TESTING/LIN/zptt05.f(3)

NAME
TESTING/LIN/zptt05.f

SYNOPSIS

  Functions/Subroutines
subroutine zptt05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
ZPTT05

Function/Subroutine Documentation

  subroutine zptt05 (integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldxact, * ) xact, integer ldxact, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)

ZPTT05

Purpose:

    !>
    !> ZPTT05 tests the error bounds from iterative refinement for the
    !> computed solution to a system of equations A*X = B, where A is a
    !> Hermitian tridiagonal matrix of order n.
    !>
    !> RESLTS(1) = test of the error bound
    !>           = norm(X - XACT) / ( norm(X) * FERR )
    !>
    !> A large value is returned if this ratio is not less than one.
    !>
    !> RESLTS(2) = residual from the iterative refinement routine
    !>           = the maximum of BERR / ( NZ*EPS + (*) ), where
    !>             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
    !>             and NZ = max. number of nonzeros in any row of A, plus 1
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of rows of the matrices X, B, and XACT, and the
    !>          order of the matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of columns of the matrices X, B, and XACT.
    !>          NRHS >= 0.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          The n diagonal elements of the tridiagonal matrix A.
    !>

    E

    !>          E is COMPLEX*16 array, dimension (N-1)
    !>          The (n-1) subdiagonal elements of the tridiagonal matrix A.
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,NRHS)
    !>          The right hand side vectors for the system of linear
    !>          equations.
    !>

    LDB

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

    X

    !>          X is COMPLEX*16 array, dimension (LDX,NRHS)
    !>          The computed solution vectors.  Each vector is stored as a
    !>          column of the matrix X.
    !>

    LDX

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

    XACT

    !>          XACT is COMPLEX*16 array, dimension (LDX,NRHS)
    !>          The exact solution vectors.  Each vector is stored as a
    !>          column of the matrix XACT.
    !>

    LDXACT

    !>          LDXACT is INTEGER
    !>          The leading dimension of the array XACT.  LDXACT >= max(1,N).
    !>

    FERR

    !>          FERR is DOUBLE PRECISION array, dimension (NRHS)
    !>          The estimated forward error bounds for each solution vector
    !>          X.  If XTRUE is the true solution, FERR bounds the magnitude
    !>          of the largest entry in (X - XTRUE) divided by the magnitude
    !>          of the largest entry in X.
    !>

    BERR

    !>          BERR is DOUBLE PRECISION array, dimension (NRHS)
    !>          The componentwise relative backward error of each solution
    !>          vector (i.e., the smallest relative change in any entry of A
    !>          or B that makes X an exact solution).
    !>

    RESLTS

    !>          RESLTS is DOUBLE PRECISION array, dimension (2)
    !>          The maximum over the NRHS solution vectors of the ratios:
    !>          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
    !>          RESLTS(2) = BERR / ( NZ*EPS + (*) )
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 148 of file zptt05.f.

Author

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