Table of Contents

Relative Error Software Manual

Routine Name: relative_error

Author: Philip Nelson

Language: C++. The code can be compiled using the GNU C++ compiler (gcc). A make file is included to compile an example program

For example,

make

will produce an executable ./error.out that can be executed.

Description/Purpose: This routine will compute the relative error of an approximation.

Relative error \(= \eta := \frac{\epsilon}{\lvert v \rvert}, \epsilon := \Big \lvert v - v_{\text{approx}} \Big \rvert \)

Input: The two inputs are the approximate value and the accurate value

@tparam T     The type of approx and value
@param approx The approximated value
@param value  The accurate value

Note: approx and value must be the same type.

Output: The relative error of type T

Usage/Example:

int main()
{
  auto value = M_PI;
  auto approx = 3.1416;

  std::cout << std::setprecision(15) << "Real Value:  " << value
            << "\nApproximate: " << approx << std::endl
            << std::endl;

  std::cout << "Relative: " << relative_error(approx, value) << std::endl;
}

Output from the lines above

Real Value:  3.14159265358979
Approximate: 3.1416

Relative Error: 2.33843499679617e-06

explanation of output: The first two lines show the real/accurate value and the approximate value. The relative error is computed and displayed.

Implementation/Code: The following is the code for relative_error

template <typename T>
inline T relative_error(const T approx, const T value)
{
  return std::abs((value - approx) / value);
}

Last Modified: September 2018