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sgtrfs.f(3)				      LAPACK				      sgtrfs.f(3)

NAME
       sgtrfs.f -

SYNOPSIS
   Functions/Subroutines
       subroutine sgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX,
	   FERR, BERR, WORK, IWORK, INFO)
	   SGTRFS

Function/Subroutine Documentation
   subroutine sgtrfs (characterTRANS, integerN, integerNRHS, real, dimension( * )DL, real,
       dimension( * )D, real, dimension( * )DU, real, dimension( * )DLF, real, dimension( * )DF,
       real, dimension( * )DUF, real, dimension( * )DU2, integer, dimension( * )IPIV, real,
       dimension( ldb, * )B, integerLDB, real, dimension( ldx, * )X, integerLDX, real, dimension(
       * )FERR, real, dimension( * )BERR, real, dimension( * )WORK, integer, dimension( * )IWORK,
       integerINFO)
       SGTRFS

       Purpose:

	    SGTRFS improves the computed solution to a system of linear
	    equations when the coefficient matrix is tridiagonal, and provides
	    error bounds and backward error estimates for the solution.

       Parameters:
	   TRANS

		     TRANS is CHARACTER*1
		     Specifies the form of the system of equations:
		     = 'N':  A * X = B	   (No transpose)
		     = 'T':  A**T * X = B  (Transpose)
		     = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   NRHS

		     NRHS is INTEGER
		     The number of right hand sides, i.e., the number of columns
		     of the matrix B.  NRHS >= 0.

	   DL

		     DL is REAL array, dimension (N-1)
		     The (n-1) subdiagonal elements of A.

	   D

		     D is REAL array, dimension (N)
		     The diagonal elements of A.

	   DU

		     DU is REAL array, dimension (N-1)
		     The (n-1) superdiagonal elements of A.

	   DLF

		     DLF is REAL array, dimension (N-1)
		     The (n-1) multipliers that define the matrix L from the
		     LU factorization of A as computed by SGTTRF.

	   DF

		     DF is REAL array, dimension (N)
		     The n diagonal elements of the upper triangular matrix U from
		     the LU factorization of A.

	   DUF

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

	   DU2

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

	   IPIV

		     IPIV is 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.

	   B

		     B is REAL array, dimension (LDB,NRHS)
		     The right hand side matrix B.

	   LDB

		     LDB is INTEGER
		     The leading dimension of the array B.  LDB >= max(1,N).

	   X

		     X is REAL array, dimension (LDX,NRHS)
		     On entry, the solution matrix X, as computed by SGTTRS.
		     On exit, the improved solution matrix X.

	   LDX

		     LDX is INTEGER
		     The leading dimension of the array X.  LDX >= max(1,N).

	   FERR

		     FERR is REAL array, dimension (NRHS)
		     The estimated forward error bound for each solution vector
		     X(j) (the j-th column of the solution matrix X).
		     If XTRUE is the true solution corresponding to X(j), FERR(j)
		     is an estimated upper bound for the magnitude of the largest
		     element in (X(j) - XTRUE) divided by the magnitude of the
		     largest element in X(j).  The estimate is as reliable as
		     the estimate for RCOND, and is almost always a slight
		     overestimate of the true error.

	   BERR

		     BERR is REAL array, dimension (NRHS)
		     The componentwise relative backward error of each solution
		     vector X(j) (i.e., the smallest relative change in
		     any element of A or B that makes X(j) an exact solution).

	   WORK

		     WORK is REAL array, dimension (3*N)

	   IWORK

		     IWORK is INTEGER array, dimension (N)

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value

       Internal Parameters:

	     ITMAX is the maximum number of steps of iterative refinement.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Definition at line 208 of file sgtrfs.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      sgtrfs.f(3)
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