zgbcon (l) - Linux Man Pages

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

NAME

ZGBCON - 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 ZGBCON(
NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, RWORK, INFO )

    
CHARACTER NORM

    
INTEGER INFO, KL, KU, LDAB, N

    
DOUBLE PRECISION ANORM, RCOND

    
INTEGER IPIV( * )

    
DOUBLE PRECISION RWORK( * )

    
COMPLEX*16 AB( LDAB, * ), WORK( * )

PURPOSE

ZGBCON estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGBTRF.
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) COMPLEX*16 array, dimension (LDAB,N)
Details of the LU factorization of the band matrix A, as computed by ZGBTRF. 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) DOUBLE PRECISION
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) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value