DGBCON - estimate the reciprocal of the condition number
of a real general band matrix A, in either the 1-norm or
the infinity-norm,
SYNOPSIS
SUBROUTINE DGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM,
RCOND, WORK, IWORK, INFO )
CHARACTER NORM
INTEGER INFO, KL, KU, LDAB, N
DOUBLE PRECISION ANORM, RCOND
INTEGER IPIV( * ), IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), WORK( * )
PURPOSE
DGBCON 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 DGB
TRF.
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) DOUBLE PRECISION array, dimension (LDAB,N)
Details of the LU factorization of the band matrix
A, as computed by DGBTRF. 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
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) DOUBLE PRECISION
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 (output) DOUBLE PRECISION
The reciprocal of the condition number of the
matrix A, computed as RCOND = 1/(norm(A) *
norm(inv(A))).
WORK (workspace) DOUBLE PRECISION 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
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