aeglon97

aeglon97

# The Gaussian probability density function is equal to:
#     (1 / sqrt(2 * pi * sigma^2)) * e^ ((-(x - mu)^2) / 2 * sigma^2)
#         - mu = the average
#         - sigma = standard deviation

import math
import numpy as np

def gaussian_density(x, mu, sigma):    
    two_pi_sigma_squared = 2 * np.pi * np.power(sigma, 2)

aeglon97

#Calculate the area under a Gaussian curve between 2 points, given their x-values and y-values (probability density functions).
#scipy norm() uses a Z-distribution table approach (standard normal table) to calculate the area under the curve between x1 and x2.

#NOTE: The area under the curve is the probability of the scenario happeniing between x1 and x2.
#   example: how likely will San Francisco fluctuate between 20 to 30 degrees celsius on a random day?

from scipy.stats import norm
import numpy as np
import math

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def central_limit_theorem(population, sample_size, iterations):
    sample_means = []
    for i in range(iterations):
        random_sample = np.random.choice(population, size = sample_size)
        sample_mean = np.mean(random_sample)
        
        sample_means.append(sample_mean)
        
    return sample_means

aeglon97

p=[0.2, 0.2, 0.2, 0.2, 0.2]
world=['green', 'red', 'red', 'green', 'green']
Z = 'red'
pHit = 0.6
pMiss = 0.2

def sense(p, Z):
    for i in range(len(p)):
        at_Z = (Z == world[i])
        

aeglon97

#######################APPROACH 1#######################
def shift1(lst, shift_by):
    shift_by = shift_by % len(lst)
    
    #retrieves last -U number of elements (counting backwards)
    last_elements_shifted = lst[-shift_by:] 
    
    #removes last -U number of elements (retrieves front of list)
    first_elements_shifted = lst[:-shift_by]
    

aeglon97

p=[0.2, 0.2, 0.2, 0.2, 0.2]

#sense variables
world=['green', 'red', 'red', 'green', 'green']
measurements = ['red', 'red']
pHit = 0.6
pMiss = 0.2

#move variables
motions = [1,1]

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#measurement
def update(mean1, var1, mean2, var2):
    new_mean = float(var2 * mean1 + var1 * mean2) / (var1 + var2)
    new_var = 1./(1./var1 + 1./var2)
    return [new_mean, new_var]

#motion
def predict(mean1, var1, mean2, var2):
    new_mean = mean1 + mean2
    new_var = var1 + var2

aeglon97

#state = initial state, [intial_x_pos, velocity]
#dt = change in time
#predicted_state = change in state.

#constant velocity model, displacement
def predict_state_mtx(state, dt):
    const_vel_matrix = matrix.Matrix([ [1, dt], 
                                       [0, 1] ])
    predicted_state = const_vel_matrix * state    
    return predicted_state

aeglon97

#Vector Addition
def add(vector_1, vector_2):
    if len(vector_1) != len(vector_2):
        print("error! vectors must be same size to add")
        return 
    
    new_vector = []
    for i in range(len(vector_1)):
        new_vector.append(vector_1[i] + vector_2[i])