cptrfs.f(3)							      LAPACK							       cptrfs.f(3)

NAME

       cptrfs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cptrfs (UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
	   CPTRFS

Function/Subroutine Documentation
   subroutine cptrfs (characterUPLO, integerN, integerNRHS, real, dimension( * )D, complex, dimension( * )E, real, dimension( * )DF, complex,
       dimension( * )EF, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real,
       dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)
       CPTRFS

       Purpose:

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

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     Specifies whether the superdiagonal or the subdiagonal of the
		     tridiagonal matrix A is stored and the form of the
		     factorization:
		     = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
		     = 'L':  E is the subdiagonal of A, and A = L*D*L**H.
		     (The two forms are equivalent if A is real.)

	   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.

	   D

		     D is REAL array, dimension (N)
		     The n real diagonal elements of the tridiagonal matrix A.

	   E

		     E is COMPLEX array, dimension (N-1)
		     The (n-1) off-diagonal elements of the tridiagonal matrix A
		     (see UPLO).

	   DF

		     DF is REAL array, dimension (N)
		     The n diagonal elements of the diagonal matrix D from
		     the factorization computed by CPTTRF.

	   EF

		     EF is COMPLEX array, dimension (N-1)
		     The (n-1) off-diagonal elements of the unit bidiagonal
		     factor U or L from the factorization computed by CPTTRF
		     (see UPLO).

	   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 CPTTRS.
		     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 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).

	   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 (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 183 of file cptrfs.f.

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

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