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dgtcon(3P)		    Sun Performance Library		    dgtcon(3P)

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

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

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

       SUBROUTINE DGTCON_64(NORM, N, LOW, D, UP1, UP2, IPIVOT, ANORM,
	     RCOND, WORK, IWORK2, INFO)

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

   C INTERFACE
       #include <sunperf.h>

       void dgtcon(char norm, int n, double *low, double *d, double *up1, dou‐
		 ble  *up2,  int  *ipivot,  double  anorm,  double *rcond, int
		 *info);

       void dgtcon_64(char norm, long n, double *low, double *d, double	 *up1,
		 double	 *up2, long *ipivot, double anorm, double *rcond, long
		 *info);

PURPOSE
       dgtcon estimates the reciprocal of  the	condition  number  of  a  real
       tridiagonal matrix A using the LU factorization as computed by DGTTRF.

       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	infin‐
		 ity-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 DGTTRF.

       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, com‐
		 puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
		 mate of the 1-norm of inv(A) computed in this routine.

       WORK (workspace) DOUBLE PRECISION array, dimension (2*N)

       IWORK2 (workspace) INTEGER array, dimension (N)

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

				  6 Mar 2009			    dgtcon(3P)
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