SGBT05 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 band matrix of order n with kl subdiagonals and ku


 superdiagonals 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, B, and XACT, and the


          order of the matrix A.  N >= 0.

KL

          KL is INTEGER


          The number of subdiagonals within the band of A.  KL >= 0.

KU

          KU is INTEGER


          The number of superdiagonals within the band of A.  KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.


          The j-th column of A is stored in the j-th column of the


          array AB as follows:


          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KL+KU+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 + (*) )

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