Contents


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, LOW, D, UP1, UP2, IPIVOT, ANORM, RCOND,
           WORK, IWORK2, INFO)

     CHARACTER * 1 NORM
     INTEGER N, INFO
     INTEGER IPIVOT(*), IWORK2(*)
     REAL ANORM, RCOND
     REAL LOW(*), D(*), UP1(*), UP2(*), WORK(*)

     SUBROUTINE SGTCON_64(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
           RCOND, WORK, IWORK2, INFO)

     CHARACTER * 1 NORM
     INTEGER*8 N, INFO
     INTEGER*8 IPIVOT(*), IWORK2(*)
     REAL ANORM, RCOND
     REAL LOW(*), D(*), UP1(*), UP2(*), WORK(*)

  F95 INTERFACE
     SUBROUTINE GTCON(NORM, [N], LOW, D, UP1, UP2, IPIVOT, ANORM,
            RCOND, [WORK], [IWORK2], [INFO])

     CHARACTER(LEN=1) :: NORM
     INTEGER :: N, INFO
     INTEGER, DIMENSION(:) :: IPIVOT, IWORK2
     REAL :: ANORM, RCOND
     REAL, DIMENSION(:) :: LOW, D, UP1, UP2, WORK

     SUBROUTINE GTCON_64(NORM, [N], LOW, D, UP1, UP2, IPIVOT, ANORM,
            RCOND, [WORK], [IWORK2], [INFO])

     CHARACTER(LEN=1) :: NORM
     INTEGER(8) :: N, INFO
     INTEGER(8), DIMENSION(:) :: IPIVOT, IWORK2
     REAL :: ANORM, RCOND
     REAL, DIMENSION(:) :: LOW, D, UP1, UP2, WORK

  C INTERFACE
     #include <sunperf.h>
     void sgtcon(char norm, int n, float *low, float *diag, float
               *up1,  float *up2, int *ipivot, float anorm, float
               *rcond, int *info);

     void sgtcon_64(char norm, long n, float *low,  float  *diag,
               float *up1, float *up2, long *ipivot, float anorm,
               float *rcond, long *info);

PURPOSE

     sgtcon estimates the reciprocal of the condition number of a
     real tridiagonal matrix A using the LU factorization as com-
     puted 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)
               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) The order of the matrix A.  N >= 0.

     LOW (input)
               The (n-1) multipliers that  define  the  matrix  L
               from  the  LU  factorization  of  A as computed by
               SGTTRF.

     D (input) The n diagonal elements of  the  upper  triangular
               matrix U from the LU factorization of A.

     UP1 (input)
               The (n-1) elements of the first  superdiagonal  of
               U.

     UP2 (input)
               The (n-2) elements of the second superdiagonal  of
               U.

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

     ANORM (input)
               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)
               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)
               dimension(2*N)

     IWORK2 (workspace)

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value