TESTING/LIN/ctbt05.f(3)    Library Functions Manual    TESTING/LIN/ctbt05.f(3)

NAME
       TESTING/LIN/ctbt05.f

SYNOPSIS
   Functions/Subroutines
       subroutine ctbt05 (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x,
           ldx, xact, ldxact, ferr, berr, reslts)
           CTBT05

Function/Subroutine Documentation
   subroutine ctbt05 (character uplo, character trans, character diag, integer
       n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer
       ldab, complex, dimension( ldb, * ) b, integer ldb, complex, dimension(
       ldx, * ) x, integer ldx, complex, dimension( ldxact, * ) xact, integer
       ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real,
       dimension( * ) reslts)
       CTBT05

       Purpose:


            CTBT05 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

       Parameters
           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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 187 of file ctbt05.f.

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

LAPACK                          Version 3.12.0         TESTING/LIN/ctbt05.f(3)