STBT05 tests the error bounds from iterative refinement for the


 computed solution to a system of equations A*X = B, where A is a


 triangular band 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 / ( NZ*EPS + (*) ), where


             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )


             and NZ = max. number of nonzeros in any row of A, plus 1

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.

KD

          KD is INTEGER


          The number of super-diagonals of the matrix A if UPLO = 'U',


          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

NRHS

          NRHS is INTEGER


          The number of columns of the matrices X, B, and XACT.


          NRHS >= 0.

AB

          AB is REAL array, dimension (LDAB,N)


          The upper or lower triangular band matrix A, stored in the


          first kd+1 rows of the array. The j-th column of A is stored


          in the j-th column of the array AB as follows:


          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          If DIAG = 'U', the diagonal elements of A are not referenced


          and are assumed to be 1.

LDAB

          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

B

          B is REAL 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 REAL 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 REAL 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 + (*) )

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.