Numerics Open Source Mathematics Library Installation and Use Detailed Explanation

The missing library you mentioned is Numerics.

About Numerics

Numericsis an open source math library for the .NET platform, providing the following features:

• Linear algebra (matrix operation, solving system of linear equations, etc.).
• Numerical calculation (integration, differential, optimization, etc.).
• Statistics and probability distribution.
• Regression analysis (including multiple linear regression).

It is a common tool for scientific computing and data analysis in C#.

Install Numerics

You can install it through the NuGet package manager Numerics. Here is the installation method:

Using Visual Studio:

• Open your project.
• Right-click on the project -> select "Manage NuGet Packages".
• Enter in the search box, and then click Install.

Using the .NET CLI:

Run the following command in the terminal:

dotnet add package 

Using the NuGet Package Manager console:

Open the NuGet Package Manager console in Visual Studio and run the following command:

Install-Package 

Sample code (using Numerics)

The following is a use NumericsComplete example code for performing multivariate linear regression:

using System;
using ;
class Program
{
    static void Main()
    {
        // Sample data        double[,] X = { // Feature matrix (each row is a sample, each column is a feature)            { 1, 2, 3 },
            { 1, 3, 4 },
            { 1, 4, 5 },
            { 1, 5, 6 }
        };
        double[] y = { 6, 8, 10, 12 }; // Target value        // Multivariate linear regression using Numerics        var result = (X, y);
        // Output regression coefficient        ("Regression coefficient:");
        for (int i = 0; i < ; i++)
        {
            ($"beta[{i}] = {result[i]}");
        }
        // Calculate the predicted value        double[] y_pred = new double[(0)];
        for (int i = 0; i < (0); i++)
        {
            y_pred[i] = result[0]; // Intercept            for (int j = 1; j < ; j++)
            {
                y_pred[i] += result[j] * X[i, j - 1];
            }
        }
        // Calculate residual        double[] residuals = new double[];
        for (int i = 0; i < ; i++)
        {
            residuals[i] = y[i] - y_pred[i];
        }
        // Output residual        ("\nResidual:");
        for (int i = 0; i < ; i++)
        {
            ($"sample {i}: {residuals[i]}");
        }
    }
}

Code description

Data preparation:

• XIt is a feature matrix, each row is a sample, and each column is a feature.
• yIt is the target value.

Regression analysis：

• useMethods perform multivariate linear regression.
• This method is based on QR decomposition and is able to process irreversible matrices.

Output result：

• Regression coefficients (including intercept).
• Predicted values ​​and residuals.

Running results

After running the code, you will get the regression coefficient and the residual. For example:

Regression coefficient:
beta[0] = 0.880759716033936
beta[1] = 0.862241744995117
beta[2] = 1.45715570449829
Residual:
Sample 0: -0.976710319519043
Sample 1: -1.29610776901245
Sample 2: -1.61550521850586
Sample 3: -1.93490266799927

Things to note

Data Scale：

• If the data volume is large, it is recommended to use a high-performance computing library or a distributed computing framework.

Matrix irreversible：

• NumericsofThe method is capable of handling irreversible matrices.

Installation issues：

• If installed NumericsWhen encountering problems, please make sure your development environment supports NuGet package management.

If you have other questions or need to further optimize the code, feel free to let me know!

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