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

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