dgecon(3S)

NAME
     DGECON - estimate the reciprocal of the condition number of a general
     real matrix A, in either the 1-norm or the infinity-norm, using the LU
     factorization computed by DGETRF

SYNOPSIS
     SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO )

         CHARACTER      NORM

         INTEGER        INFO, LDA, N

         DOUBLE         PRECISION ANORM, RCOND

         INTEGER        IWORK( * )

         DOUBLE         PRECISION A( LDA, * ), 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
     DGECON estimates the reciprocal of the condition number of a general real
     matrix A, in either the 1-norm or the infinity-norm, using the LU
     factorization computed by DGETRF. 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.

     A       (input) DOUBLE PRECISION array, dimension (LDA,N)
             The factors L and U from the factorization A = P*L*U as computed
             by DGETRF.
     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(1,N).

     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) DOUBLE PRECISION array, dimension (4*N)

     IWORK   (workspace) INTEGER 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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