TESTING/LIN/zget07.f(3)

NAME
TESTING/LIN/zget07.f

SYNOPSIS

  Functions/Subroutines
subroutine zget07 (trans, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact, ferr, chkferr, berr, reslts)
ZGET07

Function/Subroutine Documentation

  subroutine zget07 (character trans, 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, logical chkferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)

ZGET07

Purpose:

     ZGET07 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 n by n matrix 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 / ( (n+1)*EPS + (*) ), where
                 (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )

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 and XACT.  N >= 0.

    NRHS

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

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              The original n by n matrix A.

    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.

    CHKFERR

              CHKFERR is LOGICAL
              Set to .TRUE. to check FERR, .FALSE. not to check FERR.
              When the test system is ill-conditioned, the 'true'
              solution in XACT may be incorrect.

    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 164 of file zget07.f.

Author

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