Adds Gaussian Function in maths section

maths/gaussian.py

@@ -0,0 +1,59 @@
+"""
+Reference: https://en.wikipedia.org/wiki/Gaussian_function
+
+python/black : True
+
+
+"""
+from numpy import pi, sqrt, exp
+
+
+def gaussian(x, mu: float = 0.0, sigma: float = 1.0) -> int:
+    """
+    >>> gaussian(1)
+    0.24197072451914337
+
+    >>> gaussian(24)
+    3.342714441794458e-126
+
+    # Supports NumPy Arrays
+    # Use numpy.meshgrid with this to generate gaussian blur on images.
+    >>> import numpy as np
+    >>> x = np.arange(15)
+    >>> gaussian(x)
+    array([3.98942280e-01, 2.41970725e-01, 5.39909665e-02, 4.43184841e-03,
+           1.33830226e-04, 1.48671951e-06, 6.07588285e-09, 9.13472041e-12,
+           5.05227108e-15, 1.02797736e-18, 7.69459863e-23, 2.11881925e-27,
+           2.14638374e-32, 7.99882776e-38, 1.09660656e-43])
+
+    >>> gaussian(15)
+    5.530709549844416e-50
+
+    >>> gaussian([1,2, 'string'])
+    Traceback (most recent call last):
+        ...
+    TypeError: unsupported operand type(s) for -: 'list' and 'float'
+
+    >>> gaussian('hello world')
+    Traceback (most recent call last):
+        ...
+    TypeError: unsupported operand type(s) for -: 'str' and 'float'
+
+    >>> gaussian(10**234)
+    Traceback (most recent call last):
+        ...
+    OverflowError: (34, 'Result too large')
+
+    >>> gaussian(10**-326)
+    0.3989422804014327
+
+    >>> gaussian(2523, mu=234234, sigma=3425)
+    0.0
+  """
+    return 1 / sqrt(2 * pi * sigma ** 2) * exp(-(x - mu) ** 2 / 2 * sigma ** 2)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

physics/harmonic_oscillator.py

@@ -0,0 +1,87 @@
+"""
+Class to return properties of harmonic motion at x displacement.
+This object can be used in game physics too.
+
+python/black: True
+"""
+__authors__ = ["n0vice"]
+__created__ = "2-14-2019"
+__last_modified__ = "7-20-2019"
+
+from numpy import sqrt, linspace, cos
+
+
+class HarmonicOscillator:
+    """
+    Harmonic Oscillator object.
+    Parameters:
+    mass
+    k                            ==> stifness of the oscillator
+    angular_frequency ==>
+    Amplitude
+    """
+
+    def __init__(self):
+        self.mass = 1
+        self.k = 1
+        self.angular_frequency = sqrt(self.k / self.mass)
+        self.AMPLITUDE = 6
+        self.E = 0.5 * self.k * self.AMPLITUDE ** 2
+
+    def force(self, x):
+        return -self.k * x
+
+    def position(self, t, A, phase):
+        return A * cos(self.angular_frequency * t + phase)
+
+    def kinetic_energy(self, x):
+        return (0.5 * self.mass * self.angular_frequency ** 2) * (
+            self.AMPLITUDE ** 2 - x ** 2
+        )
+
+    def potential_energy(self, x):
+        return self.E - self.kinetic_energy(x)
+
+    def hamiltonian(self, x):
+        return self.potential_energy(x) + self.kinetic_energy(x)
+
+    def lagrangian(self, x):
+        return self.kinetic_energy(x) - self.potential_energy(x)
+
+    def demo(self):
+        import matplotlib.pyplot as plt
+
+        oscillator = self
+        # Displacement of oscillator
+        x = linspace(-6, 6, 100)
+
+        plt.title("Properties of Harmonic Oscillator")
+
+        plt.subplot(2, 2, 1)
+        plt.plot(oscillator.force(x), oscillator.potential_energy(x))
+        plt.xlabel("Applied Force")
+        plt.ylabel("Potential")
+
+        plt.subplot(2, 2, 2)
+        plt.plot(oscillator.force(x), oscillator.position(x, 1, 1))
+        plt.xlabel("Applied Force")
+        plt.ylabel("Position")
+
+        plt.subplot(2, 2, 3)
+        plt.plot(oscillator.potential_energy(x), label="Potential Energy")
+        plt.plot(oscillator.kinetic_energy(x), label="Kinetic Energy")
+        plt.xlabel("Displacement")
+        plt.ylabel("Energy")
+        plt.legend()
+
+        plt.subplot(2, 2, 4)
+        plt.plot(oscillator.hamiltonian(x), label="Hamiltonian")
+        plt.plot(oscillator.lagrangian(x), label="Lagrangian")
+        plt.xlabel("Displacement")
+        plt.ylabel("Energy")
+        plt.legend()
+        plt.show()
+
+
+if __name__ == "__main__":
+    HarmonicOscillator().demo()