TESTING/LIN/sgbt05.f(3)    Library Functions Manual    TESTING/LIN/sgbt05.f(3)

NAME
       TESTING/LIN/sgbt05.f

SYNOPSIS
   Functions/Subroutines
       subroutine sgbt05 (trans, n, kl, ku, nrhs, ab, ldab, b, ldb, x, ldx,
           xact, ldxact, ferr, berr, reslts)
           SGBT05

Function/Subroutine Documentation
   subroutine sgbt05 (character trans, integer n, integer kl, integer ku,
       integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real,
       dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x,
       integer ldx, real, dimension( ldxact, * ) xact, integer ldxact, real,
       dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * )
       reslts)
       SGBT05

       Purpose:


            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

       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, 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 + (*) )

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 174 of file sgbt05.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/LIN/sgbt05.f(3)