/* nag_correg_corrmat_nearest_rank (g02akc) Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 *
 * Mark 27.2, 2021.
 */
#include <math.h>
#include <nag.h>
#include <stdio.h>

int main(void) {
  Integer exit_status = 0;
  Integer i, j, pdg, pdx, maxit, maxits, n, nsub, rank;

  double errtol, f, rankerr, ranktol;
  double *g = 0, *x = 0;

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

  INIT_FAIL(fail);

#define G(I, J) g[(J - 1) * pdg + I - 1]

  printf(
      "nag_correg_corrmat_nearest_rank (g02akc) Example Program Results\n\n");

  /* skip heading in data file */
  scanf("%*[^\n] ");

  /* read in the problem size */
  scanf("%" NAG_IFMT "%*[^\n] ", &n);

  pdg = n;
  pdx = n;
  if (!(g = NAG_ALLOC(pdg * n, double)) || !(x = NAG_ALLOC(pdx * n, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* read in the rank constraint */
  scanf("%" NAG_IFMT "%*[^\n] ", &rank);

  /* read in the matrix g */
  for (i = 1; i <= n; i++)
    for (j = 1; j <= n; j++)
      scanf("%lf", &G(i, j));
  scanf("%*[^\n] ");

  /* use the defaults for errtol , ranktol, maxits, maxit */
  errtol = 0.0;
  ranktol = 0.0;
  maxits = 0;
  maxit = 0;

  /* nag_correg_corrmat_nearest_rank (g02akc)
   * computes the nearest correlation matrix subject to rank constraint
   * to a real square matrix using majorized penalty approach of Gao and Sun
   */
  nag_correg_corrmat_nearest_rank(g, pdg, n, rank, errtol, ranktol, maxits,
                                  maxit, x, pdx, &f, &rankerr, &nsub, &fail);

  if (fail.code != NE_NOERROR) {
    printf("Error from nag_correg_corrmat_nearest_rank (g02akc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Display results */

  order = Nag_ColMajor;

  /*
   * nag_file_print_matrix_real_gen (x04cac).
   * Prints real general matrix
   */
  nag_file_print_matrix_real_gen(
      order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, x, pdx,
      "Nearest correlation matrix with rank constraint", NULL, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
           fail.message);
    exit_status = 2;
    goto END;
  }

  printf("\n");
  printf(" Number of subproblems solved:%12" NAG_IFMT "\n\n", nsub);
  printf(" Squared Frobenius norm of difference: %11.3e\n\n", f);
  printf(" Rank error: %37.3e\n\n", rankerr);

END:
  NAG_FREE(g);
  NAG_FREE(x);

  return exit_status;
}