Calculate the Absolute Error of Two Vectors Using the Infinity Norm

This is a part of the student software manual project for Math 5610: Computational Linear Algebra and Solution of Systems of Equations.

Routine Name: abs_err_vecl_inf

Author: Christian Bolander

Language: Fortran. This code can be compiled using the GNU Fortran compiler by $ gfortran -c abs_err_vecl_inf.f90

and can be added to a program using

$ gfortran program.f90 abs_err_vecl_inf.o l_inf_vec_norm.o

Description/Purpose: This routine calculates the error between an arbitrary vector a and its approximation, , using the -norm of the difference, i.e.

Input:

n : INTEGER - the length of the vector, a

a : REAL - an arbitrary vector of length n

approx : REAL - approximation of the vector a

Output:

error : REAL - the absolute error between a and approx using the -norm.

Usage/Example:

This routine can be implemented in a program as follows

n = 3
ALLOCATE(a(1:n), approx(1:n))
a(1) = 1D0
a(2) = 100D0
a(3) = 9D0
approx(1) = 1.1D0
approx(2) = 99D0
approx(3) = 11D0
CALL abs_err_vecl_inf(a, approx, n, norm)
WRITE(*,*) norm 

The output from the above code:

   2.0000000000000000      

which is the absolute error between a and approx using the -norm.

Implementation/Code: The code for abs_err_vecl_inf can be seen. Note that the l_inf_vec_norm subroutine is also called

SUBROUTINE abs_err_vecl_inf(a, approx, n, error)
IMPLICIT NONE

INTEGER, INTENT(IN) :: n
REAL*8, INTENT(IN) :: a(1:n), approx(1:n)
REAL*8, INTENT(OUT) :: error

INTEGER :: i
REAL*8 :: diff(1:n)

!~ Find the difference between *a* and its approximation for each
!~ element.
DO i = 1, n
	diff(i) = approx(i) - a(i)
END DO

!~ Calculate the l_inf vector norm using the difference between the
!~ vectors to find the error.
CALL l_inf_vec_norm(diff, n, error)

END SUBROUTINE