TESTING/LIN/dpbt05.f(3)

NAME
TESTING/LIN/dpbt05.f

SYNOPSIS

  Functions/Subroutines
subroutine dpbt05 (uplo, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
DPBT05

Function/Subroutine Documentation

  subroutine dpbt05 (character uplo, integer n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( ldxact, * ) xact, integer ldxact, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)

DPBT05

Purpose:

    !>
    !> DPBT05 tests the error bounds from iterative refinement for the
    !> computed solution to a system of equations A*X = B, where A is a
    !> symmetric band matrix.
    !>
    !> 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
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is stored.
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    N

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

    KD

    !>          KD is INTEGER
    !>          The number of super-diagonals of the matrix A if UPLO = 'U',
    !>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
    !>

    NRHS

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

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          The upper or lower triangle of the symmetric band matrix A,
    !>          stored in the first KD+1 rows of the array.  The j-th column
    !>          of A is stored in the j-th column of the array AB as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD+1.
    !>

    B

    !>          B is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 169 of file dpbt05.f.

Author

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