TESTING/LIN/cgtt05.f(3)

NAME
TESTING/LIN/cgtt05.f

SYNOPSIS

  Functions/Subroutines
subroutine cgtt05 (trans, n, nrhs, dl, d, du, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
CGTT05

Function/Subroutine Documentation

  subroutine cgtt05 (character trans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, 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)

CGTT05

Purpose:

     CGTT05 tests the error bounds from iterative refinement for the
     computed solution to a system of equations A*X = B, where A is a
     general tridiagonal matrix of order n 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 and XACT.  N >= 0.

    NRHS

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

    DL

              DL is COMPLEX array, dimension (N-1)
              The (n-1) sub-diagonal elements of A.

    D

              D is COMPLEX array, dimension (N)
              The diagonal elements of A.

    DU

              DU is COMPLEX array, dimension (N-1)
              The (n-1) super-diagonal elements of A.

    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 163 of file cgtt05.f.

Author

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