SRC/cptrfs.f(3)

NAME
SRC/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 (character uplo, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, real, dimension( * ) df, complex, dimension( * ) ef, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

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.

Definition at line 181 of file cptrfs.f.

Author

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