zhpcon(3S)

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

SYNOPSIS
     SUBROUTINE ZHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, N

         DOUBLE         PRECISION ANORM, RCOND

         INTEGER        IPIV( * )

         COMPLEX*16     AP( * ), 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
     ZHPCON estimates the reciprocal of the condition number of a complex
     Hermitian packed matrix A using the factorization A = U*D*U**H or A =
     L*D*L**H computed by ZHPTRF. 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.

     AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
             The block diagonal matrix D and the multipliers used to obtain
             the factor U or L as computed by ZHPTRF, stored as a packed
             triangular matrix.

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

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

     RCOND   (output) DOUBLE PRECISION
             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*16 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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