Commons Math学习笔记

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 stubpoisson();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 stubNormalDistribution 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 blocke.printStackTrace();}}private static void poisson() {// TODO Auto-generated method stubPoissonDistribution 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 blocke.printStackTrace();}}private static void normal() {// TODO Auto-generated method stubNormalDistribution 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 blocke.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 stubintegration();}private static void integration() {// TODO Auto-generated method stubUnivariateFunction f = new Sin();BaseAbstractUnivariateIntegrator integrator = new SimpsonIntegrator();// integrateSystem.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 blocke.printStackTrace();} catch (IllegalArgumentException e) {// TODO Auto-generated catch blocke.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 stubpolynomialsInterpolation();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 = 0.5try {f = i.interpolate(x, y);System.out.println("when x = 0.5, y = " + f.value(0.5));} catch (MathArithmeticException e) {// TODO Auto-generated catch blocke.printStackTrace();}// check polynomials functionsPolynomialFunction 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 stubdouble x[] = { 0.0, -1.0, 0.5 };double y[] = { -3.0, -6.0, 0.0 };PolynomialFunctionLagrangeForm p = new PolynomialFunctionLagrangeForm(x, y);// output directlySystem.out.println("ugly output is " + p);// interpolate y when x = 1.0try {System.out.println("when x = 1.0, y = " + p.value(1.0));} catch (MathArithmeticException e) {// TODO Auto-generated catch blocke.printStackTrace();}// degreeSystem.out.println("polynomial degree is " + p.degree());// coefficientsfor (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 stubpolynomials();System.out.println("-----------------------------------------------");polynomialsSpline();}private static void polynomialsSpline() {// TODO Auto-generated method stubPolynomialFunction[] 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 directlySystem.out.println("poly spline func is " + spline);// get the value when x = 0.5try {System.out.println("f(0.5) = " + spline.value(0.5));} catch (Exception e) {// TODO Auto-generated catch blocke.printStackTrace();}// the number of spline segmentsSystem.out.println("spline segments number is " + spline.getN());// the polynomials functionsfor (int i = 0; i < spline.getN(); i++) {System.out.println("spline:f" + i + "(x) = "+ spline.getPolynomials()[i]);}// function derivativeSystem.out.println("spline func derivative is " + spline.derivative());}private static void polynomials() {// TODO Auto-generated method stubdouble[] 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 directlySystem.out.println("f1(x) is : " + f1);System.out.println("f2(x) is : " + f2);// polynomial degreeSystem.out.println("f1(x)'s degree is " + f1.degree());// get the value when x = 2System.out.println("f1(2) = " + f1.value(2));// function addSystem.out.println("f1(x)+f2(x) = " + f1.add(f2));// function substractSystem.out.println("f1(x)-f2(x) = " + f1.subtract(f2));// function multiplySystem.out.println("f1(x)*f2(x) = " + f1.multiply(f2));// function derivativeSystem.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 stubrandom();}private static void random() {// TODO Auto-generated method stubRandomDataGenerator randomData = new RandomDataGenerator();// Generate a random int value uniformly distributed between lower and// upper, inclusiveSystem.out.println("a uniform value: " + randomData.nextInt(1, 6));// Returns a random value from an Exponential distribution with the// given meanSystem.out.println("a Exponential value: "+ randomData.nextExponential(5));// Generate a random value from a NormalSystem.out.println("a Normal value: " + randomData.nextGaussian(0, 1));// Generates a random value from the Poisson distribution with the given// meanSystem.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-1int[] 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 distributionFrequency 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 testdouble[] 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 columnsdouble[][] matrixData = { {1d,2d,3d}, {2d,5d,3d}};RealMatrix m = new Array2DRowRealMatrix(matrixData);System.out.println(m);// One more with three rows, two columnsdouble[][] matrixData2 = { {1d,2d}, {2d,5d}, {1d, 7d}};RealMatrix n = new Array2DRowRealMatrix(matrixData2); // Note: The constructor copies  the input double[][] array. // Now multiply m by nRealMatrix p = m.multiply(n);System.out.println("p:"+p);System.out.println(p.getRowDimension());    // 2System.out.println(p.getColumnDimension()); // 2 // Invert p, using LU decompositionRealMatrix pInverse = new LUDecomposition(p).getSolver().getInverse();System.out.println(pInverse);}}

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