/* nag_linsys_complex_square_solve (f04cac) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 */

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

int main(void) {
  /* Scalars */
  double errbnd, rcond;
  Integer exit_status, i, j, n, nrhs, pda, pdb;

  /* Arrays */
  char *clabs = 0, *rlabs = 0;
  Complex *a = 0, *b = 0;
  Integer *ipiv = 0;

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

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

  exit_status = 0;
  INIT_FAIL(fail);

  printf(
      "nag_linsys_complex_square_solve (f04cac) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &nrhs);
  if (n > 0 && nrhs > 0) {
    /* Allocate memory */
    if (!(clabs = NAG_ALLOC(2, char)) || !(rlabs = NAG_ALLOC(2, char)) ||
        !(a = NAG_ALLOC(n * n, Complex)) ||
        !(b = NAG_ALLOC(n * nrhs, Complex)) ||
        !(ipiv = NAG_ALLOC(8, Integer))) {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
#ifdef NAG_COLUMN_MAJOR
    pda = n;
    pdb = n;
#else
    pda = n;
    pdb = nrhs;
#endif

    /* Read A and B from data file */
  } else {
    printf("%s\n", "NMAX and/or NRHSMX too small");
    exit_status = 1;
    return exit_status;
  }

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

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

  /* Solve the equations AX = B for X */
  /* nag_linsys_complex_square_solve (f04cac).
   * Computes the solution and error-bound to a complex system
   * of linear equations
   */
  nag_linsys_complex_square_solve(order, n, nrhs, a, pda, ipiv, b, pdb, &rcond,
                                  &errbnd, &fail);
  if (fail.code == NE_NOERROR) {
    /* Print solution, estimate of condition number and approximate */
    /* error bound */

    /* nag_file_print_matrix_complex_gen_comp (x04dbc).
     * Print complex general matrix (comprehensive)
     */
    fflush(stdout);
    nag_file_print_matrix_complex_gen_comp(
        order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb,
        Nag_BracketForm, "%7.4f", "Solution", 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");
    printf("%s\n%8s%10.1e\n", "Estimate of condition number", "", 1.0 / rcond);
    printf("\n\n");
    printf("%s\n%8s%10.1e\n\n",
           "Estimate of error bound for computed solutions", "", errbnd);
  } else if (fail.code == NE_RCOND) {
    /* Matrix is numerically singular.  Print estimate of */
    /* reciprocal of condition number and solution */

    printf("\n");
    printf("%s\n%8s%10.1e\n\n\n", "Estimate of reciprocal of condition number",
           "", rcond);
    /* nag_file_print_matrix_complex_gen_comp (x04dbc), see above. */
    fflush(stdout);
    nag_file_print_matrix_complex_gen_comp(
        order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb,
        Nag_BracketForm, 0, "Solution", 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;
    }
  } else if (fail.code == NE_SINGULAR) {
    /* The upper triangular matrix U is exactly singular.  Print */
    /* details of factorization */
    printf("\n");
    /* nag_file_print_matrix_complex_gen_comp (x04dbc), see above. */
    fflush(stdout);
    nag_file_print_matrix_complex_gen_comp(
        order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda,
        Nag_BracketForm, "%7.4f", "Details of factorization", 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;
    }

    /* Print pivot indices */
    printf("\n");
    printf("%s\n", "Pivot indices");
    printf("%1s", "");
    for (i = 1; i <= n; ++i) {
      printf("%11" NAG_IFMT "%s", ipiv[i - 1],
             i % 7 == 0 || i == n ? "\n" : " ");
    }
    printf("\n");
  } else {
    printf("Error from nag_linsys_complex_square_solve (f04cac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
END:
  NAG_FREE(clabs);
  NAG_FREE(rlabs);
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(ipiv);

  return exit_status;
}