Source code for function

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Mathematical functions.

:Date: 2019-10-27

.. module:: function
  :platform: *nix, Windows
  :synopsis: Mathematical functions.

.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
"""
import math

def sine_wave(A=1, k=1, f=1, phi=0, D=0, degree=False):
  r"""A sine wave or sinusoid is a mathematical curve that describes a
  smooth periodic oscillation.

  :param A: amplitude
  :type A: float or int
  :param k: (angular) wave number
  :type k: float or int
  :param f: ordinary frequency
  :type f: float or int
  :param phi: phase
  :type phi: float or int
  :param D: non-zero center amplitude
  :type D: float or int
  :param degree: boolean to switch between radians and degree. If
    False phi is interpreted in radians and if True then phi is
    interpreted in degrees.

  In general, the function is:

  .. math::
    y(x,t) = A\sin(kx + 2\pi f t + \varphi) + D \\
    y(x,t) = A\sin(kx + \omega t + \varphi) + D

  where:

    * A, amplitude, the peak deviation of the function from zero.
    * f, ordinary frequency, the number of oscillations (cycles) that
      occur each second of time.
    * ω = 2πf, angular frequency, the rate of change of the function
      argument in units of radians per second. If ω < 0 the wave is
      moving to the right, if ω > 0 the wave is moving to the left.
    * φ, phase, specifies (in radians) where in its cycle the
      oscillation is at t = 0.
    * x, spatial variable that represents the position on the
      dimension on which the wave propagates.
    * k, characteristic parameter called wave number (or angular wave
      number), which represents the proportionality between the
      angular frequency ω and the linear speed (speed of propagation)
      ν.
    * D, non-zero center amplitude.

  The wavenumber is related to the angular frequency by:

  .. math::
    k={\omega \over v}={2\pi f \over v}={2\pi \over \lambda }

  where λ (lambda) is the wavelength, f is the frequency, and v is the
  linear speed.

  .. seealso::
    :meth:`function_cosine_wave_degree`
  """
  if degree:
    phi = math.radians(phi)
  return lambda x, t=0: A*math.sin(k*x + 2*math.pi*f*t + phi) + D

def cosine_wave(A=1, k=1, f=1, phi=0, D=0, degree=False):
  r"""A cosine wave is said to be sinusoidal, because,
  :math:`\cos(x) = \sin(x + \pi/2)`, which is also a sine wave with a
  phase-shift of π/2 radians. Because of this head start, it is often
  said that the cosine function leads the sine function or the sine
  lags the cosine.

  :param A: amplitude
  :type A: float or int
  :param k: (angular) wave number
  :type k: float or int
  :param f: ordinary frequency
  :type f: float or int
  :param phi: phase
  :type phi: float or int
  :param D: non-zero center amplitude
  :type D: float or int
  :param degree: boolean to switch between radians and degree. If
    False phi is interpreted in radians and if True then phi is
    interpreted in degrees.

  .. seealso::
    :meth:`function_sine_wave_degree`
  """
  if degree:
    phi = phi + 90
  else:
    phi = phi + math.pi/2
  return sine_wave(A=A, k=k, f=f, phi=phi, D=D, degree=degree)