Calculate the Double Precision Relative Error Between 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: rel_err_n

Author: Christian Bolander

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

and can be added to a program using

$ gfortran program.f90 rel_err_n.o

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

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

Input:

x : REAL - actual value, double precision

y : REAL - approximation, double precision

Output:

e_rel : REAL - double precision relative error between x and y.

Usage/Example:

This routine can be implemented in a program as follows

x = 7.124645
y = 8.0
CALL rel_err_n(x, y, e_rel)
WRITE(*,*) e_rel

The output from the above code:

  0.12286292695280730 

which is the relative error between x and y.

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

SUBROUTINE rel_err_n(x, y, e_rel)
IMPLICIT NONE
REAL*8, INTENT(IN) :: x, y
REAL*8, INTENT(OUT) :: e_rel

! Calculates the relative error between two numbers, x and y, where
! y is the approximation to x.
e_rel = ABS(x - y)/ABS(x)

END SUBROUTINE