TESTING/LIN/cgbt05.f(3)

NAME
TESTING/LIN/cgbt05.f

SYNOPSIS

  Functions/Subroutines
subroutine cgbt05 (trans, n, kl, ku, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
CGBT05

Function/Subroutine Documentation

  subroutine cgbt05 (character trans, integer n, integer kl, integer ku, integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, complex, dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) reslts)

CGBT05

Purpose:

    !>
    !> CGBT05 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, A**T, or A**H, 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 COMPLEX 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 COMPLEX 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 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 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 REAL 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 REAL 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 REAL 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 cgbt05.f.

Author

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