How to Use NumPy Pi in Python: A Comprehensive Guide

pip install numpy

import numpy as np

# Calculate Circumference using NumPy Pi
def calculate_circumference(radius):
    return 2 * np.pi * radius

# Example
radius = 5
circumference = calculate_circumference(radius)
print(f"The circumference of the circle with radius {radius} is {circumference}.")

# Calculate Area using NumPy Pi
def calculate_area(radius):
    return np.pi * (radius ** 2)

# Example
radius = 5
area = calculate_area(radius)
print(f"The area of the circle with radius {radius} is {area}.")

angle_degrees = 45
angle_radians = np.radians(angle_degrees)

# Calculate sine
sine_value = np.sin(angle_radians)

# Calculate cosine
cosine_value = np.cos(angle_radians)

# Calculate tangent
tangent_value = np.tan(angle_radians)

print(f"Sine: {sine_value}, Cosine: {cosine_value}, Tangent: {tangent_value}")

def calculate_arc_length(radius, central_angle_degrees):
    central_angle_radians = np.radians(central_angle_degrees)
    return 2 * np.pi * radius * (central_angle_radians / (2 * np.pi))

# Example
radius = 6
central_angle_degrees = 45
arc_length = calculate_arc_length(radius, central_angle_degrees)
print(f"The arc length of the circle with radius {radius} and central angle {central_angle_degrees} degrees is {arc_length}.")

# Accessing other Constants
euler_number = np.e
golden_ratio = np.golden

print(f"Euler's number: {euler_number}, Golden Ratio: {golden_ratio}")

# Array Operations with NumPy Pi
arr = np.array([0, np.pi/2, np.pi, 3*np.pi/2, 2*np.pi])

# Calculate Sine of all elements
sine_arr = np.sin(arr)

# Calculate Cosine of all elements
cosine_arr = np.cos(arr)

print(f"Sine Array: {sine_arr}, Cosine Array: {cosine_arr}")

# Random Number Generation with NumPy Pi
random_num = np.random.rand() * np.pi
print(f"A random number between 0 and Pi: {random_num}")

import matplotlib.pyplot as plt

# Plotting a Sine Wave using NumPy Pi
x = np.linspace(0, 2 * np.pi, 100)
y = np.sin(x)

plt.plot(x, y)
plt.xlabel('x-axis')
plt.ylabel('y = sin(x)')
plt.title('Sine Wave')
plt.grid(True)
plt.show()

def calculate_sector_area(radius, central_angle_degrees):
    central_angle_radians = np.radians(central_angle_degrees)
    return 0.5 * (radius ** 2) * central_angle_radians

# Example
radius = 8
central_angle_degrees = 90
sector_area = calculate_sector_area(radius, central_angle_degrees)
print(f"The area of the sector with radius {radius} and central angle {central_angle_degrees} degrees is {sector_area}.")

# Solving a Trigonometric Equation using NumPy Pi
angle = np.arcsin(0.5)
print(f"The angle whose sine is 0.5 radians is {np.degrees(angle)} degrees.")

from scipy.integrate import quad

# Define the sine function
def sine_function(x):
    return np.sin(x)

# Calculate the integral of sine from 0 to Pi
integral_result, _ = quad(sine_function, 0, np.pi)

print(f"The integral of sine from 0 to Pi is {integral_result}.")

# N-dimensional Arrays with NumPy Pi
n_dim_array = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# Sum of all elements in the array
array_sum = np.sum(n_dim_array)

# Mean of all elements in the array
array_mean = np.mean(n_dim_array)

print(f"Sum of elements: {array_sum}, Mean of elements: {array_mean}")

# NumPy Pi Broadcasting
a = np.array([1, 2, 3])
b = 2

result = a * b
print(f"Broadcasting result: {result}")

# Statistical Analysis with NumPy Pi
data = np.array([10, 15, 20, 25, 30])

# Calculate Mean
mean_value = np.mean(data)

# Calculate Median
median_value = np.median(data)

# Calculate Standard Deviation
std_deviation = np.std(data)

print(f"Mean: {mean_value}, Median: {median_value}, Standard Deviation: {std_deviation}")

# Linear Algebra with NumPy Pi
matrix_a = np.array([[1, 2], [3, 4]])
matrix_b = np.array([[5, 6], [7, 8]])

# Matrix Multiplication
result_matrix = np.matmul(matrix_a, matrix_b)

# Determinant of Matrix
determinant = np.linalg.det(matrix_a)

print(f"Matrix Multiplication Result: {result_matrix}, Determinant: {determinant}")

# Generating Random Numbers from Gaussian Distribution with NumPy Pi
mean = 0
standard_deviation = 1
random_numbers = np.random.normal(mean, standard_deviation, 10)

print(f"Random numbers from Gaussian Distribution: {random_numbers}")

import time

# Performance Comparison: NumPy Pi vs. Native Python
size = 1000000

# Using NumPy Pi
start_time = time.time()
np_arr = np.arange(size)
result_np = np_arr + 1
end_time = time.time()
np_time = end_time - start_time

# Using Native Python
start_time = time.time()
py_list = list(range(size))
result_py = [x + 1 for x in py_list]
end_time = time.time()
py_time = end_time - start_time

print(f"Time taken using NumPy Pi: {np_time}, Time taken using Native Python: {py_time}")