MAN page from OpenSuSE 12.X lapack-man-3.3.1-15.1.noarch.rpm

CGBCON

Section: LAPACK routine (version 3.3.1) (1)
Updated: April 2011
Index

NAME

LAPACK-3 - estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,

SYNOPSIS

SUBROUTINE CGBCON(: NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,WORK, RWORK, INFO )
: CHARACTERNORM
: INTEGERINFO, KL, KU, LDAB, N
: REALANORM, RCOND
: INTEGERIPIV( * )
: REALRWORK( * )
: COMPLEXAB( LDAB, * ), WORK( * )

PURPOSE

CGBCON estimates the reciprocal of the condition number of a complexgeneral band matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by CGBTRF.

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)) ).

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) COMPLEX array, dimension (LDAB,N): Details of the LU factorization of the band matrix A, as
computed by CGBTRF. 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) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER: = 0: successful exit

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

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