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Green Team answered on March 19, 2022 Popularity 6/10 Helpfulness 1/10

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# Import required libraries
import numpy as np
import sympy as sym
from scipy.optimize import minimize, shgo, differential_evolution
import plotly.graph_objects as go
import pandas as pd

# Definition of the function to be researched
x = sym.Symbol('x')
y = sym.Symbol('y')
f = (x**2 + y - 11)**2 + (x + y**2 - 7)**2
f2 = sym.lambdify((x, y), f)

# Generate the domain
def generateDomain():
    X_cord_val = np.linspace(-5, 5, 100)
    Y_cord_val = np.linspace(-5, 5, 100)
    return X_cord_val, Y_cord_val

# Function to calculate the function value at a point
def Function2Calc(point2Calc):
    x, y = point2Calc
    return f2(x, y)

# Function to calculate the derivatives of the function for Jacobian and Hessian matrices
dFdX = sym.lambdify((x, y), f.diff(x))
dFdY = sym.lambdify((x, y), f.diff(y))
d2FdX2 = sym.lambdify((x, y), f.diff(x, 2))
d2FdY2 = sym.lambdify((x, y), f.diff(y, 2))
d2FdXdY = sym.lambdify((x, y), f.diff(x).diff(y))

# Function to calculate the Jacobian matrix of f
def JacobianCalc(point2Calc):
    x, y = point2Calc
    return np.array((dFdX(x, y), dFdY(x, y)))

# Function to calculate the Hessian matrix of f
def HesCalc(point2Calc):
    x, y = point2Calc
    return np.array(((d2FdX2(x, y), d2FdXdY(x, y)), (d2FdXdY(x, y), d2FdY2(x, y))))

# Function to find local minimization of f using different optimization algorithms
def findLocalMinimizationOfF():
    X_cord_val, Y_cord_val = generateDomain()
    np.random.seed(1000)
    random_x = np.random.uniform(X_cord_val[0], X_cord_val[-1], size=100)
    random_y = np.random.uniform(Y_cord_val[0], Y_cord_val[-1], size=100)
    pointsArray = np.array([random_x, random_y]).transpose()
    methods = ["CG", "BFGS", "Newton-CG", "L-BFGS-B"]
    PointsArrayAnswers = np.zeros((100 * 4, 6))
    for i, point2Calc in zip(range(0, 400, len(methods)), pointsArray):
        for AlgIdx, method in zip(range(1, 5), methods):
            result = minimize(Function2Calc, point2Calc, method=method, jac=JacobianCalc, hess=HesCalc)
            PointsArrayAnswers[i + AlgIdx - 1, 0:2] = point2Calc
            PointsArrayAnswers[i + AlgIdx - 1, 2:4] = result.x
            PointsArrayAnswers[i + AlgIdx - 1, 4] = result.fun
            PointsArrayAnswers[i + AlgIdx - 1, 5] = AlgIdx

    return PointsArrayAnswers

# Function to perform global optimization of f over D using differential_evolution
def globalOptimizationOfFOverDUsingDifferentialEvolution():
    X_cord_val, Y_cord_val = generateDomain()
    result = differential_evolution(Function2Calc, bounds=[(-5, 5), (-5, 5)])
    xBar, yBar = result.x
    fBar = result.fun
    print(f"f({xBar}; {yBar}) = {fBar}")
    return xBar, yBar

# Function to calculate the matrix inverse
def calculateMatrixInverse():
    A = np.array([[3, 1], [1, 2]])
    A_inv = np.linalg.inv(A)
    print("Matrix A:")
    print(A)
    print("Inverse of Matrix A:")
    print(A_inv)
    return A, A_inv

# Visualization of the function in 3D using Plotly
def Draw3dVersionFunction():
    X_cord_val, Y_cord_val = generateDomain()
    X_grid, Y_grid = np.meshgrid(X_cord_val, Y_cord_val)
    Z_grid = Function2Calc([X_grid, Y_grid])

    fig = go.Figure(data=[go.Surface(x=X_cord_val, y=Y_cord_val, z=Z_grid)])
    fig.update_layout(title="3D Visualization of the Function", scene=dict(xaxis_title="X", yaxis_title="Y", zaxis_title="Z"))
    fig.show()

# Draw the function as a 2D matrix using Plotly
def Draw2dMatrixVersionFunction():
    X_cord_val, Y_cord_val = generateDomain()
    Z_grid = Function2Calc([X_cord_val, Y_cord_val])

    fig = go.Figure(data=[go.Heatmap(x=X_cord_val, y=Y_cord_val, z=Z_grid)])
    fig.update_layout(title="2D Matrix Visualization of the Function", xaxis_title="X", yaxis_title="Y")
    fig.show()

# Main function to run all the tasks
def main():
    # Task 1: Visualization of the function in 3D using Plotly
    Draw3dVersionFunction()

    # Task 2: Draw the function as a 2D matrix using Plotly
    Draw2dMatrixVersionFunction()

    # Task 3: Local Minimization of the function
    PointsArrayAnswers = findLocalMinimizationOfF()
    df = pd.DataFrame(PointsArrayAnswers, columns=["Initial X", "Initial Y", "Minimized X", "Minimized Y", "Minimized Value", "Algorithm"])
    print("Local Minimization of the Function:")
    print(df)

    # Task 4: Global Optimization of the function using differential_evolution
    globalOptimizationOfFOverDUsingDifferentialEvolution()

    # Task 5: Comparison of Matrix Inverse
    A, A_inv = calculateMatrixInverse()

if __name__ == "__main__":
    main()

Popularity 6/10 Helpfulness 1/10 Language python

Source: chat.openai.com

Tags: optimization project python

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Contributed on Jul 30 2023

Green Team

0 Answers Avg Quality 2/10

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import numpy as np
from scipy.optimize import minimize

# Define a cubic function to minimize: z = Ax^3 + By + C
def cubic_function(x, A, B, C):
    return A * x[0]**3 + B * x[1] + C

# Coefficients for the cubic function
A_coefficient = 2.0
B_coefficient = -3.0
C_constant = 5.0

# Initial guess
initial_guess = [1, 1]

# Minimize the cubic function
result = minimize(cubic_function, initial_guess, args=(A_coefficient, B_coefficient, C_constant), method='Nelder-Mead')

# Print the result
print("Minimum found at x:", result.x)
print("Minimum function value (z):", result.fun)

Popularity 8/10 Helpfulness 5/10 Language python

Source: Grepper

Tags: optimization python optimizati

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Contributed on Jan 07 2024

Innocent Iguana

0 Answers Avg Quality 2/10

optimization in python

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-2

OPTIMIZATION FOR PYTHON: TIP 2 - 4

2 - When importing modules you can import them all in a single line:

import module_1, module_2, module_3, etc...


3 - When importing everything from a module use *:

from random import *

We imported everything from the 'random' module using *, now we dont need to use 'random.'
FUN FACT: Not using module. increases performance since module. uses the get_attr function which
decreases performance


4 - When importing only a few things from a module combine the two tips above:

from random import randint, choice

#Now we only import the things we want while also iincreasing performance and start-up time

Popularity 9/10 Helpfulness 1/10 Language python

Source: Grepper

Tags: python optimization optimizati

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Contributed on Mar 19 2022

Victorious Vulture

0 Answers Avg Quality 2/10

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