TESTING/LIN/sptt05.f(3)    Library Functions Manual    TESTING/LIN/sptt05.f(3)

NAME
       TESTING/LIN/sptt05.f

SYNOPSIS
   Functions/Subroutines
       subroutine sptt05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr,
           berr, reslts)
           SPTT05

Function/Subroutine Documentation
   subroutine sptt05 (integer n, integer nrhs, real, dimension( * ) d, real,
       dimension( * ) e, 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)
       SPTT05

       Purpose:


            SPTT05 tests the error bounds from iterative refinement for the
            computed solution to a system of equations A*X = B, where A is a
            symmetric tridiagonal matrix of order n.

            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

       Parameters
           N

                     N is INTEGER
                     The number of rows of the matrices X, B, and XACT, and the
                     order of the matrix A.  N >= 0.

           NRHS

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

           D

                     D is REAL array, dimension (N)
                     The n diagonal elements of the tridiagonal matrix A.

           E

                     E is REAL array, dimension (N-1)
                     The (n-1) subdiagonal elements of the tridiagonal matrix A.

           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 148 of file sptt05.f.

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

LAPACK                          Version 3.12.0         TESTING/LIN/sptt05.f(3)