sgtcon(3S)

NAME
     SGTCON - estimate the reciprocal of the condition number of a real
     tridiagonal matrix A using the LU factorization as computed by SGTTRF

SYNOPSIS
     SUBROUTINE SGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK,
                        IWORK, INFO )

         CHARACTER      NORM

         INTEGER        INFO, N

         REAL           ANORM, RCOND

         INTEGER        IPIV( * ), IWORK( * )

         REAL           D( * ), DL( * ), DU( * ), DU2( * ), 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
     SGTCON estimates the reciprocal of the condition number of a real
     tridiagonal matrix A using the LU factorization as computed by SGTTRF. 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
     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.

     DL      (input) REAL array, dimension (N-1)
             The (n-1) multipliers that define the matrix L from the LU
             factorization of A as computed by SGTTRF.
     D       (input) REAL array, dimension (N)
             The n diagonal elements of the upper triangular matrix U from the
             LU factorization of A.

     DU      (input) REAL array, dimension (N-1)
             The (n-1) elements of the first superdiagonal of U.

     DU2     (input) REAL array, dimension (N-2)
             The (n-2) elements of the second superdiagonal of U.

     IPIV    (input) INTEGER array, dimension (N)
             The pivot indices; for 1 <= i <= n, row i of the matrix was
             interchanged with row IPIV(i).  IPIV(i) will always be either i
             or i+1; IPIV(i) = i indicates a row interchange was not required.

     ANORM   (input) REAL
             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) 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) REAL array, dimension (2*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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