Vorcyc.Mathematics 0.6.0

Vorcyc.Mathematics

A high performance math library.

Vorcyc® Mathematics is a math library for .NET, designed to fully leverage the latest features of .NET and provide high-performance and accurate mathematical functions and operations. It is written in C# and can be used in any .NET application.

Vorcyc® Mathematics 是一套主要面向.NET的数学库，旨在充分利用.NET的最新特性并提供高性能和准确度的数学函数和运算。它是用C#编写的，可以在任何.NET应用程序中使用。

主要意义有：

1. 充分利用.NET最新特性以获得最佳性能。
2. 补充.NET内建常用数学函数的不足。
3. 提供额外的数学算法和运算。

面向.NET版本：.NET 9.0及以上。
This package targets a minimum of .NET 9.

Features

• SIMD加速的CPU串行计算
• 并行计算
• 泛型数学
• GPU计算（未完成）

依赖项

• ILGPU: 版本 1.5.1
• ILGPU.Algorithms: 版本 1.5.1
• System.Numerics.Tensors: 版本 9.0.0

核心模块：本模块提供了基本的数学运算、常用函数和扩展方法，涵盖数组操作、进制转换、位运算、组合数学、常量定义、数值映射、可固定数组、随机数生成、三角运算和多种数学函数。
Core Module: Contains basic mathematical operations and common functions.
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深度学习模块：目前只提供神经网络层的定义。
Deep Learning Module: Provides functions and operations related to deep learning.
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实验性模块：包含一些实验性的功能，可能会在未来版本中更改或删除。
Experimental Module: Contains some experimental features that may change or be removed in future versions.
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线性代数模块：包含多种线性代数类和结构，这些类和结构提供了丰富的线性代数操作和运算方法，如基变换、线性方程组求解、矩阵运算、四元数运算、张量运算和向量运算等，适用于各种数学和科学计算需求。
Linear Algebra Module: Contains various linear algebra classes and structures, which provide a wealth of linear algebra operations and methods, such as basis transformation, linear equation solving, matrix operations, quaternion operations, tensor operations, and vector operations, suitable for various mathematical and scientific computing needs.
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机器学习模块: 提包含多种机器学习算法和工具类，包括决策树、K 最近邻、多元线性回归、随机森林、简单线性回归、支持向量机、朴素贝叶斯分类器、DBSCAN 聚类、期望最大化、高斯混合模型、层次聚类、K 均值聚类、矢量量化、因子分析、主成分分析 (PCA)、t-SNE 降维算法等。此外，还包括多种距离度量类，如 Angular、ArgMax、BrayCurtis、Canberra、Chebyshev、Cosine、Dice、Euclidean、Hamming、Hellinger、Jaccard、Kulczynski、Levenshtein、Manhattan、Matching、Minkowski、PearsonCorrelation、RogersTanimoto、RusselRao、SokalMichener、SokalSneath、WeightedEuclidean、WeightedSquareEuclidean 和 Yule。这些类提供了丰富的机器学习和数据分析功能，适用于各种分类、回归、聚类和降维任务。
Machine Learning Module: Includes various machine learning algorithms and tool classes, such as decision trees, K-nearest neighbors, multiple linear regression, random forests, simple linear regression, support vector machines, naive Bayes classifiers, DBSCAN clustering, expectation-maximization, Gaussian mixture models, hierarchical clustering, K-means clustering, vector quantization, factor analysis, principal component analysis (PCA), and t-SNE dimensionality reduction. Additionally, it includes various distance metrics such as Angular, ArgMax, BrayCurtis, Canberra, Chebyshev, Cosine, Dice, Euclidean, Hamming, Hellinger, Jaccard, Kulczynski, Levenshtein, Manhattan, Matching, Minkowski, PearsonCorrelation, RogersTanimoto, RusselRao, SokalMichener, SokalSneath, WeightedEuclidean, WeightedSquareEuclidean, and Yule. These classes provide rich machine learning and data analysis functionalities, suitable for various classification, regression, clustering, and dimensionality reduction tasks.
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信号处理模块：该模块提供了丰富的信号处理功能，涵盖了音效处理、特征提取、滤波、傅里叶变换、常用操作、信号定义与操作、变换操作和窗函数等多个方面，适用于各种信号处理需求。
Signal Processing Module: This module provides rich signal processing functionalities, covering audio effects, feature extraction, filtering, Fourier transforms, common operations, signal definitions and operations, transformation operations, and window functions, suitable for various signal processing needs.
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数值模块：本模块提供了多个与数值计算相关的类型。这些类型包括整数、浮点数、复数、有理数、分数等。这些类型提供了高精度的数值计算功能，并且可以与其他数值类型进行转换。 Numerics Module: This module provides several types related to numerical computation, including integers, floating-point numbers, complex numbers, rational numbers, and fractions. These types offer high-precision numerical computation capabilities and can be converted between different numeric types.
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统计模块：用于对数值数据进行统计分析，支持多种数据结构和数值类型。它包括查找极值、计算总和、平均值、方差，以及识别最大值和最小值及其索引的方法。该类在可能的情况下利用硬件加速以优化性能。
Statistics Module: Used for statistical analysis of numerical data, supporting various data structures and numeric types. It includes methods for finding extrema, calculating sums, means, variances, and identifying maximum and minimum values along with their indices. This module utilizes hardware acceleration where possible to optimize performance.
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