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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