Will Yuan's Blog

How to calculate the distance between two coordinate points (knowing longitude and latitude) in Python? Three methods are given here:

Implement the Haversine Formula

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import math
from math import radians, sin, cos, asin

def haversine(lat1, lon1, lat2, lon2):
    # The average radius of the earth is approximately 6371.393km
    EARTH_RADIUS = 6371

    # Convert to radians
    lat1 = radians(lat1)
    lon1 = radians(lon1)
    lat2 = radians(lat2)
    lon2 = radians(lon2)

    # Calculate the difference between converted latitude and longitude
    delta_lat = lat2 - lat1
    delta_lon = lon2 - lon1

    # Haversine formula
    temp = math.pow(sin(delta_lat / 2), 2) + cos(lat1) * cos(lat2) * math.pow(sin(delta_lon / 2), 2)
    distance = 2 * asin(math.sqrt(temp)) * EARTH_RADIUS

    return distance

new_dist = haversine(36.1628, 114.2581, 36.5935, 114.6296)
print("The distance calculated using the Haversine formula is:", new_dist, "km")

The output is as follows:

Install GitHub Copilot for PyCharm Plugin

Click Settings and search Copilot in the plug-in market:

Install the plugin and restart the IDE:

Primal Problem

$$Max:2x_1+x_2+6x_3-x_4\\ s.t.\begin{cases} x_1+2x_2+x_3-x_4<=10\\ x_1+2x_3+x_4>=5\\ x_2+x_3+2x_4=20\\ x_1>=0,x_2<=0,x_3<=0 \end{cases}$$

The general vector form of the primal problem can be expressed as:

$$Max:z=CX\\ s.t.\begin{cases}AX<=B\\ X>=0 \end{cases}$$

We can represent the coefficients of the original problem as matrices:

Install the Gurobi Library

This package only allows solving problems on a limited scale.

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pip install gurobipy

Then, import it as follows:

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import gurobipy as grb

• This is an introduction to Google OR-Tools:

  https://developers.google.com/optimization/introduction.

• This is the official tutorial for solving optimization problems in Python:

  https://developers.google.com/optimization/introduction/python.

Now, let's use this tool to solve a simple mixed integer programming problem in Python.

Install the OR-Tools Library

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pip install ortools

Install the CPLEX Library

Install the CPLEX library in Python:

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pip install cplex

Example

itertools.combinations

Generates all possible combinations of elements of a specified length:

$$C(5,2)$$

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import itertools

str = ['A', 'B', 'C', 'D', 'E']
# Compute combinations of length 2 without replacement
combinations_result = list(itertools.combinations(str, 2))
print(combinations_result)

The output is as follows:

Installation and Import of OpenCV in Python

Execute the following pip command to complete the installation of the OpenCV library:

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pip install opencv-python

After the installation is complete, import the cv2 module:

Install NexT Theme

First, you need to install the NexT theme, you can enter the following code:

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npm install hexo-theme-next

Install Node.js and Git

First, you'll need to install Node.js and Git, download and install the Node.js from [here](Node.js — Run JavaScript Everywhere (nodejs.org)).

You can check if the Node.js and Git installation are successful by typing these:

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git version
node -v
npm -v