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 = 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) 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 = '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) 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