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