sgbcon(3)

NAME

SGBCON - estimate the reciprocal of the condition number

of a real general band matrix A, in either the 1-norm or the in

finity-norm,

SYNOPSIS

SUBROUTINE SGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM,
RCOND, WORK, IWORK, INFO )
    CHARACTER      NORM
    INTEGER        INFO, KL, KU, LDAB, N
    REAL           ANORM, RCOND
    INTEGER        IPIV( * ), IWORK( * )
    REAL           AB( LDAB, * ), WORK( * )

PURPOSE

SGBCON estimates the reciprocal of the condition number of

a real general band matrix A, in either the 1-norm or the infini

ty-norm, using the LU factorization computed by SGBTRF.

An estimate is obtained for norm(inv(A)), and the recipro

cal of the condition number is computed as

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

ARGUMENTS

NORM (input) 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 (input) INTEGER

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

KL (input) INTEGER

The number of subdiagonals within the band of A.

KL >= 0.

KU (input) INTEGER

The number of superdiagonals within the band of A.

KU >= 0.

AB (input) 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 (input) INTEGER

The leading dimension of the array AB. LDAB >=

2*KL+KU+1.

IPIV (input) INTEGER array, dimension (N)

The pivot indices; for 1 <= i <= N, row i of the

matrix was interchanged with row IPIV(i).

ANORM (input) REAL

If NORM = '1' or 'O', the 1-norm of the original

matrix A. If NORM = 'I', the infinity-norm of the original ma

trix A.

RCOND (output) REAL

The reciprocal of the condition number of the ma

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

WORK (workspace) REAL array, dimension (3*N)

IWORK (workspace) INTEGER array, dimension (N)

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

LAPACK version 3.0 15 June 2000

SGBCON(3)