zgbcon.f man page

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

ZGBCON  

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)) ).

Parameters:

NORM

          NORM is 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

          N is INTEGER
          The order of the matrix A.  N >= 0.

KL

          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.

KU

          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.

AB

          AB is 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

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

IPIV

          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= N, row i of the matrix was
          interchanged with row IPIV(i).

ANORM

          ANORM is 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

          RCOND is DOUBLE PRECISION
          The reciprocal of the condition number of the matrix A,
          computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK

          WORK is COMPLEX*16 array, dimension (2*N)

RWORK

          RWORK is DOUBLE PRECISION array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 147 of file zgbcon.f.