/* nag_lapackeig_ztpqrt (f08bpc) Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 *
 * Mark 27.3, 2021.
 */

#include <nag.h>

int main(void) {
  /* Scalars */
  double rnorm;
  Integer exit_status = 0;
  Integer pda, pdb, pdt;
  Integer i, j, m, n, nb, nrhs;
  /* Arrays */
  Complex *a = 0, *b = 0, *c = 0, *t = 0;
  /* Nag Types */
  Nag_OrderType order;
  NagError fail;

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

  INIT_FAIL(fail);

  printf("nag_lapackeig_ztpqrt (f08bpc) Example Program Results\n\n");
  fflush(stdout);

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n, &nrhs);
  nb = MIN(m, n);
  if (!(a = NAG_ALLOC(m * n, Complex)) || !(b = NAG_ALLOC(m * nrhs, Complex)) ||
      !(c = NAG_ALLOC(m * nrhs, Complex)) ||
      !(t = NAG_ALLOC(nb * MIN(m, n), Complex))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdb = m;
  pdt = nb;
#else
  pda = n;
  pdb = nrhs;
  pdt = MIN(m, n);
#endif

  /* Read A and B from data file */
  for (i = 1; i <= m; ++i)
    for (j = 1; j <= n; ++j)
      scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
  scanf("%*[^\n]");

  for (i = 1; i <= m; ++i)
    for (j = 1; j <= nrhs; ++j)
      scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im);
  scanf("%*[^\n]");

  for (i = 1; i <= m; ++i)
    for (j = 1; j <= nrhs; ++j)
      C(i, j) = B(i, j);

  /* nag_lapackeig_zgeqrt (f08apc).
   * Compute the QR factorization of first n rows of A by recursive algorithm.
   */
  nag_lapackeig_zgeqrt(order, n, n, nb, a, pda, t, pdt, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zgeqrt (f08apc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_lapackeig_zgemqrt (f08aqc).
   * Compute C = (C1) = (Q^H)*B, storing the result in C
   *             (C2)
   * by applying Q^H from left.
   */
  nag_lapackeig_zgemqrt(order, Nag_LeftSide, Nag_ConjTrans, n, nrhs, n, nb, a,
                        pda, t, pdt, c, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zgemqrt (f08aqc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  for (i = 1; i <= n; ++i)
    for (j = 1; j <= nrhs; ++j)
      B(i, j) = C(i, j);

  /* nag_lapacklin_ztrtrs (f07tsc).
   * Compute least squares solutions for first n rows
   * by back-substitution in R*X = C1.
   */
  nag_lapacklin_ztrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs,
                       a, pda, c, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapacklin_ztrtrs (f07tsc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_file_print_matrix_complex_gen_comp (x04dbc).
   * Print least squares solutions using first n rows.
   */
  nag_file_print_matrix_complex_gen_comp(
      order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, c, pdb,
      Nag_BracketForm, "%7.4f", "Solution(s) for n rows", Nag_IntegerLabels, 0,
      Nag_IntegerLabels, 0, 80, 0, 0, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_lapackeig_ztpqrt (f08bpc).
   * Now add the remaining rows and perform QR update.
   */
  nag_lapackeig_ztpqrt(order, m - n, n, 0, nb, a, pda, &A(n + 1, 1), pda, t,
                       pdt, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_ztpqrt (f08bpc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_lapackeig_ztpmqrt (f08bqc).
   * Apply orthogonal transformations to C.
   */
  nag_lapackeig_ztpmqrt(order, Nag_LeftSide, Nag_ConjTrans, m - n, nrhs, n, 0,
                        nb, &A(n + 1, 1), pda, t, pdt, b, pdb, &B(5, 1), pdb,
                        &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_ztpmqrt (f08bqc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_lapacklin_ztrtrs (f07tsc).
   * Compute least squares solutions for first n rows
   * by back-substitution in R*X = C1.
   */
  nag_lapacklin_ztrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs,
                       a, pda, b, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapacklin_ztrtrs (f07tsc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_file_print_matrix_complex_gen_comp (x04dbc).
   * Print least squares solutions.
   */
  printf("\n");
  fflush(stdout);
  nag_file_print_matrix_complex_gen_comp(
      order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb,
      Nag_BracketForm, "%7.4f", "Least squares solution(s) for all rows",
      Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  printf("\n Square root(s) of the residual sum(s) of squares\n");
  for (j = 1; j <= nrhs; j++) {
    /* nag_blast_zge_norm (f16uac).
     * Compute and print estimate of the square root of the residual
     * sum of squares.
     */
    nag_blast_zge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(n + 1, j), pdb,
                       &rnorm, &fail);
    if (fail.code != NE_NOERROR) {
      printf("\nError from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
    printf("  %11.2e ", rnorm);
  }
  printf("\n");

END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(c);
  NAG_FREE(t);

  return exit_status;
}