実対称正定値連立一次方程式の解及び誤差限界の計算

nag_real_sym_posdef_lin_solve (f04bdc) Example Program Data

   4      2                  :Values of n and nrhs
   Nag_Upper                 :Value of uplo
   4.16  -3.12   0.56  -0.10
          5.03  -0.83   1.18
                 0.76   0.34
                        1.18 :End of matrix A

   8.70   8.30
 -13.35   2.13
   1.89   1.61
  -4.14   5.00               :End of matrix B

nag_real_sym_posdef_lin_solve (f04bdc) Example Program Results

 Solution
            1          2
 1      1.0000     4.0000
 2     -1.0000     3.0000
 3      2.0000     2.0000
 4     -3.0000     1.0000

Estimate of condition number
         9.7e+01


Estimate of error bound for computed solutions
         1.1e-14

/* nag_real_sym_posdef_lin_solve (f04bdc) Example Program.
 *
 * CLL6I261D/CLL6I261DL Version.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.1, 2017.
 */

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf04.h>
#include <nagx04.h>

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

  /* Arrays */
  char nag_enum_arg[40];
  double *a = 0, *b = 0;

  /* Nag Types */
  Nag_OrderType order;
  Nag_UploType uplo;
  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]
  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_real_sym_posdef_lin_solve (f04bdc) Example Program Results\n\n");

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

  scanf("%ld%ld%*[^\n] ", &n, &nrhs);
  if (n >= 0 && nrhs >= 0) {
    /* Allocate memory */
    if (!(a = nAG_ALLOC(n * n, double)) || !(b = nAG_ALLOC(n * nrhs, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
#ifdef nAG_COLUMN_MAJOR
    pda = n;
    pdb = n;
#else
    pda = n;
    pdb = nrhs;
#endif
  }
  else {
    printf("%s\n", "n and/or nrhs too small");
    exit_status = 1;
    return exit_status;
  }

  scanf("%39s%*[^\n] ", nag_enum_arg);
  /* nag_enum_name_to_value (x04nac).
   * Converts nAG enum member name to value
   */
  uplo = (Nag_UploType) nag_enum_name_to_value(nag_enum_arg);

  if (uplo == Nag_Upper) {
    /* Read the upper triangular part of A from data file */
    for (i = 1; i <= n; ++i) {
      for (j = i; j <= n; ++j) {
        scanf("%lf", &A(i, j));
      }
    }
    scanf("%*[^\n] ");
  }
  else {
    /* Read the lower triangular part of A from data file */
    for (i = 1; i <= n; ++i) {
      for (j = 1; j <= i; ++j) {
        scanf("%lf", &A(i, j));
      }
    }
    scanf("%*[^\n] ");
  }

  /* Read B from data file */
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= nrhs; ++j) {
      scanf("%lf", &B(i, j));
    }
  }
  scanf("%*[^\n] ");

  /* Solve the equations AX = B for X */

  /* nag_real_sym_posdef_lin_solve (f04bdc).
   * Computes the solution and error-bound to a real symmetric
   * positive-definite system of linear equations
   */
  nag_real_sym_posdef_lin_solve(order, uplo, n, nrhs, a, pda, b, pdb,
                                &rcond, &errbnd, &fail);
  if (fail.code == NE_NOERROR) {
    /* Print solution, estimate of condition number and approximate */
    /* error bound */

    /* nag_gen_real_mat_print (x04cac).
     * Print real general matrix (easy-to-use)
     */
    fflush(stdout);
    nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                           nrhs, b, pdb, "Solution", 0, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }
    printf("\n");
    printf("%s\n%6s%10.1e\n", "Estimate of condition number", "",
           1.0 / rcond);
    printf("\n\n");

    printf("%s\n%6s%10.1e\n\n",
           "Estimate of error bound for computed solutions", "", errbnd);
  }
  else if (fail.code == NE_RCOND) {
    /* Matrix A is numerically singular.  Print estimate of */
    /* reciprocal of condition number and solution */

    printf("\n%s\n%6s%10.1e\n\n\n",
           "Estimate of reciprocal of condition number", "", rcond);
    /* nag_gen_real_mat_print (x04cac), see above. */
    fflush(stdout);
    nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                           nrhs, b, pdb, "Solution", 0, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }
  }
  else if (fail.code == NE_POS_DEF) {
    /* The matrix A is not positive definite to working precision */
    printf("%s%3ld%s\n\n", "The leading minor of order ",
           fail.errnum, " is not positive definite");
  }
  else {
    printf("Error from nag_real_sym_posdef_lin_solve (f04bdc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

END:
  nAG_FREE(a);
  nAG_FREE(b);

  return exit_status;
}