# YiShape-Math **Repository Path**: scalefree-tech/yishape-math ## Basic Information - **Project Name**: YiShape-Math - **Description**: YiShape-Math是一个Java数学库，它提供了类似NumPy的API，功能包括向量和矩阵运算、可视化、统计学、最优化、时间序列、信号处理、音频分析、图像处理、机器学习等。 - **Primary Language**: Java - **License**: MIT - **Default Branch**: main - **Homepage**: None - **GVP Project**: No ## Statistics - **Stars**: 1 - **Forks**: 0 - **Created**: 2025-09-08 - **Last Updated**: 2025-09-24 ## Categories & Tags **Categories**: Uncategorized **Tags**: Java-math, 向量, 矩阵, 可视化, 统计学 ## README # YiShape-Math 易形数学 [![Java](https://img.shields.io/badge/Java-21+-blue.svg)](https://www.oracle.com/java/) [![License](https://img.shields.io/badge/License-MIT-green.svg)](LICENSE) [![Version](https://img.shields.io/badge/Version-0.2.1-blue.svg)]() ## 项目简介 / Project Introduction **易形数学（YiShape-Math）** 是一个基于Java开发的数学计算库，提供向量&矩阵运算、数据可视化、统计学、最优化、时间序列、信号处理、音频分析、图像处理和机器学习等核心功能，其API设计最大程度拟合了Python NumPy和SciPy的API。本库的初始目的是用于 电子科技大学、西南财经大学、河南工业大学 的《商务统计》、《商业大数据》、《数据分析与决策》、《机器学习和数据挖掘》、《人工智能理论与应用》等课程的实验教学，通过亲自动手编程以学习线性代数、统计学、最优化、机器学习等领域算法的底层计算原理。本库当前也是 [易形空间 向量数据库管理系统（YiShape VecDB）](https://github.com/ScaleFree-Tech/YiShape-VecDB) 的底层数值计算组件。本库支持OpenCL GPU（包括华为昇腾系列）计算，性能优异，适用于大规模科学计算、数据分析和机器学习等各类应用。 **YiShape-Math** is a Java-based mathematical computing library that provides functionalities including vector & matrix operations, data visualization, statistics, optimization, time series, signal processing, audio analysis, image processing and machine learning models. Its API design closely mirrors that of the Python NumPy and SciPy API. The initial purpose of this library is to be used for the experimental teaching of courses such as Business Statistics, Business Big Data, Data Analysis and Decision Making, Machine Learning and Data Mining, and Theory and Application of Artificial Intelligence at UESTC, SWUFE and HAUT. Through hands-on programming, students can learn the underlying computational principles of algorithms in fields such as linear algebra, statistics, optimization, and machine learning. The library now also serves as the underlying numerical computing component for the [YiShape Vector DataBase](https://github.com/ScaleFree-Tech/YiShape-VecDB). The library supports OpenCL GPUs computing, with excellent performance. It is suitable for a wide range of applications such as large-scale scientific computing, data analysis, and machine learning. ### 核心模块 ![核心模块关系图](docs/images/mindmap.png) ## 主要功能 / Key Functions ### 🔢 核心数学运算 / Core Mathematical Operations - **向量运算** / **Vector Operations**: 向量创建、数学运算、统计运算、切片索引等 / Vector creation, mathematical operations, statistical operations, slicing and indexing - **矩阵运算** / **Matrix Operations**: 矩阵创建、基本运算、线性代数、矩阵变换、矩阵分解等 / Matrix creation, basic operations, linear algebra, matrix transformations, matrix decompositions - **数学工具** / **Math Utilities**: 类型转换、随机数生成、数学函数 / Type conversion, random number generation, mathematical functions ### 📋 数据框操作 / DataFrame Operations - **结构化数据处理** / **Structured Data Processing**: 完整的DataFrame数据处理功能 - *Complete DataFrame data processing functionality* - CSV文件读写：支持自定义分隔符、表头、编码设置 / CSV file read/write: custom delimiters, headers, encoding settings - 灵活数据切片：行切片、列切片、通用切片，支持负数索引和步长 / Flexible data slicing: row, column, general slicing with negative indices and steps ### 📈 统计学运算 / Statistical Methods - **概率分布** / **Probability Distributions**: 14种概率分布（正态、t、卡方、F、均匀、指数、Beta、Gamma、伯努利、二项、泊松、几何、负二项、离散均匀）和多元分布 / 14 probability distributions (Normal, t, Chi-squared, F, Uniform, Exponential, Beta, Gamma, Bernoulli, Binomial, Poisson, Geometric, Negative Binomial, Discrete Uniform) and multivariate distributions - **概率函数** / **Probability Functions**: PDF、CDF、PPF、SF、ISF计算 / PDF, CDF, PPF, SF, ISF calculations - **统计描述** / **Statistical Descriptions**: 均值、方差、标准差、中位数、众数、偏度、峰度等 / Mean, variance, standard deviation, median, mode, skewness, kurtosis and more - **假设检验** / **Hypothesis Testing**: t检验、卡方检验、F检验、参数估计、置信区间估计 / t-tests, Chi-squared tests, F-tests, parameter estimation, confidence interval estimation - **方差分析** / **Analysis of Variance**: 单因素ANOVA、双因素ANOVA、重复测量ANOVA / One-way ANOVA, Two-way ANOVA, Repeated Measures ANOVA - **统计模型** / **Statistical Models**: 高斯混合模型(GMM)、EM算法 / Gaussian Mixture Model (GMM), EM Algorithm - **相关性分析** / **Correlation Analysis**: 皮尔逊相关系数、协方差计算 / Pearson correlation coefficient, covariance calculation ### 📊 数据可视化 / Data Visualization - **基础图表** / **Basic Charts**: 线图、散点图、饼图、柱状图、直方图 / Line, scatter, pie, bar, histogram charts - **统计图表** / **Statsistical Charts**: 箱线图、K线图、小提琴图 / Boxplot, candlestick charts, violinplot - **特殊图表** / **Special Charts**: 漏斗图、桑基图、旭日图、热力图、雷达图等 / Funnel, Sankey, Sunburst, heatmap, radar charts - **统一样式系统** / **Unified Style System**: matplotlib风格样式表达式、流式API、主题管理 / matplotlib-style expressions, fluent API, theme management ### 🧠 机器学习算法 / Machine Learning Algorithms - **线性回归** / **Linear Regression**: 支持L1、L2、ElasticNet正则化，LBFGS优化 / Support for L1, L2, ElasticNet regularization with LBFGS optimization - **逻辑回归** / **Logistic Regression**: 二分类和多分类逻辑回归 / Binary and multi-class logistic regression - **聚类算法** / **Clustering Algorithms**: K-Means++聚类、高斯混合模型聚类、聚类质量评估 / K-Means++ clustering, Gaussian Mixture Model clustering, clustering quality evaluation - **降维算法** / **Dimensionality Reduction**: PCA、SVD、t-SNE、UMAP等降维方法 / PCA, SVD, t-SNE, UMAP dimensionality reduction methods - **模型评估** / **Model Evaluation**: 回归结果分析和分类结果分析 / Regression and classification result analysis ### ⚡ 优化算法 / Optimization Algorithms - **优化器** / **Optimizers**: L-BFGS、SGD、Adam - *Quasi-Newton optimization algorithm* - **线搜索** / **Line Search**: 一维搜索优化方法 - *One-dimensional search optimization methods* - **目标函数接口** / **Objective Function Interface**: 灵活的优化目标定义 - *Flexible optimization objective definition* ### 📡 信号处理 / Signal Processing - **信号生成与滤波** / **Signal Generation & Filtering**: 基本波形生成、噪声信号、移动平均、中值滤波、巴特沃斯滤波器等 / Basic waveform generation, noise signals, moving average, median filtering, Butterworth filters - **频谱分析** / **Spectral Analysis**: FFT变换、功率谱密度、短时傅里叶变换、自相关分析等 / FFT transform, power spectral density, STFT, autocorrelation analysis - **小波分析** / **Wavelet Analysis**: 离散小波变换(DWT)、连续小波变换(CWT)、小波去噪、小波压缩等 / Discrete Wavelet Transform (DWT), Continuous Wavelet Transform (CWT), wavelet denoising, wavelet compression ### ⏰ 时间序列分析 / Time Series Analysis - **数据管理** / **Data Management**: 单变量/多变量时间序列、数据切片、重采样、时间戳处理等 / Univariate/multivariate time series, data slicing, resampling, timestamp handling - **预测方法** / **Forecasting Methods**: 移动平均、指数平滑、ARIMA模型、Holt-Winters、自动模型选择等 / Moving average, exponential smoothing, ARIMA models, Holt-Winters, automatic model selection - **滤波与分解** / **Filtering & Decomposition**: 时域/频域滤波、趋势/季节性分解、STL分解、小波分解等 / Time/frequency domain filtering, trend/seasonal decomposition, STL decomposition, wavelet decomposition ### 🚀 GPU加速计算 / GPU-Accelerated Computing - **GPU并行计算** / **GPU Parallel Computing**: GPU矩阵运算、向量运算、高级运算，支持自动回退机制 / GPU matrix/vector operations, advanced computing with automatic fallback ## 快速开始 / Quick Start ### 环境要求 / Requirements - Java 21 或更高版本 / Java 21 or higher - Maven 3.6+ / Maven 3.6+ ### 安装依赖 / Installation **Jar:** 直接从右侧的Releases中下载最新的[Jar包](https://github.com/ScaleFree-Tech/yishape-math/releases)。Directly download the latest [Jar package](https://github.com/ScaleFree-Tech/yishape-math/releases) from the Releases on the right. **Maven:** ```xml com.reremouse.lab yishape-math 0.2.x ``` ### 基本使用示例 / Basic Usage Examples #### 向量运算 / Vector Operations ```java // 创建向量 / Create vectors IVector v1 = Linalg.vector(new double[]{1, 2, 3, 4}); IVector v2 = Linalg.range(10); // 基本运算 / Basic operations IVector sum = v1.add(v2.slice("1:10:2")); double dotProduct = v1.dot(v2.slice(5, -1, 1)); // 统计运算 / Statsistical operations double mean = v1.mean(); double std = v1.std(1);//ddof = 1, 计算样本标准差/ sample std ``` #### 矩阵运算 / Matrix Operations ```java // 创建矩阵 / Create matrices IMatrix matrix1 = Linalg.ones(3, 3); var matrix2 = Linalg.eye(3, 3); var matrix3 = Linalg.rand(3, 3); // 矩阵运算 / Matrix operations var result = matrix1.add(matrix2).mmul(2.0); var transposed = matrix2.t(); ``` #### DataFrame 数据框操作 / DataFrame Operations ```java // 从CSV文件读取数据 / Read data from CSV file DataFrame df = DataFrame.readCsv("data.csv", ",", true); // 数据切片 / Data slicing DataFrame sliced = df.slice("1:3", "0:2"); // 行1-2，列0-1 // 转换为矩阵 / Convert to matrix IMatrix matrix = df.toMatrix(); // 保存数据 / Save data df.toCsv("output.csv"); ``` #### 统计学分布 / Statistical Distributions ```java // 创建分布 / Create distributions NormalDistribution normal = Stats.norm(0, 1); // 正态分布 / Normal distribution StudentDistribution tDist = Stats.t(10); // t分布 / t-distribution Chi2Distribution chi2Dist = Stats.chi2(5); // 卡方分布 / Chi-squared distribution FDistribution fDist = Stats.f(3, 7); // F分布 / F-distribution UniformDistribution uniform = Stats.uniform(0, 1); // 均匀分布 / Uniform distribution ExponentialDistribution exp = Stats.exponential(2.0); // 指数分布 / Exponential distribution BetaDistribution beta = Stats.beta(2, 3); // Beta分布 / Beta distribution GammaDistribution gamma = Stats.gamma(2, 1); // Gamma分布 / Gamma distribution BernoulliDistribution bernoulli = Stats.bernoulli(0.3); // 伯努利分布 / Bernoulli distribution BinomialDistribution binomial = Stats.binomial(10, 0.5); // 二项分布 / Binomial distribution PoissonDistribution poisson = Stats.poisson(2.5); // 泊松分布 / Poisson distribution // 概率函数计算 / Probability function calculations double pdf = normal.pdf(1.0); // 概率密度函数 / PDF double cdf = normal.cdf(1.0); // 累积分布函数 / CDF double ppf = normal.ppf(0.95); // 百分点函数 / PPF double mean_val = normal.mean(); // 均值 / Mean double variance = normal.var(); // 方差 / Variance double[] samples = normal.sample(1000); // 随机采样 / Random sampling ``` #### 假设检验与参数估计 / Hypothesis Testing and Parameter Estimation ```java // 创建样本数据 / Create sample data IVector sample = Linalg.vector(new double[]{1.2, 2.3, 1.8, 3.1, 2.7, 1.5, 2.9, 3.2, 2.1, 2.8}); // 参数估计 / Parameter estimation Tuple2 meanInterval = Stats.estimator.estimateMeanIntevalWithT(sample, 0.95); // 均值置信区间 / Mean confidence interval // 假设检验 / Hypothesis testing TestingResult meanTest = Stats.tester.testMeanEqualWithT(2.0, sample, 0.95); // 均值检验 / Mean test // 方差分析 / Analysis of Variance IVector group1 = Linalg.vector(new double[]{1, 2, 3, 4, 5}); IVector group2 = Linalg.vector(new double[]{2, 3, 4, 5, 6}); ANOVAResult result = Stats.anova.performOneWayANOVA(group1, group2); // 单因素方差分析 / One-way ANOVA // 相关性分析 / Correlation analysis IVector x = Linalg.vector(new double[]{1, 2, 3, 4, 5}); IVector y = Linalg.vector(new double[]{2, 4, 6, 8, 10}); double correlation = Stats.corr(x, y); // 皮尔逊相关系数 / Pearson correlation coefficient ``` #### 数据可视化 / Data Visualization ```java // 基础线图 / Basic line chart IVector x = Linalg.vector(new double[]{1, 2, 3, 4, 5}); IVector y = Linalg.vector(new double[]{10, 20, 15, 30, 25}); Plots.of(800, 600) .line(x, y) .title("销售趋势图", "2024年各月销售数据") .xlabel("月份") .ylabel("销售额（万元）") .show(); // matplotlib风格样式表达式 / matplotlib-style style expressions Plots.of(800, 600) .line(x, y, "r-") // 红色实线 .line(x, y, "b--o") // 蓝色虚线带圆圈 .scatter(x, y, "ko") // 黑色圆圈散点 .title("样式表达式示例") .show(); // 高级颜色操作 / Advanced color operations PlotStyle style = new PlotStyle() .color("#3498DB") .lineWidth(2.5) .opacity(0.8) .emphasis(new PlotStyle().color("#E74C3C").lineWidth(4.0)) .blur(new PlotStyle().opacity(0.3)); Plots.of(800, 600) .line(x, y, style) .title("高级样式应用") .show(); // 主题管理 / Theme management Plots.of(800, 600, "dark") // 使用dark主题 .line(x, y) .title("暗色主题图表") .show(); // 散点图 / Scatter chart Plots.scatter(x, y) .title("身高体重关系图") .xlabel("身高（cm）") .ylabel("体重（kg）") .saveAsHtml("scatter_chart.html"); // 饼图 / Pie chart IVector data = Linalg.vector(new double[]{30, 25, 20, 15, 10}); Plots.pie(data) .title("市场份额分布") .saveAsHtml("pie_chart.html"); // 柱状图 / Bar chart Plots.bar(data) .title("销售业绩对比") .xlabel("季度") .ylabel("销售额（万元）") .saveAsHtml("bar_chart.html"); // 直方图 / Histogram IVector histData = Linalg.vector(new double[]{1.2, 2.3, 1.8, 3.1, 2.7, 1.5, 2.9, 3.2, 2.1, 2.8}); Plots.hist(histData, true) // true表示显示拟合线 .title("数据分布直方图") .xlabel("数值区间") .ylabel("频次") .saveAsHtml("histogram_chart.html"); // 箱线图 / Box plot IVector boxData = Linalg.vector(new double[]{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}); List labels = Arrays.asList("数据集"); Plots.boxplot(boxData, labels) .title("数据分布箱线图") .xlabel("指标") .ylabel("数值") .saveAsHtml("boxplot_chart.html"); // K线图 / Candlestick chart double[][] candlestickArray = {{100, 110, 95, 115}, {110, 120, 105, 125}, {120, 115, 110, 130}}; IMatrix candlestickData = Linalg.vector(candlestickArray); List dates = Arrays.asList("2024-01-01", "2024-01-02", "2024-01-03"); Plots.candlestick(candlestickData, dates) .title("股票价格K线图") .xlabel("日期") .ylabel("价格（元）") .saveAsHtml("candlestick_chart.html"); // 小提琴图 / Violin plot IVector violinData = Linalg.vector(new double[]{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}); Plots.violinplot(violinData, labels) .title("数据分布小提琴图") .xlabel("指标") .ylabel("数值") .saveAsHtml("violin_chart.html"); ``` #### 图表展示 / Chart Gallery 以下展示了YiShape-Math支持的各种图表类型，点击图片可查看详细的使用示例： The following showcases various chart types supported by YiShape-Math. Click on the images to view detailed usage examples: ##### 基础图表 / Basic Charts | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | |---------------------|------------------|-------------------|---------------------|------------------|-------------------| | **线图 / Line Chart** | [![单向量线图示例](docs/images/line.png)](./docs/Visualization-Plotting.md#单向量线图--single-vector-line-chart) | 展示数据随时间的变化趋势 / Display data trends over time | **多组线图 / Multi-group Line Chart** | [![多组线图示例](docs/images/line_multi.png)](./docs/Visualization-Plotting.md#多组线图--multi-group-line-chart) | 比较不同组别的数据趋势 / Compare data trends across different groups | | **散点图 / Scatter Chart** | [![散点图示例](docs/images/scatter.png)](./docs/Visualization-Plotting.md#基础散点图--basic-scatter-chart) | 展示两个变量之间的关系 / Display relationships between two variables | **多组散点图 / Multi-group Scatter Chart** | [![多组散点图示例](docs/images/scatter_multi.png)](./docs/Visualization-Plotting.md#多组散点图--multi-group-scatter-chart) | 比较不同组别的数据分布 / Compare data distributions across different groups | | **饼图 / Pie Chart** | [![饼图示例](docs/images/pie.png)](./docs/Visualization-Plotting.md#饼图--pie-charts) | 展示各部分占整体的比例 / Display proportion of each part to the whole | **柱状图 / Bar Chart** | [![柱状图示例](docs/images/bar.png)](./docs/Visualization-Plotting.md#基础柱状图--basic-bar-chart) | 比较不同类别的数值大小 / Compare numerical values across different categories | | **分组柱状图 / Grouped Bar Chart** | [![分组柱状图示例](docs/images/grouped_bar.png)](./docs/Visualization-Plotting.md#分组柱状图--grouped-bar-chart) | 多维度比较分析 / Multi-dimensional comparative analysis | **直方图 / Histogram** | [![直方图示例](docs/images/hist.png)](./docs/Visualization-Plotting.md#直方图--histograms) | 展示数据的分布情况 / Display data distribution | ##### 极坐标图表 / Polar Coordinate Charts | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | |---------------------|------------------|-------------------|---------------------|------------------|-------------------| | **极坐标柱状图 / Polar Bar Chart** | [![极坐标柱状图示例](docs/images/polar_bar.png)](./docs/Visualization-Plotting.md#极坐标柱状图--polar-bar-chart) | 在极坐标系中展示柱状图 / Display bar charts in polar coordinate system | **极坐标线图 / Polar Line Chart** | [![极坐标线图示例](docs/images/polar_line.png)](./docs/Visualization-Plotting.md#极坐标线图--polar-line-chart) | 在极坐标系中展示线图 / Display line charts in polar coordinate system | | **极坐标散点图 / Polar Scatter Chart** | [![极坐标散点图示例](docs/images/polar_scatter.png)](./docs/Visualization-Plotting.md#极坐标散点图--polar-scatter-chart) | 在极坐标系中展示散点图 / Display scatter charts in polar coordinate system | | | | ##### 统计图表 / Statsistical Charts | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | |---------------------|------------------|-------------------|---------------------|------------------|-------------------| | **单组箱线图 / Single Box Plot** | [![单组箱线图示例](docs/images/boxplot.png)](./docs/Visualization-Plotting.md#单组箱线图--single-box-plot) | 展示单个数据集的分布特征和异常值 / Display distribution characteristics and outliers of a single dataset | **多组箱线图 / Multi-group Box Plot** | [![多组箱线图示例](docs/images/boxplot_multi.png)](./docs/Visualization-Plotting.md#多组箱线图--multi-group-box-plot) | 比较多个数据集的分布特征 / Compare distribution characteristics across multiple datasets | | **单组小提琴图 / Single Violin Plot** | [![单组小提琴图示例](docs/images/violinplot.png)](./docs/Visualization-Plotting.md#单组小提琴图--single-violin-plot) | 结合箱线图和密度图的特点，展示单个数据集 / Combine characteristics of box plots and density plots for a single dataset | **多组小提琴图 / Multi-group Violin Plot** | [![多组小提琴图示例](docs/images/violinplot_multi.png)](./docs/Visualization-Plotting.md#多组小提琴图--multi-group-violin-plot) | 比较多个数据集的分布密度 / Compare distribution densities across multiple datasets | | **K线图 / Candlestick Chart** | [![K线图示例](docs/images/candlestick.png)](./docs/Visualization-Plotting.md#k线图蜡烛图--candlestick-chart) | 展示金融数据的开盘价、收盘价等 / Display financial data including opening, closing prices | | | | ##### 特殊图表 / Special Charts | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | |---------------------|------------------|-------------------|---------------------|------------------|-------------------| | **漏斗图 / Funnel Chart** | [![漏斗图示例](docs/images/funnel.png)](./docs/Visualization-Plotting.md#漏斗图--funnel-chart) | 展示流程中各个阶段的转化情况 / Display conversion rates at each stage of a process | **桑基图 / Sankey Diagram** | [![桑基图示例](docs/images/sankey.png)](./docs/Visualization-Plotting.md#桑基图--sankey-diagram) | 展示数据在多个节点之间的流动 / Display data flow between multiple nodes | | **旭日图 / Sunburst Chart** | [![旭日图示例](docs/images/sunburst.png)](./docs/Visualization-Plotting.md#旭日图--sunburst-chart) | 展示层次数据的比例关系 / Display proportional relationships in hierarchical data | **主题河流图 / Theme River Chart** | [![主题河流图示例](docs/images/theme_river.png)](./docs/Visualization-Plotting.md#主题河流图--theme-river-chart) | 展示时间序列数据中不同主题的变化 / Display trends of different themes in time series data | | **树图 / Tree Chart** | [![树图示例](docs/images/tree.png)](./docs/Visualization-Plotting.md#树图--tree-chart) | 展示层次结构数据 / Display hierarchical structure data | **矩形树图 / Treemap Chart** | [![矩形树图示例](docs/images/treemap.png)](./docs/Visualization-Plotting.md#矩形树图--treemap-chart) | 通过矩形面积大小表示数据量 / Represent data volumes through rectangle sizes | | **关系图 / Graph Chart** | [![关系图示例](docs/images/graph.png)](./docs/Visualization-Plotting.md#关系图--graph-chart) | 展示节点之间的连接关系 / Display connections between nodes | **平行坐标图 / Parallel Coordinates Chart** | [![平行坐标图示例](docs/images/parallel.png)](./docs/Visualization-Plotting.md#平行坐标图--parallel-coordinates-chart) | 展示多维数据的分布和关系 / Display distribution and relationships of multi-dimensional data | ##### 扩展图表 / Enhanced Charts | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | 图表类型 / Chart Type | 示例图片 / Example | 描述 / Description | |---------------------|------------------|-------------------|---------------------|------------------|-------------------| | **热力图 / Heatmap** | [![热力图示例](docs/images/heatmap.png)](./docs/Visualization-Plotting.md#热力图--heatmap) | 通过颜色深浅表示二维数据大小 / Represent two-dimensional data magnitude through color intensity | **雷达图 / Radar Chart** | [![雷达图示例](docs/images/radar.png)](./docs/Visualization-Plotting.md#雷达图--radar-chart) | 展示多维数据的分布情况 / Display distribution of multi-dimensional data | | **仪表盘 / Gauge Chart** | [![仪表盘示例](docs/images/gauge.png)](./docs/Visualization-Plotting.md#仪表盘--gauge-chart) | 展示单一指标的当前值 / Display current values of single indicators | | | | #### 线性回归 / Linear Regression ```java // 创建线性回归模型 / Create linear regression model RereLinearRegression lr = new RereLinearRegression(); lr.setRegularizationType(RegularizationType.L2); lr.setLambda2(0.1f); // 训练模型 / Train model RegressionResult result = lr.fit(featureMatrix, labelVector); // 预测 / Predict double prediction = lr.predict(newFeatureVector); ``` #### PCA降维 / PCA Dimensionality Reduction ```java // 创建PCA降维器 / Create PCA reducer RerePCA pca = new RerePCA(); // 执行降维 / Perform dimensionality reduction IMatrix reducedData = pca.dimensionReduction(originalData, 2); ``` #### 逻辑回归分类 / Logistic Regression Classification ```java // 创建逻辑回归分类器 / Create logistic regression classifier RereLogisticRegression lr = new RereLogisticRegression(); // 训练模型 / Train model ClassificationResult result = lr.fit(featureMatrix, labelVector); // 预测分类 / Predict classification int prediction = lr.predict(newFeatureVector); double[] probabilities = lr.predictProbabilities(newFeatureVector); ``` #### 信号处理 / Signal Processing ```java // 生成信号 / Generate signals IVector time = Signals.linspace(0, 1, 1000); IVector signal = Signals.sin(2 * Math.PI * 5 * time); // 5Hz正弦波 / 5Hz sine wave // 添加噪声 / Add noise IVector noise = Signals.randn(1000).mul(0.1); IVector noisySignal = signal.add(noise); // 卡尔曼滤波 / Signal filtering IVector filteredSignal = Signals.kalmanFilter(noisySignal, 0.1); // 信号可视化 / Signal visualization Plots.of(800, 400) .line(time, signal, "b-", "原始信号 / Original Signal") .line(time, noisySignal, "r-", "含噪声信号 / Noisy Signal") .line(time, filteredSignal, "g-", "滤波后信号 / Filtered Signal") .xlabel("时间 (秒) / Time (s)") .ylabel("幅度 / Amplitude") .title("信号处理示例 / Signal Processing Example") .legend() .show(); ``` #### 时间序列分析 / Time Series Analysis ```java // 创建时间序列数据 / Create time series data IVector timestamps = Linalg.vector(new double[]{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}); IVector values = Linalg.vector(new double[]{10, 12, 13, 15, 18, 20, 22, 25, 28, 30}); // 创建时间序列对象 / Create time series object TimeSeriesData ts = new TimeSeriesData(timestamps, values); // 时间序列分析 / Time series analysis TimeSeriesAnalyzer analyzer = new TimeSeriesAnalyzer(); double trend = analyzer.calculateTrend(ts); // 计算趋势 / Calculate trend double[] forecast = analyzer.forecast(ts, 3); // 预测未来3个点 / Forecast next 3 points // 时间序列可视化 / Time series visualization Plots.of(800, 400) .line(timestamps, values, "bo-", "历史数据 / Historical Data") .scatter(Linalg.vector(new double[]{11, 12, 13}), Linalg.vector(forecast), "ro-", "预测数据 / Forecast Data") .xlabel("时间 / Time") .ylabel("数值 / Value") .title("时间序列分析示例 / Time Series Analysis Example") .legend() .show(); ``` ## 核心类文档 / Core Classes Documentation - [向量操作 (Vector Operations)](./docs/Vector-Operations.md) / [Vector Operations Documentation](./docs/Vector-Operations.md) - [矩阵操作 (Matrix Operations)](./docs/Matrix-Operations.md) / [Matrix Operations Documentation](./docs/Matrix-Operations.md) - [DataFrame 数据框操作 (DataFrame Operations)](./docs/DataFrame-Operations.md) / [DataFrame Operations Documentation](./docs/DataFrame-Operations.md) - [数学工具类 (Math Utilities)](./docs/Math-Utilities.md) / [Math Utilities Documentation](./docs/Math-Utilities.md) - [统计操作 (Statsistics Operations)](./docs/Statistics-Operations.md) / [Statistics Operations Documentation](./docs/Statsistics-Operations.md) - [数据可视化 (Data Visualization)](./docs/Visualization-Plotting.md) / [Data Visualization Documentation](./docs/Visualization-Plotting.md) - [机器学习 (Machine-Learning)](./docs/Machine-Learning.md) / [Machine-Learning Documentation](./docs/Machine-Learning.md) - [优化算法 (Optimization Algorithms)](./docs/Optimization-Algorithms.md) / [Optimization Algorithms Documentation](./docs/Optimization-Algorithms.md) - [信号处理 (Signal Processing)](./docs/Signal-Processing.md) / [Signal Processing Documentation](./docs/Signal-Processing.md) - [时间序列分析 (Time Series Analysis)](./docs/Time-Series-Analysis.md) / [Time Series Analysis Documentation](./docs/Time-Series-Analysis.md) - [API参考手册 (API Reference)](./docs/API-Reference.md) / [API Reference Manual](./docs/API-Reference.md) ## 使用示例 / Usage Examples - [向量运算示例](./docs/examples/Vector-Examples.md) / [Vector Operations Examples](./docs/examples/Vector-Examples.md) - [矩阵运算示例](./docs/examples/Matrix-Examples.md) / [Matrix Operations Examples](./docs/examples/Matrix-Examples.md) - [DataFrame 数据框示例](./docs/examples/DataFrame-Examples.md) / [DataFrame Examples](./docs/examples/DataFrame-Examples.md) - [数学工具类示例](./docs/examples/Math-Utilities-Examples.md) / [Math Utilities Examples](./docs/examples/Math-Utilities-Examples.md) - [统计操作示例](./docs/examples/Statistics-Examples.md) / [Statistics Operations Examples](./docs/examples/Statsistics-Examples.md) - [数据可视化示例](./docs/examples/Visualization-Plotting-Examples.md) / [Data Visualization Examples](./docs/examples/Visualization-Plotting-Examples.md) - [机器学习示例](./docs/examples/Machine-Learning-Examples.md) / [Machine Learning Examples](./docs/examples/Machine-Learning-Examples.md) - [优化算法示例](./docs/examples/Optimization-Examples.md) / [Optimization Algorithms Examples](./docs/examples/Optimization-Examples.md) - [信号处理示例](./docs/examples/Signal-Processing-Examples.md) / [Signal Processing Examples](./docs/examples/Signal-Processing-Examples.md) - [时间序列分析示例](./docs/examples/Time-Series-Examples.md) / [Time Series Analysis Examples](./docs/examples/Time-Series-Examples.md) ## 项目结构 / Project Structure ### 整体架构图 / Overall Architecture ```mermaid graph TB subgraph "应用层 (Application Layer)" VIZ[数据可视化层
Data Visualization Layer
RerePlot, IPlot, Plots
ColorPalette, ThemeManager] ML[机器学习层
Machine Learning Layer
RereLinearRegression, RereLogisticRegression
KMeansPlusPlus, GMMClustering
RerePCA, RereSVD, RereTSNE, RereUMAP] STAT[统计分析层
Statistical Analysis Layer
Stats, Distributions
ANOVA, HypothesisTesting
GaussianMixtureModel, EMAlgorithm] TS[时间序列层
Time Series Layer
Series, TimeSeriesData
TimeSeriesAnalyzer, TimeSeriesForecasting
ARIMA, GARCH, VAR] SIG[信号处理层
Signal Processing Layer
Signals, SignalGeneration
SignalUtilities, WaveletAnalysis
RereFFT, RereDCT, RereHilbert] AUD[音频处理层
Audio Processing Layer
AudioAnalyzer, AudioProcessor
MusicAnalyzer, MusicGenerator
AudioFeatures, AudioVisualizer] IMG[图像处理层
Image Processing Layer
ImageData, ImageFilter
ImageSegmentation, ImageTransform
SIFTFeatureDetector, SURFFeatureDetector] end subgraph "中间层 (Middle Layer)" DATA[数据处理层
Data Processing Layer
DataFrame, Column
ColumnType] OPT[优化算法层
Optimization Layer
RereLBFGS, RereLineSearch
RereOnlineAdam, RereOnlineSGD
IOptimizer, IObjectiveFunction] COMP[计算加速层
Computing Acceleration Layer
CPUComputeUtils, GPUComputeUtils
GPUConfig] end subgraph "基础层 (Foundation Layer)" MATH[基础数学层
Core Math Layer
IMatrix, IVector
RereDoubleMatrix, RereFloatMatrix
RereDoubleVector, RereFloatVector
Linalg, SliceExpressionParser] UTIL[工具类层
Utility Layer
RereMathUtil, StringUtils
Tuple2-9, RereTree] end VIZ --> MATH VIZ --> DATA VIZ --> COMP ML --> MATH ML --> OPT ML --> COMP STAT --> MATH STAT --> COMP TS --> MATH TS --> DATA TS --> COMP SIG --> MATH SIG --> DATA SIG --> COMP AUD --> MATH AUD --> DATA AUD --> COMP IMG --> MATH IMG --> DATA IMG --> COMP DATA --> MATH DATA --> UTIL OPT --> MATH OPT --> COMP COMP --> MATH ``` ### 文件结构 / File Structure ``` src/main/java/com/reremouse/lab/ ├── audio/ # 音频处理模块 / Audio Processing Module │ ├── AudioAnalyzer.java # 音频分析器 / Audio Analyzer │ ├── AudioData.java # 音频数据类 / Audio Data Class │ ├── AudioEnhancer.java # 音频增强器 / Audio Enhancer │ ├── AudioFeatures.java # 音频特征提取 / Audio Features │ ├── AudioIO.java # 音频输入输出 / Audio I/O │ ├── AudioProcessor.java # 音频处理器 / Audio Processor │ ├── AudioStatistics.java # 音频统计分析 / Audio Statistics │ ├── AudioVisualizer.java # 音频可视化 / Audio Visualizer │ ├── MusicAnalyzer.java # 音乐分析器 / Music Analyzer │ ├── MusicGenerator.java # 音乐生成器 / Music Generator │ ├── MusicTheory.java # 音乐理论 / Music Theory │ ├── core/ # 核心接口 / Core Interfaces │ │ ├── IAudioAnalyzer.java # 音频分析接口 / Audio Analysis Interface │ │ ├── IAudioProcessor.java # 音频处理接口 / Audio Processing Interface │ │ ├── IMusicAnalyzer.java # 音乐分析接口 / Music Analysis Interface │ │ └── IMusicProcessor.java # 音乐处理接口 / Music Processing Interface │ ├── embedding/ # 音频嵌入 / Audio Embedding │ │ ├── IAudioEmbedding.java # 音频嵌入接口 / Audio Embedding Interface │ │ └── IVectorModel.java # 向量模型接口 / Vector Model Interface │ ├── features/ # 高级特征 / Advanced Features │ │ └── AdvancedAudioFeatures.java # 高级音频特征 / Advanced Audio Features │ ├── music/ # 音乐处理 / Music Processing │ │ ├── AdvancedMusicFeatureAnalyzer.java # 高级音乐特征分析 / Advanced Music Feature Analysis │ │ ├── IntegratedMusicAnalyzer.java # 集成音乐分析器 / Integrated Music Analyzer │ │ └── MusicTheoryProcessor.java # 音乐理论处理器 / Music Theory Processor │ └── processing/ # 高级处理 / Advanced Processing │ └── AdvancedAudioProcessing.java # 高级音频处理 / Advanced Audio Processing ├── image/ # 图像处理模块 / Image Processing Module │ ├── ImageData.java # 图像数据类 / Image Data Class │ ├── ImageFeatures.java # 图像特征提取 / Image Features │ ├── ImageFilter.java # 图像滤波器 / Image Filter │ ├── ImageMorphology.java # 图像形态学 / Image Morphology │ ├── ImageSegmentation.java # 图像分割 / Image Segmentation │ ├── ImageTransform.java # 图像变换 / Image Transform │ ├── ImageUtils.java # 图像工具类 / Image Utilities │ ├── core/ # 核心接口 / Core Interfaces │ │ ├── IImageAnalyzer.java # 图像分析接口 / Image Analysis Interface │ │ ├── IImageProcessor.java # 图像处理接口 / Image Processing Interface │ │ └── IImageSegmenter.java # 图像分割接口 / Image Segmentation Interface │ ├── detection/ # 特征检测 / Feature Detection │ │ └── AdvancedFeatureDetection.java # 高级特征检测 / Advanced Feature Detection │ ├── enhancement/ # 图像增强 / Image Enhancement │ │ └── AdvancedImageEnhancement.java # 高级图像增强 / Advanced Image Enhancement │ ├── features/ # 图像特征 / Image Features │ │ ├── AdvancedImageFeatures.java # 高级图像特征 / Advanced Image Features │ │ ├── SIFTFeatureDetector.java # SIFT特征检测器 / SIFT Feature Detector │ │ └── SURFFeatureDetector.java # SURF特征检测器 / SURF Feature Detector │ └── tracking/ # 目标跟踪 / Object Tracking │ └── OpticalFlowTracker.java # 光流跟踪器 / Optical Flow Tracker ├── math/ # 数学计算模块 / Mathematical Computing Module │ ├── RereMathUtil.java # 数学工具类 / Math Utilities Class │ ├── YishapeMath.java # 主入口类 / Main Entry Class │ ├── compute/ # 计算模块 / Computing Module │ │ ├── CPUComputeDoubleUtils.java # CPU双精度计算工具类 / CPU Double Computing Utilities │ │ ├── CPUComputeFloatUtils.java # CPU单精度计算工具类 / CPU Float Computing Utilities │ │ ├── GPUComputeDoubleUtils.java # GPU双精度计算工具类 / GPU Double Computing Utilities │ │ ├── GPUComputeFloatUtils.java # GPU单精度计算工具类 / GPU Float Computing Utilities │ │ └── GPUConfig.java # GPU配置类 / GPU Configuration │ ├── data/ # 数据结构模块 / Data Structure Module │ │ ├── DataFrame.java # 数据框类 / DataFrame Class │ │ ├── Column.java # 列类 / Column Class │ │ └── ColumnType.java # 列类型枚举 / Column Type Enum │ ├── linalg/ # 线性代数模块 / Linear Algebra Module │ │ ├── IVector.java # 向量操作接口 / Vector Operations Interface │ │ ├── IDoubleVector.java # 双精度向量接口 / Double Vector Interface │ │ ├── IFloatVector.java # 单精度向量接口 / Float Vector Interface │ │ ├── RereDoubleVector.java # 双精度向量实现类 / Double Vector Implementation │ │ ├── RereFloatVector.java # 单精度向量实现类 / Float Vector Implementation │ │ ├── IMatrix.java # 矩阵操作接口 / Matrix Operations Interface │ │ ├── IDoubleMatrix.java # 双精度矩阵接口 / Double Matrix Interface │ │ ├── IFloatMatrix.java # 单精度矩阵接口 / Float Matrix Interface │ │ ├── RereDoubleMatrix.java # 双精度矩阵实现类 / Double Matrix Implementation │ │ ├── RereFloatMatrix.java # 单精度矩阵实现类 / Float Matrix Implementation │ │ ├── Linalg.java # 线性代数工具类 / Linear Algebra Utilities │ │ └── SliceExpressionParser.java # 切片表达式解析器 / Slice Expression Parser │ ├── stats/ # 统计学模块 / Statistics Module │ │ ├── Stats.java # 统计分布工厂类 / Statistical Distribution Factory Class │ │ ├── distribution/ # 概率分布实现 / Probability Distribution Implementations │ │ │ ├── NormalDistribution.java # 正态分布 / Normal Distribution │ │ │ ├── StudentDistribution.java # t分布 / Student's t-Distribution │ │ │ ├── Chi2Distribution.java # 卡方分布 / Chi-squared Distribution │ │ │ ├── FDistribution.java # F分布 / F-Distribution │ │ │ ├── UniformDistribution.java # 均匀分布 / Uniform Distribution │ │ │ ├── ExponentialDistribution.java # 指数分布 / Exponential Distribution │ │ │ ├── BetaDistribution.java # Beta分布 / Beta Distribution │ │ │ ├── GammaDistribution.java # Gamma分布 / Gamma Distribution │ │ │ ├── BinomialDistribution.java # 二项分布 / Binomial Distribution │ │ │ ├── PoissonDistribution.java # 泊松分布 / Poisson Distribution │ │ │ ├── GeometricDistribution.java # 几何分布 / Geometric Distribution │ │ │ ├── NegativeBinomialDistribution.java # 负二项分布 / Negative Binomial Distribution │ │ │ ├── BernoulliDistribution.java # 伯努利分布 / Bernoulli Distribution │ │ │ ├── DiscreteUniformDistribution.java # 离散均匀分布 / Discrete Uniform Distribution │ │ │ ├── IContinuousDistribution.java # 连续分布接口 / Continuous Distribution Interface │ │ │ ├── IDiscreteDistribution.java # 离散分布接口 / Discrete Distribution Interface │ │ │ └── multiv/ # 多变量分布 / Multivariate Distributions │ │ │ ├── IMultivariateDistribution.java # 多变量分布接口 / Multivariate Distribution Interface │ │ │ ├── MultivariateDistributions.java # 多变量分布工厂类 / Multivariate Distributions Factory │ │ │ ├── MultivariateNormalDistribution.java # 多变量正态分布 / Multivariate Normal Distribution │ │ │ ├── MultivariateTDistribution.java # 多变量t分布 / Multivariate t-Distribution │ │ │ ├── MultivariateBetaDistribution.java # 多变量Beta分布 / Multivariate Beta Distribution │ │ │ ├── MultivariateExponentialDistribution.java # 多变量指数分布 / Multivariate Exponential Distribution │ │ │ └── MultivariateUniformDistribution.java # 多变量均匀分布 / Multivariate Uniform Distribution │ │ ├── anova/ # 方差分析模块 / ANOVA Module │ │ │ ├── ANOVA.java # 方差分析 / ANOVA │ │ │ ├── ANOVAResult.java # 方差分析结果 / ANOVA Result │ │ │ ├── ANOVATest.java # 方差分析测试 / ANOVA Test │ │ │ ├── RepeatedMeasuresANOVAResult.java # 重复测量方差分析结果 / Repeated Measures ANOVA Result │ │ │ └── TwoWayANOVAResult.java # 双因素方差分析结果 / Two-Way ANOVA Result │ │ ├── model/ # 统计模型 / Statistical Models │ │ │ ├── EMAlgorithm.java # EM算法 / EM Algorithm │ │ │ └── GaussianMixtureModel.java # 高斯混合模型 / Gaussian Mixture Model │ │ └── testing/ # 假设检验模块 / Hypothesis Testing Module │ │ ├── HypothesisTesting.java # 假设检验 / Hypothesis Testing │ │ ├── ParameterEstimation.java # 参数估计 / Parameter Estimation │ │ └── TestingResult.java # 检验结果 / Testing Result │ ├── ml/ # 机器学习算法 / Machine Learning Algorithms │ │ ├── lr/ # 线性回归 / Linear Regression │ │ │ ├── IRegression.java # 回归接口 / Regression Interface │ │ │ ├── RereLinearRegression.java # 线性回归实现 / Linear Regression Implementation │ │ │ └── RegressionResult.java # 回归结果 / Regression Result │ │ ├── cls/ # 分类算法 / Classification Algorithms │ │ │ ├── IClassification.java # 分类接口 / Classification Interface │ │ │ ├── RereLogisticRegression.java # 逻辑回归实现 / Logistic Regression Implementation │ │ │ ├── ClassificationResult.java # 分类结果 / Classification Result │ │ │ └── LogisticRegressionResult.java # 逻辑回归结果 / Logistic Regression Result │ │ ├── clustering/ # 聚类算法 / Clustering Algorithms │ │ │ ├── IClustering.java # 聚类接口 / Clustering Interface │ │ │ ├── KMeansPlusPlus.java # K-Means++聚类 / K-Means++ Clustering │ │ │ ├── GMMClustering.java # 高斯混合模型聚类 / GMM Clustering │ │ │ └── ClusteringMetrics.java # 聚类评估指标 / Clustering Metrics │ │ └── dimreduce/ # 降维算法 / Dimensionality Reduction Algorithms │ │ ├── IDimReduce.java # 降维接口 / Dimensionality Reduction Interface │ │ ├── RerePCA.java # PCA降维 / PCA Dimensionality Reduction │ │ ├── RereSVD.java # SVD降维 / SVD Dimensionality Reduction │ │ ├── RereTSNE.java # t-SNE降维 / t-SNE Dimensionality Reduction │ │ └── RereUMAP.java # UMAP降维 / UMAP Dimensionality Reduction │ ├── optimize/ # 优化算法 / Optimization Algorithms │ │ ├── IOptimizer.java # 优化器接口 / Optimizer Interface │ │ ├── IObjectiveFunction.java # 目标函数接口 / Objective Function Interface │ │ ├── IGradientFunction.java # 梯度函数接口 / Gradient Function Interface │ │ ├── IOnlineOptimizer.java # 在线优化器接口 / Online Optimizer Interface │ │ ├── Opts.java # 优化工具类 / Optimization Utilities │ │ ├── RereLBFGS.java # L-BFGS优化器 / L-BFGS Optimizer │ │ ├── RereLineSearch.java # 线搜索 / Line Search │ │ ├── RereOnlineAdam.java # 在线Adam优化器 / Online Adam Optimizer │ │ └── RereOnlineSGD.java # 在线SGD优化器 / Online SGD Optimizer │ ├── signal/ # 信号处理模块 / Signal Processing Module │ │ ├── Signals.java # 信号处理工具类 / Signal Processing Utilities │ │ ├── SignalUtilities.java # 信号工具类 / Signal Utilities │ │ ├── SignalVisualizer.java # 信号可视化 / Signal Visualizer │ │ ├── RereFFT.java # 快速傅里叶变换 / Fast Fourier Transform │ │ ├── RereDCT.java # 离散余弦变换 / Discrete Cosine Transform │ │ ├── RereHilbert.java # 希尔伯特变换 / Hilbert Transform │ │ ├── WaveletAnalysis.java # 小波分析 / Wavelet Analysis │ │ ├── WaveletFilters.java # 小波滤波器 / Wavelet Filters │ │ ├── WaveletUtilities.java # 小波工具类 / Wavelet Utilities │ │ ├── WaveletVisualizer.java # 小波可视化 / Wavelet Visualizer │ │ ├── Complex.java # 复数类 / Complex Number Class │ │ ├── analysis/ # 信号分析 / Signal Analysis │ │ │ ├── ISignalAnalyzer.java # 信号分析接口 / Signal Analysis Interface │ │ │ └── SpectrumAnalyzer.java # 频谱分析器 / Spectrum Analyzer │ │ ├── core/ # 核心接口 / Core Interfaces │ │ │ ├── AbstractSignalProcessor.java # 抽象信号处理器 / Abstract Signal Processor │ │ │ ├── ISignalProcessor.java # 信号处理接口 / Signal Processing Interface │ │ │ └── SignalProcessingException.java # 信号处理异常 / Signal Processing Exception │ │ ├── factory/ # 信号处理器工厂 / Signal Processor Factory │ │ │ └── SignalProcessorFactory.java # 信号处理器工厂类 / Signal Processor Factory Class │ │ ├── filter/ # 信号滤波器 / Signal Filters │ │ │ ├── ISignalFilter.java # 信号滤波接口 / Signal Filter Interface │ │ │ ├── BandpassFilter.java # 带通滤波器 / Bandpass Filter │ │ │ ├── BandStopFilter.java # 带阻滤波器 / Band Stop Filter │ │ │ ├── BesselFilter.java # 贝塞尔滤波器 / Bessel Filter │ │ │ ├── ButterworthFilter.java # 巴特沃斯滤波器 / Butterworth Filter │ │ │ ├── ChebyshevFilter.java # 切比雪夫滤波器 / Chebyshev Filter │ │ │ ├── EllipticFilter.java # 椭圆滤波器 / Elliptic Filter │ │ │ ├── GaussianFilter.java # 高斯滤波器 / Gaussian Filter │ │ │ ├── KalmanFilter.java # 卡尔曼滤波器 / Kalman Filter │ │ │ ├── MedianFilter.java # 中值滤波器 / Median Filter │ │ │ ├── MovingAverageFilter.java # 移动平均滤波器 / Moving Average Filter │ │ │ └── WienerFilter.java # 维纳滤波器 / Wiener Filter │ │ ├── generation/ # 信号生成 / Signal Generation │ │ │ ├── ISignalGenerator.java # 信号生成接口 / Signal Generator Interface │ │ │ └── SignalGenerator.java # 信号生成器 / Signal Generator │ │ └── transform/ # 信号变换 / Signal Transforms │ │ ├── ISignalTransform.java # 信号变换接口 / Signal Transform Interface │ │ ├── ChirpZTransform.java # Chirp Z变换 / Chirp Z Transform │ │ ├── HilbertTransform.java # 希尔伯特变换 / Hilbert Transform │ │ ├── WalshHadamardTransform.java # 沃尔什-哈达玛变换 / Walsh-Hadamard Transform │ │ ├── WaveletTransform.java # 小波变换 / Wavelet Transform │ │ └── ZTransform.java # Z变换 / Z Transform │ ├── timeseries/ # 时间序列分析模块 / Time Series Analysis Module │ │ ├── Series.java # 时间序列类 / Time Series Class │ │ ├── TimeSeriesData.java # 时间序列数据 / Time Series Data │ │ ├── TimeSeriesAnalyzer.java # 时间序列分析器 / Time Series Analyzer │ │ ├── TimeSeriesDecomposition.java # 时间序列分解 / Time Series Decomposition │ │ ├── TimeSeriesFiltering.java # 时间序列滤波 / Time Series Filtering │ │ ├── TimeSeriesForecasting.java # 时间序列预测 / Time Series Forecasting │ │ ├── TimeSeriesUtils.java # 时间序列工具类 / Time Series Utilities │ │ ├── TimeSeriesVisualizer.java # 时间序列可视化 / Time Series Visualizer │ │ ├── TimeSeriesUnifiedExample.java # 时间序列统一示例 / Time Series Unified Example │ │ ├── CointegrationAnalysis.java # 协整分析 / Cointegration Analysis │ │ └── model/ # 时间序列模型 / Time Series Models │ │ ├── ITimeSeriesModel.java # 时间序列模型接口 / Time Series Model Interface │ │ ├── ITimeSeriesDiagnostics.java # 时间序列诊断接口 / Time Series Diagnostics Interface │ │ ├── ITimeSeriesForecastResult.java # 时间序列预测结果接口 / Time Series Forecast Result Interface │ │ ├── TimeSeriesModelFactory.java # 时间序列模型工厂 / Time Series Model Factory │ │ ├── TimeSeriesForecastResult.java # 时间序列预测结果 / Time Series Forecast Result │ │ ├── UnifiedARIMAModel.java # 统一ARIMA模型 / Unified ARIMA Model │ │ ├── ARIMADiagnostics.java # ARIMA诊断 / ARIMA Diagnostics │ │ ├── ExponentialSmoothingModels.java # 指数平滑模型 / Exponential Smoothing Models │ │ ├── GARCHModel.java # GARCH模型 / GARCH Model │ │ ├── StateSpaceModel.java # 状态空间模型 / State Space Model │ │ └── VARModel.java # VAR模型 / VAR Model │ ├── viz/ # 数据可视化模块 / Data Visualization Module │ │ ├── IPlot.java # 绘图接口 / Plotting Interface │ │ ├── RerePlot.java # 绘图实现类 / Plotting Implementation Class │ │ ├── Plots.java # 绘图工厂类 / Plotting Factory Class │ │ ├── AxisTicks.java # 坐标轴刻度类 / Axis Ticks Class │ │ ├── PlotException.java # 绘图异常类 / Plotting Exception Class │ │ ├── ColorPalette.java # 颜色调色板类 / Color Palette Class │ │ ├── PlotStyle.java # 绘图样式类 / Plot Style Class │ │ ├── SeabornStyleMapper.java # Seaborn样式映射器 / Seaborn Style Mapper │ │ ├── StyleConverter.java # 样式转换器 / Style Converter │ │ ├── StyleExpression.java # 样式表达式 / Style Expression │ │ ├── ThemeManager.java # 主题管理器 / Theme Manager │ │ └── UniversalStyleApplier.java # 通用样式应用器 / Universal Style Applier │ └── examples/ # 示例代码模块 / Examples Module └── util/ # 工具类模块 / Utility Module ├── RereCollectionUtil.java # 集合工具类 / Collection Utility Class ├── RereExecutor.java # 执行器工具类 / Executor Utility Class ├── RereTree.java # 树结构工具类 / Tree Structure Utility Class ├── RereTreeNode.java # 树节点工具类 / Tree Node Utility Class ├── StringUtils.java # 字符串工具类 / String Utility Class ├── Tuple2.java # 二元组 / Tuple2 ├── Tuple3.java # 三元组 / Tuple3 ├── Tuple4.java # 四元组 / Tuple4 ├── Tuple5.java # 五元组 / Tuple5 ├── Tuple6.java # 六元组 / Tuple6 ├── Tuple7.java # 七元组 / Tuple7 ├── Tuple8.java # 八元组 / Tuple8 └── Tuple9.java # 九元组 / Tuple9 ``` ## 性能特性 / Performance Features - **内存优化** / **Memory Optimization**: 高效的数组操作和内存管理，支持大矩阵运算 - *Efficient array operations and memory management, supporting large matrix operations* - **算法优化** / **Algorithm Optimization**: 优化的数学算法实现，包括LBFGS优化器 - *Optimized mathematical algorithm implementations, including LBFGS optimizer* - **类型安全** / **Type Safety**: 强类型系统，避免运行时错误，提供完整的类型检查 - *Strong type system, avoiding runtime errors, providing complete type checking* - **接口设计** / **Interface Design**: 清晰的接口设计，易于扩展和自定义实现 - *Clear interface design, easy to extend and customize implementations* - **数值稳定性** / **Numerical Stability**: 采用数值稳定的算法实现，确保计算精度 - *Numerically stable algorithm implementations, ensuring computational accuracy* - **并行计算支持** / **Parallel Computing Support**: 支持多线程并行计算，提高大规模数据处理效率 - *Multi-threaded parallel computing support, improving efficiency for large-scale data processing* ## 扩展计算 / Extentions Java的主流社区主要面向Server端应用开发。虽然我们已尽最大努力实现Java数值计算，但终归而言，Java数值计算的社区生态有限。为了弥补Java天生的数值计算能力不足，我们构建了一个专门的与Julia语言（数学专用语言）进行桥接的中间件库：[Ju4Ja](https://github.com/lteb2002/ju4ja), [https://github.com/lteb2002/ju4ja](https://github.com/lteb2002/ju4ja)。如果您有复杂的数值计算需求，可以使用Julia语言实现，然后在Java中通过Ju4Ja库来调用Julia功能。 Java's mainstream community is oriented towards server-side application development. While we've done our best to implement numerical computing in Java, the community ecosystem for Java numerical computing is ultimately limited. To address the inherent limitations of Java's numerical computing capabilities, we've built a specialized middleware library, [Ju4Ja](https://github.com/lteb2002/ju4ja), [https://github.com/lteb2002/ju4ja](https://github.com/lteb2002/ju4ja), to bridge the gap with the mathematically specialized Julia language. If you have complex numerical computing needs, you can implement them in Julia and call Julia functionality from Java using the Ju4Ja library. ## 贡献指南 / Contributing 我们欢迎社区贡献！请遵循以下步骤： We welcome community contributions! Please follow these steps: 1. Fork 本项目 / Fork this project 2. 创建特性分支 / Create a feature branch (`git checkout -b feature/AmazingFeature`) 3. 提交更改 / Commit your changes (`git commit -m 'Add some AmazingFeature'`) 4. 推送到分支 / Push to the branch (`git push origin feature/AmazingFeature`) 5. 开启 Pull Request / Open a Pull Request ### 贡献指南 / Contribution Guidelines - 请确保代码符合项目的编码规范 / Please ensure your code follows the project's coding standards - 添加适当的测试用例 / Add appropriate test cases - 更新相关文档 / Update relevant documentation - 确保所有测试通过 / Ensure all tests pass ## 许可证 / License 本项目采用 MIT 许可证 - 查看 [LICENSE](LICENSE.txt) 文件了解详情。 This project is licensed under the MIT License - see the [LICENSE](LICENSE.txt) file for details. ### MIT 许可证条款 / MIT License Terms MIT 许可证是一个宽松的开源许可证，允许您自由使用、修改、分发和销售软件，只要您保留版权声明和许可证文本。 The MIT License is a permissive open-source license that allows you to freely use, modify, distribute, and sell the software, as long as you retain the copyright notice and license text. ## 联系方式 / Contact - 项目维护者 / Project Maintainer: Big Data and Decision Analytics Research Center of UESTC, Big Data Research Institute of SWUFE, School of Artificial Intelligence and Big Data of HAUT, and Chengdu Scale-Free Tech Ltd. - 项目地址 / Project URL: [https://github.com/ScaleFree-Tech/yishape-math](https://github.com/ScaleFree-Tech/yishape-math), [https://gitee.com/scalefree-tech/yishape-math](https://gitee.com/scalefree-tech/yishape-math). - 问题反馈 / Issues: [https://github.com/ScaleFree-Tech/yishape-math/issues](https://github.com/ScaleFree-Tech/yishape-math/issues) ### 获取帮助 / Getting Help 如果您在使用过程中遇到问题，可以通过以下方式获取帮助： If you encounter any issues while using the library, you can get help through the following channels: - **GitHub Issues**: 报告bug或提出功能请求 / Report bugs or request features - **文档**: 查看详细的API文档和示例 / Check detailed API documentation and examples - **社区**: 参与讨论和分享经验 / Participate in discussions and share experiences ## 更新日志 / Changelog ### v0.2.1 (2025-09) - 📡 信号处理模块：信号生成、滤波、频谱分析、小波分析 / Signal processing: generation, filtering, spectral analysis, wavelet analysis - ⏰ 时间序列分析：数据管理、预测方法、滤波分解、可视化 / Time series: data management, forecasting, filtering, visualization ### v0.2.0 (2025-09) - ⚡ GPU加速计算：矩阵运算、向量运算、高级运算，支持自动回退 / GPU acceleration: matrix/vector operations, advanced computing with auto-fallback ### v0.1.2 (2025-09) - 📊 DataFrame数据框：CSV读写、数据切片、NumPy风格切片语法 / DataFrame: CSV I/O, data slicing, NumPy-style slicing - 📊 数据可视化：基础图表、统计图表、特殊图表，ECharts集成 / Visualization: basic/statistical/special charts, ECharts integration - 📈 统计学增强：14种概率分布、统计描述、假设检验 / Statistics: 14 distributions, statistical descriptions, hypothesis testing ### v0.1.1 (2025-09) - 📊 统计学分布函数库：正态、t、卡方、F、均匀、指数分布 / Statistical distributions: normal, t, chi-squared, F, uniform, exponential - 🔢 概率密度函数和累积分布函数 / PDF and CDF functions - 📋 统计描述功能：均值、方差、中位数、众数等 / Statistical descriptions: mean, variance, median, mode ### v0.1 (2025-08) - ✨ 初始版本：核心向量矩阵运算、机器学习算法、优化算法、降维算法 / Initial release: core operations, ML algorithms, optimization, dimensionality reduction --- **YiShape-Math** - 让Java应用中的数学计算更简单、更高效！ **YiShape-Math** - Making mathematical computing simpler and more efficient for Java applications!