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cgtrfs.f(3)				      LAPACK				      cgtrfs.f(3)

NAME
       cgtrfs.f -

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

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

       Purpose:

	    CGTRFS 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)

	   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 COMPLEX array, dimension (N-1)
		     The (n-1) subdiagonal elements of A.

	   D

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

	   DU

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

	   DLF

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

	   DF

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

	   DUF

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

	   DU2

		     DU2 is COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDX,NRHS)
		     On entry, the solution matrix X, as computed by CGTTRS.
		     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 COMPLEX array, dimension (2*N)

	   RWORK

		     RWORK is REAL 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 209 of file cgtrfs.f.

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

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