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# 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

## Index

NAME
SYNOPSIS
PURPOSE
ARGUMENTS

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