Table of Contents

Error

Routine Names: absoluteError and relativeError

Author: Philip Nelson

Language: C++

Description

absoluteError calculates the absolute error given an approximation and a real value.

relativeError calculates the relative error given an approximation and a real value.

A driver program and make file are provided.

$ make
$ ./error.out

This will compile and run the driver program.

Input absoluteError

absoluteError<T>(T approx, T value) requires:

• T approx - the approximated value
• T value - the real value

absolute error \(= \epsilon := \Big \lvert v - v_{\text{approx}} \Big \rvert \)

Note: approx and value must be the same type.

Output

absoluteError returns a T with the absolute error.

Code

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

Example

int main()
{
  double approx = 3.2;
  double value = 3.14159;

  std::cout << "Approximate: " << approx
            << "\nReal Value: " << value << std::endl
            << std::endl;
  std::cout << "Absolute: " << absoluteError(approx, value) << std::endl;
}

Result

Approximate: 3.2
Real Value: 3.14159

Absolute: 0.05841

---

Input relativeError

relativeError<T>(T approx, T value) requires:

• T approx - the approximated value
• T value the real value

elative error \(= \eta := \frac{\epsilon}{\lvert v \rvert} \)

Note: approx and value must be the same type.

Output

relativeError returns a T with the relative error.

Code

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

Example

int main()
{
  double approx = 3.2;
  double value = 3.14159;

  std::cout << "Approximate: " << approx
            << "\nReal Value: " << value << std::endl
            << std::endl;
  std::cout << "Relative: " << relativeError(approx, value) << std::endl;
}

Result

Approximate: 3.2
Real Value: 3.14159

Relative: 0.0185925

Last Modification date: 11 January 2018