Calculate the Absolute Error of Two Scalars

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_n

Author: Christian Bolander

Language: Fortran. This code can be compiled using the GNU Fortran compiler by

$ gfortran -c abs_err_n.f90

and can be added to a program using

$ gfortran program.f90 abs_err_n.o

Description/Purpose: This routine will compute the double precision absolute error between two numbers. This is given by

where x is the approximation and is the actual value being approximated.

Input:

x : REAL - actual value, double precision

y : REAL - approximation, double precision

Output:

e_abs : REAL - double precision absolute error between x and y.

Usage/Example:

This routine can be implemented in a program as follows

x = 7.124645
y = 8.0
CALL abs_err_n(x, y, e_abs)
WRITE(*,*) e_abs

The output from the above code:

  0.87535476684570312 

which is the absolute error between x and y.

Implementation/Code: The code for abs_err_n can be seen below.

SUBROUTINE abs_err_n(x, y, e_abs)
IMPLICIT NONE
REAL*8, INTENT(IN) :: x, y
REAL*8, INTENT(OUT) :: e_abs

! Calculates the absolute error between an approximation, y, and
! the actual value, x. These are single, double precision values.
e_abs = ABS(y - x)

END SUBROUTINE