/* nag_sparse_direct_real_gen_refine (f11mhc) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.3, 2023.
 */

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

/* Table of constant values */

static Integer c__1 = 1;
static Integer c__80 = 80;
static Integer c__0 = 0;

int main(void) {
  double flop, thresh;
  Integer exit_status = 0, i, j;
  Integer n, nnz, nnzl, nnzu, nrhs, nzlmx, nzlumx, nzumx;
  double *a = 0, *b = 0, *berr = 0, *ferr = 0, *lval = 0;
  double *uval = 0, *x = 0;
  Integer *icolzp = 0, *il = 0, *iprm = 0, *irowix = 0;
  Integer *iu = 0;
  /* Nag types */
  Nag_OrderType order = Nag_ColMajor;
  Nag_MatrixType matrix = Nag_GeneralMatrix;
  Nag_DiagType diag = Nag_NonUnitDiag;
  Nag_ColumnPermutationType ispec;
  Nag_TransType trans;
  NagError fail;

  INIT_FAIL(fail);

  printf(
      "nag_sparse_direct_real_gen_refine (f11mhc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  /* Read order of matrix and number of right hand sides */
  scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &nrhs);
  /* Read the matrix A */
  if (!(icolzp = NAG_ALLOC(n + 1, Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  for (i = 1; i <= n + 1; ++i)
    scanf("%" NAG_IFMT "%*[^\n] ", &icolzp[i - 1]);
  nnz = icolzp[n] - 1;
  /* Allocate memory */
  if (!(irowix = NAG_ALLOC(nnz, Integer)) || !(a = NAG_ALLOC(nnz, double)) ||
      !(il = NAG_ALLOC(7 * n + 8 * nnz + 4, Integer)) ||
      !(iu = NAG_ALLOC(2 * n + 8 * nnz + 1, Integer)) ||
      !(uval = NAG_ALLOC(8 * nnz, double)) ||
      !(lval = NAG_ALLOC(8 * nnz, double)) ||
      !(b = NAG_ALLOC(n * nrhs, double)) ||
      !(x = NAG_ALLOC(n * nrhs, double)) || !(berr = NAG_ALLOC(nrhs, double)) ||
      !(ferr = NAG_ALLOC(nrhs, double)) ||
      !(iprm = NAG_ALLOC(7 * n, Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  for (i = 0; i < nnz; ++i)
    scanf("%lf%" NAG_IFMT "%*[^\n] ", &a[i], &irowix[i]);
  /* Read the right hand sides */
  for (j = 0; j < nrhs; ++j) {
    for (i = 0; i < n; ++i) {
      scanf("%lf", &x[j * n + i]);
      b[j * n + i] = x[j * n + i];
    }
    scanf("%*[^\n] ");
  }
  /* Calculate COLAMD permutation */
  ispec = Nag_Sparse_Colamd;
  /* nag_sparse_direct_real_gen_setup (f11mdc).
   * Real sparse nonsymmetric linear systems, setup for
   * nag_sparse_direct_real_gen_lu (f11mec)
   */
  nag_sparse_direct_real_gen_setup(ispec, n, icolzp, irowix, iprm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparse_direct_real_gen_setup (f11mdc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Factorise */
  thresh = 1.;
  nzlmx = 8 * nnz;
  nzlumx = 8 * nnz;
  nzumx = 8 * nnz;
  /* nag_sparse_direct_real_gen_lu (f11mec).
   * LU factorization of real sparse matrix
   */
  nag_sparse_direct_real_gen_lu(n, irowix, a, iprm, thresh, nzlmx, &nzlumx,
                                nzumx, il, lval, iu, uval, &nnzl, &nnzu, &flop,
                                &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparse_direct_real_gen_lu (f11mec).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Compute solution in array X */
  trans = Nag_NoTrans;
  /* nag_sparse_direct_real_gen_solve (f11mfc).
   * Solution of real sparse simultaneous linear equations
   * (coefficient matrix already factorized)
   */
  nag_sparse_direct_real_gen_solve(order, trans, n, iprm, il, lval, iu, uval,
                                   nrhs, x, n, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparse_direct_real_gen_solve (f11mfc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Improve solution, and compute backward errors and estimated */
  /* bounds on the forward errors */
  /* nag_sparse_direct_real_gen_refine (f11mhc).
   * Refined solution with error bounds of real system of
   * linear equations, multiple right-hand sides
   */
  nag_sparse_direct_real_gen_refine(order, trans, n, icolzp, irowix, a, iprm,
                                    il, lval, iu, uval, nrhs, b, n, x, n, ferr,
                                    berr, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparse_direct_real_gen_refine (f11mhc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Print solution */
  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, matrix, diag, n, nrhs, x, n,
                                 "Solutions", 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;
  }

  /* nag_file_print_matrix_real_gen_comp (x04cbc).
   * Print real general matrix (comprehensive)
   */
  fflush(stdout);
  nag_file_print_matrix_real_gen_comp(order, matrix, diag, nrhs, c__1, ferr,
                                      nrhs, "%8.2g", "Estimated Forward Error",
                                      Nag_NoLabels, NULL, Nag_NoLabels, NULL,
                                      c__80, c__0, 0, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_file_print_matrix_real_gen_comp (x04cbc), see above. */
  fflush(stdout);
  nag_file_print_matrix_real_gen_comp(
      order, matrix, diag, nrhs, c__1, berr, nrhs, "%8.2g", "Backward Error",
      Nag_NoLabels, NULL, Nag_NoLabels, NULL, c__80, c__0, 0, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(berr);
  NAG_FREE(ferr);
  NAG_FREE(lval);
  NAG_FREE(uval);
  NAG_FREE(x);
  NAG_FREE(icolzp);
  NAG_FREE(il);
  NAG_FREE(iprm);
  NAG_FREE(irowix);
  NAG_FREE(iu);
  return exit_status;
}