TESTING/LIN/ztrt05.f(3)

NAME
TESTING/LIN/ztrt05.f

SYNOPSIS

  Functions/Subroutines
subroutine ztrt05 (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
ZTRT05

Function/Subroutine Documentation

  subroutine ztrt05 (character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, 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)

ZTRT05

Purpose:

    !>
    !> ZTRT05 tests the error bounds from iterative refinement for the
    !> computed solution to a system of equations A*X = B, where A is a
    !> triangular n by n 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 / ( (n+1)*EPS + (*) ), where
    !>             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
    !>

Parameters
    UPLO

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

    TRANS

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

    DIAG

    !>          DIAG is CHARACTER*1
    !>          Specifies whether or not the matrix A is unit triangular.
    !>          = 'N':  Non-unit triangular
    !>          = 'U':  Unit 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.
    !>

    NRHS

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          The triangular matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of the array A contains the upper
    !>          triangular matrix, and the strictly lower triangular part of
    !>          A is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of the array A contains the lower triangular
    !>          matrix, and the strictly upper triangular part of A is not
    !>          referenced.  If DIAG = 'U', the diagonal elements of A are
    !>          also not referenced and are assumed to be 1.
    !>

    LDA

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

    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 / ( (n+1)*EPS + (*) )
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 180 of file ztrt05.f.

Author

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