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》、《项目管理实验》、《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） 的底层数值计算组件。本库支持SIMD与OpenCL GPU（包括华为昇腾系列）计算，性能优异，适用于科学计算、数据分析、运筹学和机器学习等各类应用（ModelZoo下有大量应用建模示例）。
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. The library supports SIMD and OpenCL GPUs computing, with excellent performance. It is suitable for a wide range of applications such as large-scale scientific computing, data analysis, operation research, and machine learning (ModelZoo contains numerous modeling examples).
- 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
- 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
- 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
- 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
- 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
- 分类算法 / Classification Algorithms: 逻辑回归、XGBoost、RandomForest、EnsembleClassifier
- 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
- 优化器 / Optimizers: L-BFGS、DFP、共轭梯度法、最速下降法
- Quasi-Newton optimization algorithms
- 在线优化器 / Online Optimizers: SGD、Adam
- Online stochastic optimization algorithms
- 线搜索 / Line Search: 一维搜索优化方法
- One-dimensional search optimization methods
- 线性规划求解器 / Linear Programming Solvers: 单纯形法、内点法、拉格朗日乘数法、整数规划求解器
- Linear programming solvers:Simplex method, interior point method, Lagrange multiplier method, integer programming solvers
- 约束优化 / Constrained Optimization: 拉格朗日乘数法
- Lagrange multiplier method
- 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
- 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
- 音频特征提取 / Audio Feature Extraction: MFCC特征、频谱质心、过零率、频谱分析等 / MFCC features, spectral centroid, zero crossing rate, spectrum analysis
- 音频处理 / Audio Processing: 音高检测、音频增强、音频分割、音频合成等 / Pitch detection, audio enhancement, audio segmentation, audio synthesis
- 音频嵌入向量 / Audio Embedding Vectors: i-vector模型训练、在线增量训练等 / i-vector model training, online incremental training
- SIMD (Single Instruction, Multiple Data)支持 / SIMD Support: 基于Java Vector API提供向量&矩阵乘法、通用函数、规约函数等方面的SIMD并行计算支持 / SIMD (Single Instruction, Multiple Data) parallel computing support based on Java Vector API
- 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
- Java 25 或更高版本 / Java 25 or higher
- Maven 3.6+ / Maven 3.6+
Jar:
直接从右侧的Releases中下载最新的Jar包。Directly download the latest Jar package from the Releases on the right.
Maven:
<dependency>
<groupId>com.yishape.lab</groupId>
<artifactId>yishape-math</artifactId>
<version>0.3.x</version>
</dependency>启用Java Vector API(可选) / Enable Java Vector API (Optional)
# vm args:
--add-modules=jdk.incubator.vector
// 创建向量 / Create vectors
IVector<Double> v1 = Linalg.vector(new double[]{1, 2, 3, 4});
IVector<Double> v2 = Linalg.range(10);
// 基本运算 / Basic operations
IVector<Double> 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// 创建矩阵 / Create matrices
IMatrix<Double> 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();// 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<Double> matrix = df.toMatrix();
// 保存数据 / Save data
df.toCsv("output.csv");// 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// 创建样本数据 / Create sample data
IVector<Double> 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<Double, Double> 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<Double> group1 = Linalg.vector(new double[]{1, 2, 3, 4, 5});
IVector<Double> 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<Double> x = Linalg.vector(new double[]{1, 2, 3, 4, 5});
IVector<Double> 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// 基础线图 / Basic line chart
IVector<Double> x = Linalg.vector(new double[]{1, 2, 3, 4, 5});
IVector<Double> 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<Double> 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<Double> 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<Double> boxData = Linalg.vector(new double[]{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15});
List<String> 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<Double> candlestickData = Linalg.vector(candlestickArray);
List<String> 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<Double> 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");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:
| 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 |  |
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 |  |
比较不同组别的数据趋势 / Compare data trends across different groups |
| 散点图 / 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 |  |
比较不同组别的数据分布 / Compare data distributions across different groups |
| 饼图 / Pie Chart |  |
展示各部分占整体的比例 / Display proportion of each part to the whole | 柱状图 / 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 |  |
多维度比较分析 / Multi-dimensional comparative analysis | 直方图 / Histogram |  |
展示数据的分布情况 / Display data distribution |
| 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 |  |
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 |  |
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 |  |
在极坐标系中展示散点图 / Display scatter charts in polar coordinate system |
| 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 |  |
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 |  |
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 |  |
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 |  |
比较多个数据集的分布密度 / Compare distribution densities across multiple datasets |
| K线图 / Candlestick Chart |  |
展示金融数据的开盘价、收盘价等 / Display financial data including opening, closing prices |
| 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 |  |
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 |  |
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 |  |
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 |  |
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 |  |
展示层次结构数据 / Display hierarchical structure data | 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 |  |
展示节点之间的连接关系 / Display connections between nodes | 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 |
| 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 |  |
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 |  |
展示多维数据的分布情况 / Display distribution of multi-dimensional data |
| 仪表盘 / Gauge Chart |  |
展示单一指标的当前值 / Display current values of single indicators |
// L-BFGS优化器示例 / L-BFGS Optimizer Example
RereLBFGS optimizer = new RereLBFGS();
// 定义目标函数（Rosenbrock函数）/ Define objective function (Rosenbrock function)
IObjectiveFunction objFun = new IObjectiveFunction() {
@Override
public double computeObjective(IVector x) {
double x1 = x.get(0).doubleValue();
double x2 = x.get(1).doubleValue();
return (1 - x1) * (1 - x1) + 100 * (x2 - x1 * x1) * (x2 - x1 * x1);
}
};
// 定义梯度函数 / Define gradient function
IGradientFunction grdFun = new IGradientFunction() {
@Override
public IVector computeGradient(IVector x) {
double x1 = x.get(0).doubleValue();
double x2 = x.get(1).doubleValue();
double[] grad = new double[2];
grad[0] = -2 * (1 - x1) - 400 * x1 * (x2 - x1 * x1);
grad[1] = 200 * (x2 - x1 * x1);
return Linalg.vector(grad);
}
};
// 执行优化 / Execute optimization
IVector initX = Linalg.vector(new double[]{-1.0, -1.0});
var result = optimizer.optimize(initX, objFun, grdFun);// 在线Adam优化器示例 / Online Adam Optimizer Example
RereOnlineAdam adamOptimizer = new RereOnlineAdam();
// 初始化优化器 / Initialize optimizer
IVector initialParams = Linalg.vector(new double[]{0.0, 0.0});
adamOptimizer.initialize(initialParams);
// 在线学习循环 / Online learning loop
for (int i = 0; i < numIterations; i++) {
IVector gradient = computeGradient(adamOptimizer.getCurrentParams());
double loss = computeLoss(adamOptimizer.getCurrentParams());
// 执行一步优化 / Perform one optimization step
IVector updatedParams = adamOptimizer.step(gradient, loss);
if (loss < tolerance) break;
}// 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);// 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);// 创建逻辑回归分类器 / Create logistic regression classifier
var lr = new RereLogisticRegression();
// 训练模型 / Train model
var result = lr.fit(featureMatrix, labelVector);
// 预测分类 / Predict classification
int prediction = lr.predict(newFeatureVector);
double[] probabilities = lr.predictProbabilities(newFeatureVector);// 生成信号 / Generate signals
IVector<Double> time = Signals.linspace(0, 1, 1000);
IVector<Double> signal = Signals.sin(2 * Math.PI * 5 * time); // 5Hz正弦波 / 5Hz sine wave
// 添加噪声 / Add noise
IVector<Double> noise = Signals.randn(1000).mul(0.1);
IVector<Double> noisySignal = signal.add(noise);
// 卡尔曼滤波 / Signal filtering
IVector<Double> 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();// 创建时间序列数据 / Create time series data
IVector<Double> timestamps = Linalg.vector(new double[]{1, 2, 3, 4, 5, 6, 7, 8, 9, 10});
IVector<Double> 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();// 读取音频文件 / Read audio file
AudioData audioData = Audios.readAudio("sample.wav");
// 音频特征提取 / Audio feature extraction
IMatrix<Double> mfccFeatures = Audios.calculateMFCC(audioData); // MFCC特征 / MFCC features
double spectralCentroid = Audios.calculateSpectralCentroid(audioData, 1024); // 频谱质心 / Spectral centroid
double zeroCrossingRate = Audios.calculateZeroCrossingRate(audioData); // 过零率 / Zero crossing rate
// 音频分析 / Audio analysis
double pitch = Audios.detectPitch(audioData); // 音高检测 / Pitch detection
Tuple2<IVector<Double>, IVector<Double>> spectrum = Audios.spectrum(audioData); // 频谱分析 / Spectrum analysis
// 音频综合特征提取 / Audio comprehensive feature extraction
IAudioFeatureExtractor extractor = Audios.createStandardFeatureExtractor();
AudioFeatureResult result = extractor.extractAudioFeatures(audioData); // 提取时域、频域、谱域综合音频特征 / Extract time-domain, frequency-domain, and spectral features
Tuple2<List<String>, IVector<Double>> result.toNumericalFeatures(); // 转换为数值特征(特征名、特征的值)
// 音频嵌入向量 / Audio embedding vector
IVectorEmbedding embedder = Audios.createAudioEmbedder(64); // 创建64维嵌入器 / Create 64-dim embedder
embedder.train(audioDataList); // 训练嵌入器
IVector<Double> embedding = embedder.embed(audioData); // 生成嵌入向量 / Generate embedding vector
- 向量操作 (Vector Operations) / Vector Operations Documentation
- 矩阵操作 (Matrix Operations) / Matrix Operations Documentation
- DataFrame 数据框操作 (DataFrame Operations) / DataFrame Operations Documentation
- 数学工具类 (Math Utilities) / Math Utilities Documentation
- 统计操作 (Statsistics Operations) / Statistics Operations Documentation
- 数据可视化 (Data Visualization) / Data Visualization Documentation
- 机器学习 (Machine-Learning) / Machine-Learning Documentation
- 优化算法 (Optimization Algorithms) / Optimization Algorithms Documentation
- 信号处理 (Signal Processing) / Signal Processing Documentation
- 时间序列分析 (Time Series Analysis) / Time Series Analysis Documentation
- 音频操作 (Audio Operations) / Audio Operations Documentation
- API参考手册 (API Reference) / API Reference Manual
- 向量运算示例 / Vector Operations Examples
- 矩阵运算示例 / Matrix Operations Examples
- DataFrame 数据框示例 / DataFrame Examples
- 数学工具类示例 / Math Utilities Examples
- 统计操作示例 / Statistics Operations Examples
- 数据可视化示例 / Data Visualization Examples
- 机器学习示例 / Machine Learning Examples
- 优化算法示例 / Optimization Algorithms Examples
- 信号处理示例 / Signal Processing Examples
- 时间序列分析示例 / Time Series Analysis Examples
- 音频处理示例 / Audio Processing Examples
graph TB
subgraph "应用层 (Application Layer)"
VIZ[数据可视化层<br/>Data Visualization Layer<br/>RerePlot, IPlot, Plots<br/>ColorPalette, ThemeManager]
ML[机器学习层<br/>Machine Learning Layer<br/>RereLinearRegression, RereLogisticRegression<br/>KMeansPlusPlus, GMMClustering<br/>RerePCA, RereSVD, RereTSNE, RereUMAP]
STAT[统计分析层<br/>Statistical Analysis Layer<br/>Stats, Distributions<br/>ANOVA, HypothesisTesting<br/>GaussianMixtureModel, EMAlgorithm]
TS[时间序列层<br/>Time Series Layer<br/>Series, TimeSeriesData<br/>TimeSeriesAnalyzer, TimeSeriesForecasting<br/>ARIMA, GARCH, VAR]
SIG[信号处理层<br/>Signal Processing Layer<br/>Signals, SignalGeneration<br/>SignalUtilities, WaveletAnalysis<br/>RereFFT, RereDCT, RereHilbert]
AUD[音频处理层<br/>Audio Processing Layer<br/>AudioAnalyzer, AudioProcessor<br/>MusicAnalyzer, MusicGenerator<br/>AudioFeatures, AudioPlots]
IMG[图像处理层<br/>Image Processing Layer<br/>ImageData, ImageFilter<br/>ImageSegmentation, ImageTransform<br/>SIFTFeatureDetector, SURFFeatureDetector]
end
subgraph "中间层 (Middle Layer)"
DATA[数据处理层<br/>Data Processing Layer<br/>DataFrame, Column<br/>ColumnType]
OPT[优化算法层<br/>Optimization Layer<br/>RereLBFGS, RereLineSearch<br/>RereOnlineAdam, RereOnlineSGD<br/>IOptimizer, IObjectiveFunction]
COMP[计算加速层<br/>Computing Acceleration Layer<br/>CPUComputeUtils, GPUComputeUtils<br/>GPUConfig]
end
subgraph "基础层 (Foundation Layer)"
MATH[基础数学层<br/>Core Math Layer<br/>IMatrix, IVector<br/>RereDoubleMatrix, RereFloatMatrix<br/>RereDoubleVector, RereFloatVector<br/>Linalg, SliceExpressionParser]
UTIL[工具类层<br/>Utility Layer<br/>RereMathUtil, StringUtils<br/>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
src/main/java/
└── com/reremouse/lab/
├── audio/ # 音频处理模块 / Audio Processing Module
│ ├── AudioPlots.java # 音频绘图 / Audio Plots
│ ├── Audios.java # 音频处理入口类 / Audio Processing Entry Class
│ ├── analysis/ # 音频分析 / Audio Analysis
│ │ ├── AbstractAudioAnalyzer.java # 抽象音频分析器 / Abstract Audio Analyzer
│ │ ├── FFTProcessor.java # FFT处理器 / FFT Processor
│ │ ├── IAudioAnalyzer.java # 音频分析接口 / Audio Analyzer Interface
│ │ ├── PitchDetector.java # 音高检测器 / Pitch Detector
│ │ ├── STFTAnalyzer.java # 短时傅里叶变换分析器 / STFT Analyzer
│ │ └── SpectrumAnalyzer.java # 频谱分析器 / Spectrum Analyzer
│ ├── core/ # 核心类 / Core Classes
│ │ ├── AudioData.java # 音频数据类 / Audio Data Class
│ │ ├── AudioFormat.java # 音频格式类 / Audio Format Class
│ │ ├── AudioIO.java # 音频输入输出 / Audio I/O
│ │ ├── AudioProcessor.java # 音频处理器 / Audio Processor
│ │ ├── AudioQuality.java # 音频质量类 / Audio Quality Class
│ │ ├── AudioStatistics.java # 音频统计类 / Audio Statistics Class
│ │ ├── AudioUtil.java # 音频工具类 / Audio Utilities Class
│ │ ├── CompressionSettings.java # 压缩设置 / Compression Settings
│ │ ├── EqualizerBand.java # 均衡器频段 / Equalizer Band
│ │ ├── EqualizerSettings.java # 均衡器设置 / Equalizer Settings
│ │ ├── IAudioCodec.java # 音频编解码接口 / Audio Codec Interface
│ │ ├── IAudioComponentStandard.java # 音频组件标准接口 / Audio Component Standard Interface
│ │ ├── IAudioListener.java # 音频监听器接口 / Audio Listener Interface
│ │ ├── NoiseProfile.java # 噪声配置文件 / Noise Profile
│ │ ├── ReverbSettings.java # 混响设置 / Reverb Settings
│ │ └── UnsupportedAudioFormatException.java # 不支持的音频格式异常 / Unsupported Audio Format Exception
│ ├── effect/ # 音频效果 / Audio Effects
│ │ ├── AbstractAudioEffect.java # 抽象音频效果 / Abstract Audio Effect
│ │ ├── IAudioEffect.java # 音频效果接口 / Audio Effect Interface
│ │ └── ReverbEffect.java # 混响效果 / Reverb Effect
│ ├── embedding/ # 音频嵌入 / Audio Embedding
│ │ ├── IAudioEmbedding.java # 音频嵌入接口 / Audio Embedding Interface
│ │ ├── IVectorEmbedding.java # i-Vector语音向量嵌入 / i-Vector Audio Embedding
│ │ └── OnlineIVectorEmbedding.java # i-Vector语音向量嵌入 / Online i-Vector Audio Embedding
│ ├── enhancement/ # 音频增强 / Audio Enhancement
│ │ ├── AbstractAudioEnhancer.java # 抽象音频增强器 / Abstract Audio Enhancer
│ │ ├── CompressorEnhancer.java # 压缩器增强 / Compressor Enhancer
│ │ ├── EqualizerEnhancer.java # 均衡器增强 / Equalizer Enhancer
│ │ ├── IAudioEnhancer.java # 音频增强接口 / Audio Enhancer Interface
│ │ ├── NoiseReductionEnhancer.java # 噪声抑制增强 / Noise Reduction Enhancer
│ │ └── ReverbEnhancer.java # 混响增强 / Reverb Enhancer
│ ├── exception/ # 音频异常 / Audio Exceptions
│ │ ├── AudioAnalysisException.java # 音频分析异常 / Audio Analysis Exception
│ │ └── AudioProcessingException.java # 音频处理异常 / Audio Processing Exception
│ ├── factory/ # 音频工厂 / Audio Factory
│ │ └── AudioComponentFactory.java # 音频组件工厂 / Audio Component Factory
│ ├── feature/ # 音频特征 / Audio Features
│ │ ├── AudioFeatureExtractor.java # 音频特征提取器 / Audio Feature Extractor
│ │ ├── AudioFeatureExtractorImpl.java # 音频特征提取器实现 / Audio Feature Extractor Implementation
│ │ ├── AudioFeatureResult.java # 音频特征结果 / Audio Feature Result
│ │ ├── FrequencyDomainFeatureResult.java # 频域特征结果 / Frequency Domain Feature Result
│ │ ├── IAudioFeatureExtractor.java # 音频特征提取接口 / Audio Feature Extractor Interface
│ │ ├── SpectralFeatureResult.java # 谱特征结果 / Spectral Feature Result
│ │ └── TimeDomainFeatureResult.java # 时域特征结果 / Time Domain Feature Result
│ ├── filter/ # 音频滤波器 / Audio Filters
│ │ ├── AbstractAdvancedAudioFilter.java # 抽象高级音频滤波器 / Abstract Advanced Audio Filter
│ │ ├── AbstractAudioFilterStandard.java # 抽象音频滤波器标准 / Abstract Audio Filter Standard
│ │ ├── AdvancedLowPassFilter.java # 高级低通滤波器 / Advanced Low Pass Filter
│ │ ├── IAdvancedAudioFilter.java # 高级音频滤波器接口 / Advanced Audio Filter Interface
│ │ ├── IBaseAudioFilter.java # 基础音频滤波器接口 / Base Audio Filter Interface
│ │ └── LowPassFilter.java # 低通滤波器 / Low Pass Filter
│ ├── generation/ # 音频生成 / Audio Generation
│ ├── pipeline/ # 音频处理管道 / Audio Pipeline
│ │ └── AudioPipelineBuilder.java # 音频管道构建器 / Audio Pipeline Builder
│ ├── preprocessing/ # 音频预处理 / Audio Preprocessing
│ │ ├── AudioPreprocessingOptions.java # 音频预处理选项 / Audio Preprocessing Options
│ │ └── AudioPreprocessor.java # 音频预处理器 / Audio Preprocessor
│ ├── processing/ # 音频处理 / Audio Processing
│ │ ├── AbstractAudioProcessorStandard.java # 抽象音频处理器标准 / Abstract Audio Processor Standard
│ │ ├── ChannelProcessor.java # 通道处理器 / Channel Processor
│ │ ├── IAdvancedAudioProcessor.java # 高级音频处理器接口 / Advanced Audio Processor Interface
│ │ ├── IAudioProcessor.java # 音频处理器接口 / Audio Processor Interface
│ │ ├── IBaseAudioProcessor.java # 基础音频处理器接口 / Base Audio Processor Interface
│ │ ├── NormalizeProcessor.java # 归一化处理器 / Normalize Processor
│ │ └── VolumeProcessor.java # 音量处理器 / Volume Processor
│ └── transform/ # 音频变换 / Audio Transform
├── 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
│ │ ├── 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
│ │ ├── 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
│ │ ├── 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
│ │ │ ├── EnsembleClassifier.java # 集成分类器 / Ensemble Classifier
│ │ │ ├── EnsembleResult.java # 集成结果 / Ensemble Result
│ │ │ └── tree/ # 树模型 / Tree Models
│ │ │ ├── RFTree.java # 随机森林树 / Random Forest Tree
│ │ │ ├── RFTreeNode.java # 随机森林树节点 / Random Forest Tree Node
│ │ │ ├── RandomForestHyperparameterOptimizer.java # 随机森林超参数优化器 / Random Forest Hyperparameter Optimizer
│ │ │ ├── RandomForestResult.java # 随机森林结果 / Random Forest Result
│ │ │ ├── RereRandomForest.java # 随机森林实现 / Random Forest Implementation
│ │ │ ├── RereXGboost.java # XGBoost实现 / XGBoost Implementation
│ │ │ ├── XGBoostLossFunction.java # XGBoost损失函数 / XGBoost Loss Function
│ │ │ ├── XGBoostResult.java # XGBoost结果 / XGBoost Result
│ │ │ ├── XGTree.java # XGBoost树 / XGBoost Tree
│ │ │ └── XGTreeNode.java # XGBoost树节点 / XGBoost Tree Node
│ │ ├── 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
│ │ ├── IGradientFunction.java # 梯度函数接口 / Gradient Function Interface
│ │ ├── IObjectiveFunction.java # 目标函数接口 / Objective Function Interface
│ │ ├── IOnlineOptimizer.java # 在线优化器接口 / Online Optimizer Interface
│ │ ├── IOptimizer.java # 优化器接口 / Optimizer Interface
│ │ ├── OptimizerExample.java # 优化器示例 / Optimizer Example
│ │ ├── Opts.java # 优化工具类 / Optimization Utilities
│ │ ├── RereLineSearch.java # 线搜索 / Line Search
│ │ ├── constraint/ # 约束优化 / Constraint Optimization
│ │ │ └── LagrangeMultiplierSolver.java # 拉格朗日乘数求解器 / Lagrange Multiplier Solver
│ │ ├── linpg/ # 线性规划 / Linear Programming
│ │ │ ├── ILinProgSolver.java # 线性规划求解器接口 / Linear Programming Solver Interface
│ │ │ ├── InteriorPointLinProgSolver.java # 内点法线性规划求解器 / Interior Point Linear Programming Solver
│ │ │ ├── LangMultiplierLinProgSolver.java # 拉格朗日乘数线性规划求解器 / Lagrange Multiplier Linear Programming Solver
│ │ │ ├── LinProgUtil.java # 线性规划工具类 / Linear Programming Utilities
│ │ │ ├── SimplexLinProgSolver.java # 单纯形法线性规划求解器 / Simplex Linear Programming Solver
│ │ │ ├── IIntegerProg.java # 整数规划接口 / Integer Programming Interface
│ │ │ └── RereIntegerProg.java # 整数规划实现 / Integer Programming Implementation
│ │ └── newton/ # 牛顿法优化 / Newton Method Optimization
│ │ ├── RereConjugateGradient.java # 共轭梯度法 / Conjugate Gradient Method
│ │ ├── RereDFP.java # DFP算法 / DFP Algorithm
│ │ ├── RereLBFGS.java # L-BFGS优化器 / L-BFGS Optimizer
│ │ ├── RereOnlineAdam.java # 在线Adam优化器 / Online Adam Optimizer
│ │ ├── RereOnlineSGD.java # 在线SGD优化器 / Online SGD Optimizer
│ │ └── RereSteepestDescent.java # 最速下降法 / Steepest Descent Method
│ ├── 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
│ │ ├── SignalPlots.java # 信号可视化 / Signal Plots
│ │ ├── 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
│ │ │ ├── Complex.java # 复数类 / Complex Number Class
│ │ │ ├── RereDCT.java # 离散余弦变换 / Discrete Cosine Transform
│ │ │ ├── RereFFT.java # 快速傅里叶变换 / Fast Fourier Transform
│ │ │ └── RereHilbert.java # 希尔伯特变换 / Hilbert Transform
│ │ ├── 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
│ │ └── wavele/ # 小波分析 / Wavelet Analysis
│ │ ├── WaveletAnalysis.java # 小波分析 / Wavelet Analysis
│ │ ├── WaveletCoefficients.java # 小波系数 / Wavelet Coefficients
│ │ ├── WaveletFilters.java # 小波滤波器 / Wavelet Filters
│ │ ├── WaveletPlots.java # 小波绘图 / Wavelet Plots
│ │ └── WaveletUtilities.java # 小波工具类 / Wavelet Utilities
│ ├── timeseries/ # 时间序列分析模块 / Time Series Analysis Module
│ │ ├── CointegrationAnalysis.java # 协整分析 / Cointegration Analysis
│ │ ├── Series.java # 时间序列类 / Time Series Class
│ │ ├── TimeSeriesAnalyzer.java # 时间序列分析器 / Time Series Analyzer
│ │ ├── TimeSeriesData.java # 时间序列数据 / Time Series Data
│ │ ├── 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
│ │ ├── TimeSeriesPlots.java # 时间序列绘图 / Time Series Plots
│ │ ├── TimeSeriesUnifiedExample.java # 时间序列统一示例 / Time Series Unified Example
│ │ ├── TimeSeriesUtils.java # 时间序列工具类 / Time Series Utilities
│ │ └── 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
└── 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
- 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
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。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, 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.
我们欢迎社区贡献！请遵循以下步骤：
We welcome community contributions! Please follow these steps:
- Fork 本项目 / Fork this project
- 创建特性分支 / Create a feature branch (
git checkout -b feature/AmazingFeature) - 提交更改 / Commit your changes (
git commit -m 'Add some AmazingFeature') - 推送到分支 / Push to the branch (
git push origin feature/AmazingFeature) - 开启 Pull Request / Open a Pull Request
- 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
本项目采用 MIT 许可证 - 查看 LICENSE 文件了解详情。
This project is licensed under the MIT License - see the LICENSE file for details.
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.
- 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://gitee.com/scalefree-tech/yishape-math.
- 问题反馈 / Issues: https://github.com/ScaleFree-Tech/yishape-math/issues
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
- SIMD (Single Instruction, Multiple Data)支持 / SIMD Support: 基于Java Vector API提供向量&矩阵乘法、通用函数、规约函数等方面的SIMD并行计算支持 / SIMD (Single Instruction, Multiple Data) parallel computing support based on Java Vector API
- Bug Fixes / Bug Fixes: 修复已知问题和错误 / Bug fixes and error corrections
- 新增音频处理功能 / New Audio Processing Features: 音频特征提取、音高检测、音频增强、i-vector模型训练等 / Audio feature extraction, pitch detection, audio enhancement, i-vector model training
- 📡 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
- ⚡ 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
- 📊 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
- 📊 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
- ✨ 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!