zgbcon(3S)

NAME
     ZGBCON - estimate 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( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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