checon(3S)

NAME
     CHECON - estimate the reciprocal of the condition number of a complex
     Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H
     computed by CHETRF

SYNOPSIS
     SUBROUTINE CHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, LDA, N

         REAL           ANORM, RCOND

         INTEGER        IPIV( * )

         COMPLEX        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
     CHECON estimates the reciprocal of the condition number of a complex
     Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H
     computed by CHETRF. An estimate is obtained for norm(inv(A)), and the
     reciprocal of the condition number is computed as RCOND = 1 / (ANORM *
     norm(inv(A))).


ARGUMENTS
     UPLO    (input) CHARACTER*1
             Specifies whether the details of the factorization are stored as
             an upper or lower triangular matrix.  = 'U':  Upper triangular,
             form is A = U*D*U**H;
             = 'L':  Lower triangular, form is A = L*D*L**H.

     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     A       (input) COMPLEX array, dimension (LDA,N)
             The block diagonal matrix D and the multipliers used to obtain
             the factor U or L as computed by CHETRF.
     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(1,N).

     IPIV    (input) INTEGER array, dimension (N)
             Details of the interchanges and the block structure of D as
             determined by CHETRF.

     ANORM   (input) REAL
             The 1-norm of the original matrix A.

     RCOND   (output) REAL
             The reciprocal of the condition number of the matrix A, computed
             as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the
             1-norm of inv(A) computed in this routine.

     WORK    (workspace) COMPLEX array, dimension (2*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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