Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  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

SYNOPSIS

       SUBROUTINE ZPTRFS( UPLO,  N,  NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
                          INFO )

           CHARACTER      UPLO

           INTEGER        INFO, LDB, LDX, N, NRHS

           DOUBLE         PRECISION BERR( * ), D( * ), DF( * ), FERR( * ), RWORK( * )

           COMPLEX*16     B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )

PURPOSE

       ZPTRFS 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.

ARGUMENTS

        UPLO    (input) 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       (input) INTEGER
                The order of the matrix A.  N >= 0.

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

        D       (input) DOUBLE PRECISION array, dimension (N)
                The n real diagonal elements of the tridiagonal matrix A.

        E       (input) COMPLEX*16 array, dimension (N-1)
                The (n-1) off-diagonal elements of the tridiagonal matrix A
                (see UPLO).

        DF      (input) DOUBLE PRECISION array, dimension (N)
                The n diagonal elements of the diagonal matrix D from
                the factorization computed by ZPTTRF.

        EF      (input) COMPLEX*16 array, dimension (N-1)
                The (n-1) off-diagonal elements of the unit bidiagonal
                factor U or L from the factorization computed by ZPTTRF
                (see UPLO).

        B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
                The right hand side matrix B.

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

        X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
                On entry, the solution matrix X, as computed by ZPTTRS.
                On exit, the improved solution matrix X.

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

        FERR    (output) DOUBLE PRECISION 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    (output) DOUBLE PRECISION 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    (workspace) COMPLEX*16 array, dimension (N)

        RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

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

PARAMETERS

        ITMAX is the maximum number of steps of iterative refinement.

 LAPACK routine (version 3.3.1)             April 2011                            ZPTRFS(3lapack)