sgbcon (l) - Linux Manuals

NAME

SGBCON - estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-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 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 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:
= aq1aq or aqOaq: 1-norm;
= aqIaq: 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 = aq1aq or aqOaq, the 1-norm of the original matrix A. If NORM = aqIaq, the infinity-norm of the original matrix A.
RCOND (output) REAL
The reciprocal of the condition number of the matrix 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 illegal value