DGTT05 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

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 DOUBLE PRECISION array, dimension (N-1)


          The (n-1) sub-diagonal elements of A.

D

          D is DOUBLE PRECISION array, dimension (N)


          The diagonal elements of A.

DU

          DU is DOUBLE PRECISION array, dimension (N-1)


          The (n-1) super-diagonal elements of A.

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 + (*) )

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.