Calculate the Absolute Error of Two Vectors Using the L2 (Euclidean) 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_vecl2

Author: Christian Bolander

Language: Fortran. This code can be compiled using the GNU Fortran compiler by $ gfortran -c abs_err_vecl2.f90

and can be added to a program using

$ gfortran program.f90 abs_err_vecl2.o l2_vec_norm.f90

Description/Purpose: This routine calculates the error between an arbitrary vector a and its approximation, , using the -norm or Euclidean 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 - an approximation to 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) = 1
a(2) = 100
a(3) = 9
approx(1) = 1.1
approx(2) = 99
approx(3) = 11
CALL abs_err_vec(a, approx, n, norm)
WRITE(*,*) norm 

The output from the above code:

   2.2383029285599392

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

Implementation/Code: The code for abs_err_vecl2 can be seen. Note that the l2_vec_norm subroutine is also called

SUBROUTINE abs_err_vecl2(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

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

!~ 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 l2 vector norm using the difference between the vectors
!~ to find the error.
CALL l2_vec_norm(diff, n, error)

END SUBROUTINE