TESTING/LIN/dgbt05.f(3)

NAME
TESTING/LIN/dgbt05.f

SYNOPSIS

  Functions/Subroutines
subroutine dgbt05 (trans, n, kl, ku, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
DGBT05

Function/Subroutine Documentation

  subroutine dgbt05 (character trans, integer n, integer kl, integer ku, 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)

DGBT05

Purpose:

     DGBT05 tests the error bounds from iterative refinement for the
     computed solution to a system of equations op(A)*X = B, where A is a
     general band matrix of order n with kl subdiagonals and ku
     superdiagonals and op(A) = A or A**T, depending on TRANS.
     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(op(A))*abs(X) +abs(b))_i )
                 and NZ = max. number of nonzeros in any row of A, plus 1

Parameters
    TRANS

              TRANS is CHARACTER*1
              Specifies the form of the system of equations.
              = 'N':  A    * X = B  (No transpose)
              = 'T':  A**T * X = B  (Transpose)
              = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

    N

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

    KL

              KL is INTEGER
              The number of subdiagonals within the band of A.  KL >= 0.

    KU

              KU is INTEGER
              The number of superdiagonals within the band of A.  KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.
              The j-th column of A is stored in the j-th column of the
              array AB as follows:
              AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

    LDAB

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KL+KU+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 174 of file dgbt05.f.

Author

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