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? 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? ? ? ? ? ? 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.eva luate(values));
? System.out.println("max: " + max.eva luate(values));
? System.out.println("mean: " + mean.eva luate(values));
? System.out.println("product: " + product.eva luate(values));
? System.out.println("sum: " + sum.eva luate(values));
? System.out.println("variance: " + variance.eva luate(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.eva luate(values, 80.0));
? System.out.println("geometric mean: " + geoMean.eva luate(values));
? System.out.println("skewness: " + skewness.eva luate(values));
? System.out.println("kurtosis: " + kurtosis.eva luate(values));
? System.out.println("sumOfSquares: " + sumOfSquares.eva luate(values));
? System.out.println("StandardDeviation: " + StandardDeviation.eva luate(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);
?}
}