Commons Math学习笔记

洪飞驰

2023-12-01

本文参考点击打开链接，由于这篇博客比较旧，我在这篇博客的基础上引用commons math 3.3库做了一些修正。

先列出一个目录：（这个目录是根据commons math 3.3库的结构设计的）

Section 1 linear 线性代数（矩阵为主）

1） Vector 向量

2） Matrix 矩阵

3） Matrix Decomposition 矩阵分解

Section 2 analysis 数学分析（函数为主）

1） Function 函数

2） Polynomial 多项式函数

3） Interpolation 插值

4） Integration 积分

5） Solver 求解

Section 3 Probabilityand Statistics 概率和统计

1）distribution 分布

2）fraction and complex 分数和复数

3）random and statistics 随机生成和统计初步

4）cluster and regression聚类和回归

1.分布

package apache.commons.math.test;

import org.apache.commons.math3.distribution.NormalDistribution;
import org.apache.commons.math3.distribution.PoissonDistribution;
import org.apache.commons.math3.exception.MathArithmeticException;

/**
 * 
 * @ClassName: DistributionTest 
 * @Description: 分布
 * @author zengfh 
 * @date 2014年11月21日 下午3:32:15 
 *
 */
public class DistributionTest {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		poisson();
		System.out.println("------------------------------------------");
		normal();
		test();
	}

	/**
	 * test for example 《饮料装填量不足与超量的概率》
	 * 某饮料公司装瓶流程严谨，每罐饮料装填量符合平均600毫升，标准差3毫升的常态分配法则
	 * 。随机选取一罐，容量超过605毫升的概率？容量小于590毫升的概率 容量超过605毫升的概率 = p ( X > 605)= p ( ((X-μ)
	 * /σ) > ( (605 – 600) / 3) )= p ( Z > 5/3) = p( Z > 1.67) = 0.0475
	 * 容量小于590毫升的概率 = p (X < 590) = p ( ((X-μ) /σ) < ( (590 – 600) / 3) )= p ( Z
	 * < -10/3) = p( Z < -3.33) = 0.0004
	 */
	private static void test() {
		// TODO Auto-generated method stub
		NormalDistribution normal = new NormalDistribution(600, 3);
		try {
			System.out.println("P(X<590) = "
					+ normal.cumulativeProbability(590));
			System.out.println("P(X>605) = "
					+ (1 - normal.cumulativeProbability(605)));
		} catch (MathArithmeticException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
	}

	private static void poisson() {
		// TODO Auto-generated method stub
		PoissonDistribution dist = new PoissonDistribution(4.0);
		try {
			System.out.println("P(X<=2) = " + dist.cumulativeProbability(2));
			System.out.println("mean value is " + dist.getMean());
			System.out.println("P(X=1) = " + dist.probability(1));
			System.out.println("P(X=x)=0.8 where x = "
					+ dist.inverseCumulativeProbability(0.8));
		} catch (MathArithmeticException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
	}

	private static void normal() {
		// TODO Auto-generated method stub
		NormalDistribution normal = new NormalDistribution(0, 1);
		try {
			System.out.println("P(X<2.0) = "
					+ normal.cumulativeProbability(2.0));
			System.out.println("mean value is " + normal.getMean());
			System.out.println("standard deviation is "
					+ normal.getStandardDeviation());
			System.out.println("P(X=1) = " + normal.density(1.0));
			System.out.println("P(X<x)=0.8 where x = "
					+ normal.inverseCumulativeProbability(0.8));
		} catch (MathArithmeticException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
	}

}

2.函数积分

package apache.commons.math.test;

import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.function.Sin;
import org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator;
import org.apache.commons.math3.analysis.integration.SimpsonIntegrator;
import org.apache.commons.math3.exception.ConvergenceException;

/**
 * 
 * @ClassName: IntegrationTest 
 * @Description: 函数积分 
 * @author zengfh 
 * @date 2014年11月21日 下午2:59:58 
 *
 */
public class IntegrationTest {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		integration();
	}

	private static void integration() {
		// TODO Auto-generated method stub
		UnivariateFunction f = new Sin();
		BaseAbstractUnivariateIntegrator integrator = new SimpsonIntegrator();

		// integrate
		System.out.println("f(x)=sin(x)");
		try {
			System.out.println("integration of f(x) from 0 to Pi is "
					+ integrator.integrate(100,f, 0, Math.PI));
		} catch (ConvergenceException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		} catch (IllegalArgumentException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
	}

}

3.函数插值

package apache.commons.math.test;

import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.interpolation.SplineInterpolator;
import org.apache.commons.math3.analysis.interpolation.UnivariateInterpolator;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunctionLagrangeForm;
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
import org.apache.commons.math3.exception.MathArithmeticException;

/**
 * 
 * @ClassName: InterpolationTest 
 * @Description: 函数插值
 * @author zengfh 
 * @date 2014年11月21日 下午3:13:39 
 *
 */
public class InterpolationTest {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		polynomialsInterpolation();
		System.out.println("-------------------------------------------");
		interpolatioin();
	}

	private static void interpolatioin() {
		// TODO Auto-generated method stub
		// double x[] = { 0.0, 0.5, 1.0 };
		// double y[] = { 0.0, 0.5, 1.0 };
		double x[] = { 0.0, Math.PI / 6d, Math.PI / 2d, 5d * Math.PI / 6d,
				Math.PI, 7d * Math.PI / 6d, 3d * Math.PI / 2d,
				11d * Math.PI / 6d, 2.d * Math.PI };
		double y[] = { 0d, 0.5d, 1d, 0.5d, 0d, -0.5d, -1d, -0.5d, 0d };
		UnivariateInterpolator i = new SplineInterpolator();
		UnivariateFunction f = null;
		// interpolate y when x = 0.5
		try {
			f = i.interpolate(x, y);
			System.out.println("when x = 0.5, y = " + f.value(0.5));
		} catch (MathArithmeticException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}

		// check polynomials functions
		PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f)
				.getPolynomials();
		for (int j = 0; j < polynomials.length; j++) {
			System.out
					.println("cubic spline:f" + j + "(x) = " + polynomials[j]);
		}
	}

	private static void polynomialsInterpolation() {
		// TODO Auto-generated method stub
		double x[] = { 0.0, -1.0, 0.5 };
		double y[] = { -3.0, -6.0, 0.0 };
		PolynomialFunctionLagrangeForm p = new PolynomialFunctionLagrangeForm(
				x, y);
		// output directly
		System.out.println("ugly output is " + p);
		// interpolate y when x = 1.0
		try {
			System.out.println("when x = 1.0, y = " + p.value(1.0));
		} catch (MathArithmeticException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
		// degree
		System.out.println("polynomial degree is " + p.degree());
		// coefficients
		for (int i = 0; i < p.getCoefficients().length; i++) {
			System.out.println("coeff[" + i + "] is " + p.getCoefficients()[i]);
		}
		//
	}

}

4.多项式函数

package apache.commons.math.test;

import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;

/**
 * 
 * @ClassName: PolinomialsFunctionTest 
 * @Description: 多项式函数 
 * @author zengfh 
 * @date 2014年11月21日 下午1:38:13 
 *
 */
public class PolinomialsFunctionTest {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		polynomials();
		System.out.println("-----------------------------------------------");
		polynomialsSpline();
	}

	private static void polynomialsSpline() {
		// TODO Auto-generated method stub
		PolynomialFunction[] polynomials = {
				new PolynomialFunction(new double[] { 0d, 1d, 1d }),
				new PolynomialFunction(new double[] { 2d, 1d, 1d }),
				new PolynomialFunction(new double[] { 4d, 1d, 1d }) };
		double[] knots = { -1, 0, 1, 2 };
		PolynomialSplineFunction spline = new PolynomialSplineFunction(knots,
				polynomials);
		// output directly
		System.out.println("poly spline func is " + spline);
		// get the value when x = 0.5
		try {
			System.out.println("f(0.5) = " + spline.value(0.5));
		} catch (Exception e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
		// the number of spline segments
		System.out.println("spline segments number is " + spline.getN());
		// the polynomials functions
		for (int i = 0; i < spline.getN(); i++) {
			System.out.println("spline:f" + i + "(x) = "
					+ spline.getPolynomials()[i]);
		}
		// function derivative
		System.out.println("spline func derivative is " + spline.derivative());
	}

	private static void polynomials() {
		// TODO Auto-generated method stub
		double[] f1_coeff = { 3.0, 6.0, -2.0, 1.0 };
		double[] f2_coeff = { 1.0, 2.0, -1.0, -2.0 };
		PolynomialFunction f1 = new PolynomialFunction(f1_coeff);
		PolynomialFunction f2 = new PolynomialFunction(f2_coeff);
		// output directly
		System.out.println("f1(x) is : " + f1);
		System.out.println("f2(x) is : " + f2);
		// polynomial degree
		System.out.println("f1(x)'s degree is " + f1.degree());
		// get the value when x = 2
		System.out.println("f1(2) = " + f1.value(2));
		// function add
		System.out.println("f1(x)+f2(x) = " + f1.add(f2));
		// function substract
		System.out.println("f1(x)-f2(x) = " + f1.subtract(f2));
		// function multiply
		System.out.println("f1(x)*f2(x) = " + f1.multiply(f2));
		// function derivative
		System.out.println("f1'(x) = " + f1.derivative());
		System.out.println("f2''(x) = "
				+ ((PolynomialFunction) f2.derivative()).derivative());

	}

}

5.随机生成和统计初步

package apache.commons.math.test;

import org.apache.commons.math3.random.RandomDataGenerator;
import org.apache.commons.math3.stat.Frequency;
import org.apache.commons.math3.stat.StatUtils;

/**
 * 
 * @ClassName: RandomTest
 * @Description: 随机生成和统计初步
 * @author zengfh
 * @date 2014年11月21日 下午2:23:04
 * 
 */
public class RandomTest {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		random();
	}

	private static void random() {
		// TODO Auto-generated method stub
		RandomDataGenerator randomData = new RandomDataGenerator();

		// Generate a random int value uniformly distributed between lower and
		// upper, inclusive
		System.out.println("a uniform value: " + randomData.nextInt(1, 6));
		// Returns a random value from an Exponential distribution with the
		// given mean
		System.out.println("a Exponential value: "
				+ randomData.nextExponential(5));
		// Generate a random value from a Normal
		System.out.println("a Normal value: " + randomData.nextGaussian(0, 1));
		// Generates a random value from the Poisson distribution with the given
		// mean
		System.out.println("a Poisson value: " + randomData.nextPoisson(3));
		// Generates an integer array of length k whose entries are selected
		// randomly, without repetition, from the integers 0 through n-1
		int[] a = randomData.nextPermutation(10, 3);
		for (int i = 0; i < a.length; i++) {
			System.out.print(a[i] + " ");
		}
		System.out.println();

		// generate 1000 numbers between 0 and 3 inclusive, then using frequency
		// to see the distribution

		Frequency freq = new Frequency();
		int value = 0;
		for (int i = 0; i < 1000; i++) {
			value = randomData.nextInt(0, 3);
			freq.addValue(value);
		}
		long[] observed = new long[4];
		double[] perc = new double[4];
		for (int i = 0; i < 4; i++) {
			observed[i] = freq.getCount(i);
			perc[i] = freq.getPct(i);
			System.out.println("there are " + observed[i] + " " + i
					+ " in dataset with " + (perc[i] * 100) + "%");
		}

		// stat test
		double[] data = { 1d, 2d, 2d, 3d };
		System.out.println("sum of data is " + StatUtils.sum(data));
		System.out.println("sum of square of data is " + StatUtils.sumSq(data));
		System.out.println("var of data is " + StatUtils.variance(data));
		System.out.println("mean of data is " + StatUtils.mean(data));
		System.out.println("max value of data is " + StatUtils.max(data));
		System.out.println("min value of data is " + StatUtils.min(data));
		System.out.println("geometry mean of data is "
				+ StatUtils.geometricMean(data));
		System.out.println("product of data is " + StatUtils.product(data));
	}

}

6.聚类和回归

package apache.commons.math.test;

import org.apache.commons.math3.stat.regression.OLSMultipleLinearRegression;
import org.apache.commons.math3.stat.regression.SimpleRegression;

/**
 * 
 * @ClassName: RegressionTest 
 * @Description: 聚类和回归
 * @author zengfh 
 * @date 2014年11月21日 下午1:56:19 
 *
 */
public class RegressionTest {
    /**
     * @param args
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        regression();
        System.out.println("-------------------------------------");
        simple();
    }

    private static void simple() {
        // TODO Auto-generated method stub
        double[][] data = { { 0.1, 0.2 }, {338.8, 337.4 }, {118.1, 118.2 }, 
                {888.0, 884.6 }, {9.2, 10.1 }, {228.1, 226.5 }, {668.5, 666.3 }, {998.5, 996.3 }, 
                {449.1, 448.6 }, {778.9, 777.0 }, {559.2, 558.2 }, {0.3, 0.4 }, {0.1, 0.6 }, {778.1, 775.5 }, 
                {668.8, 666.9 }, {339.3, 338.0 }, {448.9, 447.5 }, {10.8, 11.6 }, {557.7, 556.0 }, 
                {228.3, 228.1 }, {998.0, 995.8 }, {888.8, 887.6 }, {119.6, 120.2 }, {0.3, 0.3 }, 
                {0.6, 0.3 }, {557.6, 556.8 }, {339.3, 339.1 }, {888.0, 887.2 }, {998.5, 999.0 }, 
                {778.9, 779.0 }, {10.2, 11.1 }, {117.6, 118.3 }, {228.9, 229.2 }, {668.4, 669.1 }, 
                {449.2, 448.9 }, {0.2, 0.5 }
        };
        SimpleRegression regression = new SimpleRegression();
        for (int i = 0; i < data.length; i++) {
            regression.addData(data[i][1], data[i][0]);
        }
        System.out.println("slope is "+regression.getSlope());
        System.out.println("slope std err is "+regression.getSlopeStdErr());
        System.out.println("number of observations is "+regression.getN());
        System.out.println("intercept is "+regression.getIntercept());
        System.out.println("std err intercept is "+regression.getInterceptStdErr());
        System.out.println("r-square is "+regression.getRSquare());
        System.out.println("SSR is "+regression.getRegressionSumSquares());
        System.out.println("MSE is "+regression.getMeanSquareError());
        System.out.println("SSE is "+regression.getSumSquaredErrors());
        System.out.println("predict(0) is "+regression.predict(0));
        System.out.println("predict(1) is "+regression.predict(1));
    }

    private static void regression() {
        // TODO Auto-generated method stub
        double[] y;
        double[][] x;
        y = new double[]{11.0, 12.0, 13.0, 14.0, 15.0, 16.0};
        x = new double[6][];
        x[0] = new double[]{1.0, 0, 0, 0, 0, 0};
        x[1] = new double[]{1.0, 2.0, 0, 0, 0, 0};
        x[2] = new double[]{1.0, 0, 3.0, 0, 0, 0};
        x[3] = new double[]{1.0, 0, 0, 4.0, 0, 0};
        x[4] = new double[]{1.0, 0, 0, 0, 5.0, 0};
        x[5] = new double[]{1.0, 0, 0, 0, 0, 6.0};
        System.out.println(x[0].length+"-----------");
        OLSMultipleLinearRegression regression = new OLSMultipleLinearRegression();
        regression.newSampleData(y, x);      
        double[] betaHat = regression.estimateRegressionParameters();
        System.out.println("Estimates the regression parameters b:");
        print(betaHat);
        double[] residuals = regression.estimateResiduals();
        System.out.println("Estimates the residuals, ie u = y - X*b:");
        print(residuals);
        double vary = regression.estimateRegressandVariance();
        System.out.println("Returns the variance of the regressand Var(y):");
        System.out.println(vary);
        double[] erros = regression.estimateRegressionParametersStandardErrors();
        System.out.println("Returns the standard errors of the regression parameters:");
        print(erros);
        double[][] varb = regression.estimateRegressionParametersVariance();
    }

    private static void print(double[] v) {
        // TODO Auto-generated method stub
        for(int i=0;i<v.length;i++){
            System.out.print(v[i]+ " ");
        }
        System.out.println();
    }

}

7.math组件用法实例

package apache.commons.math.test;

import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.linear.LUDecomposition;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.stat.descriptive.moment.GeometricMean;
import org.apache.commons.math3.stat.descriptive.moment.Kurtosis;
import org.apache.commons.math3.stat.descriptive.moment.Mean;
import org.apache.commons.math3.stat.descriptive.moment.Skewness;
import org.apache.commons.math3.stat.descriptive.moment.StandardDeviation;
import org.apache.commons.math3.stat.descriptive.moment.Variance;
import org.apache.commons.math3.stat.descriptive.rank.Max;
import org.apache.commons.math3.stat.descriptive.rank.Min;
import org.apache.commons.math3.stat.descriptive.rank.Percentile;
import org.apache.commons.math3.stat.descriptive.summary.Product;
import org.apache.commons.math3.stat.descriptive.summary.Sum;
import org.apache.commons.math3.stat.descriptive.summary.SumOfSquares;

/**
 * 
 * @ClassName: TestMathUserage 
 * @Description: math组件用法实例 
 * @author zengfh 
 * @date 2014年11月21日 下午1:25:24 
 *
 */
public class TestMathUserage {
	public static void main(String[] args) {
		double[] values = new double[] { 0.33, 1.33, 0.27333, 0.3, 0.501,
				0.444, 0.44, 0.34496, 0.33, 0.3, 0.292, 0.667 };
		/*
		 * System.out.println( "min: " + StatUtils.min( values ) );
		 * System.out.println( "max: " + StatUtils.max( values ) );
		 * System.out.println( "mean: " + StatUtils.mean( values ) ); // Returns
		 * the arithmetic mean of the entries in the input array, or Double.NaN
		 * if the array is empty System.out.println( "product: " +
		 * StatUtils.product( values ) ); //Returns the product of the entries
		 * in the input array, or Double.NaN if the array is empty.
		 * System.out.println( "sum: " + StatUtils.sum( values ) ); //Returns
		 * the sum of the values in the input array, or Double.NaN if the array
		 * is empty. System.out.println( "variance: " + StatUtils.variance(
		 * values ) ); // Returns the variance of the entries in the input
		 * array, or Double.NaN if the array is empty.
		 */

		Min min = new Min();
		Max max = new Max();
		
		Mean mean = new Mean(); // 算术平均值
		Product product = new Product();//乘积
		Sum sum = new Sum();
		Variance variance = new Variance();//方差
		System.out.println("min: " + min.evaluate(values));
		System.out.println("max: " + max.evaluate(values));
		System.out.println("mean: " + mean.evaluate(values));
		System.out.println("product: " + product.evaluate(values));
		System.out.println("sum: " + sum.evaluate(values));
		System.out.println("variance: " + variance.evaluate(values));

		Percentile percentile = new Percentile(); // 百分位数
		GeometricMean geoMean = new GeometricMean(); // 几何平均数,n个正数的连乘积的n次算术根叫做这n个数的几何平均数
		Skewness skewness = new Skewness(); // Skewness();
		Kurtosis kurtosis = new Kurtosis(); // Kurtosis,峰度
		SumOfSquares sumOfSquares = new SumOfSquares(); // 平方和
		StandardDeviation StandardDeviation = new StandardDeviation();//标准差
		System.out.println("80 percentile value: "
				+ percentile.evaluate(values, 80.0));
		System.out.println("geometric mean: " + geoMean.evaluate(values));
		System.out.println("skewness: " + skewness.evaluate(values));
		System.out.println("kurtosis: " + kurtosis.evaluate(values));
		System.out.println("sumOfSquares: " + sumOfSquares.evaluate(values));
		System.out.println("StandardDeviation: " + StandardDeviation.evaluate(values));
		
		System.out.println("-------------------------------------");
		// Create a real matrix with two rows and three columns
		double[][] matrixData = { {1d,2d,3d}, {2d,5d,3d}};
		RealMatrix m = new Array2DRowRealMatrix(matrixData);
		System.out.println(m);
		// One more with three rows, two columns
		double[][] matrixData2 = { {1d,2d}, {2d,5d}, {1d, 7d}};
		RealMatrix n = new Array2DRowRealMatrix(matrixData2);		 
		// Note: The constructor copies  the input double[][] array.		 
		// Now multiply m by n
		RealMatrix p = m.multiply(n);
		System.out.println("p:"+p);
		System.out.println(p.getRowDimension());    // 2
		System.out.println(p.getColumnDimension()); // 2		 
		// Invert p, using LU decomposition
		RealMatrix pInverse = new LUDecomposition(p).getSolver().getInverse();
		System.out.println(pInverse);
	}
}

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Commons Math学习笔记

1.分布

2.函数积分

3.函数插值

4.多项式函数

5.随机生成和统计初步

6.聚类和回归

7.math组件用法实例

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