/* nag_nearest_correlation_k_factor (g02aec) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.2, 2017.
 */

#include <nag.h>
#include <nag_stdlib.h>
#include <nagf16.h>
#include <nagg02.h>
#include <nagx04.h>

int main(void)
{

  /* Scalars */
  Integer exit_status = 0;
  double errtol, nrmpgd;
  Integer feval, i, iter, j, k, pda, pdg, pdx, maxit, n;

  /* Arrays */
  double *a = 0, *g = 0, *x = 0;

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

  INIT_FAIL(fail);

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J-1)*pda + I-1]
#define G(I, J) g[(J-1)*pdg + I-1]
  order = Nag_ColMajor;
#else
#define A(I, J) a[(I-1)*pda + J-1]
#define G(I, J) g[(I-1)*pdg + J-1]
  order = Nag_RowMajor;
#endif

  /* Output preamble */
  printf("nag_nearest_correlation_k_factor (g02aec) ");
  printf("Example Program Results\n\n");
  fflush(stdout);

  /* Skip heading in data file */
  scanf("%*[^\n]");
  /* Read in the problem size */
  scanf("%" NAG_IFMT "%*[^\n]", &n);

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

  /* 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 and maxit */
  errtol = 0.0;
  maxit = 0;
  /* Set k value */
  k = 2;

  /* nag_nearest_correlation_k_factor (g02aec).
   * Computes the nearest correlation matrix with k-factor structure
   * to a real square matrix
   */
  nag_nearest_correlation_k_factor(order, g, pdg, n, k, errtol, maxit, x,
                                   pdx, &iter, &feval, &nrmpgd, &fail);
  if (fail.code != NE_NOERROR) {
    printf("%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_gen_real_mat_print (x04cac).
   * Print real general matrix (easy-to-use)
   */
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, k, x,
                         pdx, "Factor Loading Matrix X", NULL, &fail);
  if (fail.code != NE_NOERROR) {
    printf("%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  printf("\nNumber of steps taken: %" NAG_IFMT "\n", iter);
  printf("Number of function evaluations: %" NAG_IFMT "\n\n", feval);
  fflush(stdout);

  /* Generate Nearest k factor correlation matrix
   * nag_dgemm (f16yac) performs matrix-matrix multiplication for a
   * real general matrix
   */
  nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, k, 1.0, x, pdx, x, pdx,
            0.0, a, pda, &fail);
  if (fail.code != NE_NOERROR) {
    printf("%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  for (i = 1; i <= n; i++)
    A(i, i) = 1.0;

  /* nag_gen_real_mat_print (x04cac).
   * Print real general matrix (easy-to-use)
   */
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a,
                         pda, "Nearest Correlation Matrix", NULL, &fail);
  if (fail.code != NE_NOERROR) {
    printf("%s\n", fail.message);
    exit_status = 1;
  }

END:
  NAG_FREE(a);
  NAG_FREE(g);
  NAG_FREE(x);
  return exit_status;
}