SGBCON 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)) ).

NORM

          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

          N is INTEGER


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

KL

          KL is INTEGER


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

KU

          KU is INTEGER


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

AB

          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

          LDAB is INTEGER


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

IPIV

          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

          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

          RCOND is REAL


          The reciprocal of the condition number of the matrix A,


          computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK

          WORK is REAL array, dimension (3*N)

IWORK

          IWORK is INTEGER array, dimension (N)

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value

Univ. of Tennessee

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NAG Ltd.

November 2011