GBCON - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void gbcon(char *norm, integer *n, integer *kl, integer *ku, T *ab, integer *ldab, integer *ipiv, T *anorm, T *rcond, T *work, integer *iwork, integer *info)#

estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,

Purpose :

   GBCON estimates the reciprocal of the condition number of a real
   general band matrix A, in either the 1-norm or the infinity-norm,
   using the LU factorization computed by SGBTRF.

   An estimate is obtained for norm(inv(A)), and the reciprocal of the
   condition number is computed as
     RCOND = 1 / ( norm(A) * norm(inv(A))).
Parameters:
  • NORM[in]

    NORM is CHARACTER*1

    Specifies whether the 1-norm condition number or the infinity-norm condition number is required:

    = ‘1’ or ‘O’: 1-norm;

    = ‘I’: Infinity-norm.

  • N[in]

    N is INTEGER

    The order of the matrix A. N >= 0.

  • KL[in]

    KL is INTEGER

    The number of subdiagonals within the band of A. KL >= 0.

  • KU[in]

    KU is INTEGER

    The number of superdiagonals within the band of A. KU >= 0.

  • AB[in]

    AB is REAL array, dimension (LDAB,N)

    Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.

  • LDAB[in]

    LDAB is INTEGER

    The leading dimension of the array AB. LDAB >= 2*KL+KU+1.

  • IPIV[in]

    IPIV is INTEGER array, dimension (N)

    The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).

  • ANORM[in]

    ANORM is REAL

    If NORM = ‘1’ or ‘O’, the 1-norm of the original matrix A.

    If NORM = ‘I’, the infinity-norm of the original matrix A.
  • RCOND[out]

    RCOND is REAL

    The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

  • WORK[out] WORK is COMPLEX array, dimension (2*N)

  • RWORK[out] RWORK is REAL array, dimension (N)

  • INFO[out]

    INFO is INTEGER

    = 0: successful exit

    < 0: if INFO = -i, the i-th argument had an illegal value
template<typename T, typename Ta>
void gbcon(char *norm, integer *n, integer *kl, integer *ku, T *ab, integer *ldab, integer *ipiv, Ta *anorm, Ta *rcond, T *work, Ta *rwork, integer *info)#