1]
#define Q(I, J) q[(I - 1) * pdq + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_lapackeig_dgbbrd (f08lec) Example Program Results\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT
        "%*[^\n] ",
        &m, &n, &kl, &ku, &ncc);
#ifdef NAG_COLUMN_MAJOR
  pdab = kl + ku + 1;
  pdaw = m;
  pdf = m;
  pdq = m;
  pdpt = n;
  pdc = m;
#else
  pdab = kl + ku + 1;
  pdaw = n;
  pdf = n;
  pdq = m;
  pdpt = n;
  pdc = MAX(1, ncc);
#endif
  d_len = MIN(m, n);
  e_len = MIN(m, n) - 1;

  /* Allocate memory */
  if (!(ab = NAG_ALLOC((kl + ku + 1) * m, double)) ||
      !(aw = NAG_ALLOC(m * n, double)) || !(f = NAG_ALLOC(m * n, double)) ||
      !(c = NAG_ALLOC(m * MAX(1, ncc), double)) ||
      !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) ||
      !(pt = NAG_ALLOC(n * n, double)) || !(q = NAG_ALLOC(m * m, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

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

  /* Copy AB into AW */
  for (i = 1; i <= m; ++i) {
    for (j = 1; j <= n; ++j) {
      if (j >= MAX(1, i - kl) && j <= MIN(n, i + ku))
        AW(i, j) = AB(i, j);
      else
        AW(i, j) = 0;
    }
  }

  /* nag_file_print_matrix_real_gen (x04cac): Print Matrix A. */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m,
                                 n, aw, pdaw, "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;
  }

  /* Reduce A to bidiagonal form */
  /* nag_lapackeig_dgbbrd (f08lec).
   * Reduction of real rectangular band matrix to upper
   * bidiagonal form
   */
  nag_lapackeig_dgbbrd(order, Nag_FormBoth, m, n, ncc, kl, ku, ab, pdab, d, e,
                       q, pdq, pt, pdpt, c, pdc, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgbbrd (f08lec).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* F = Q*B */
  for (i = 1; i <= m; i++) {
    F(i, 1) = Q(i, 1) * d[0];
    for (j = 2; j <= n; j++) {
      F(i, j) = (Q(i, j) * d[j - 1]) + (Q(i, j - 1) * e[j - 2]);
    }
  }

  /* nag_blast_dgemm (f16yac): Compute A - Q*B*P^T from the factorization of A
   */
  /* and store in matrix AW */
  alpha = -1.0;
  beta = 1.0;
  nag_blast_dgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, n, alpha, f, pdf, pt,
                  pdpt, beta, aw, pdaw, &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 matrix AW and print warning if */
  /* it is too large */
  nag_blast_dge_norm(order, Nag_OneNorm, m, n, aw, pdaw, &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;
  }
  if (norm > pow(x02ajc(), 0.8)) {
    printf("%s\n%s\n", "Norm of A-(Q*B*P^T) is much greater than 0.",
           "Schur factorization has failed.");
  }

END:
  NAG_FREE(ab);
  NAG_FREE(aw);
  NAG_FREE(c);
  NAG_FREE(d);
  NAG_FREE(e);
  NAG_FREE(f);
  NAG_FREE(pt);
  NAG_FREE(q);

  return exit_status;
}