先列出一個目錄：（這個目錄是根據commons math 3.3庫的結構設計的）
Section 1 linear 線性代數（矩陣為主）
1） Vector 向量
2） Matrix 矩陣
3） Matrix Decomposition 矩陣分解
Section 2 analysis 數學分析（函數為主）
1） Function 函數
2） Polynomial 多項式函數
3） Interpolation 插值
4） Integration 積分
5） Solver 求解
Section 3 Probabilityand Statistics 概率和統計
1）distribution 分布
2）fraction and complex 分數和復數
3）random and statistics 隨機生成和統計初步
4）cluster and regression聚類和回歸
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 《飲料裝填量不足與超量的概率》
* 某飲料公司裝瓶流程嚴謹，每罐飲料裝填量符合平均600毫升，標准差3毫升的常態分配法則
* 。隨機選取一罐，容量超過605毫升的概率？容量小於590毫升的概率 容量超過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
* 容量小於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.函數積分
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: 函數積分
* @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.函數插值
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: 函數插值
* @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.多項式函數
package apache.commons.math.test;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
/**
*
* @ClassName: PolinomialsFunctionTest
* @Description: 多項式函數
* @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.隨機生成和統計初步
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: 隨機生成和統計初步
* @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.聚類和回歸
package apache.commons.math.test;
import org.apache.commons.math3.stat.regression.OLSMultipleLinearRegression;
import org.apache.commons.math3.stat.regression.SimpleRegression;
/**
*
* @ClassName: RegressionTest
* @Description: 聚類和回歸
* @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組件用法實例
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組件用法實例
* @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(); // 算術平均值
Product product = new Product();//乘積
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(); // 百分位數
GeometricMean geoMean = new GeometricMean(); // 幾何平均數,n個正數的連乘積的n次算術根叫做這n個數的幾何平均數
Skewness skewness = new Skewness(); // Skewness();
Kurtosis kurtosis = new Kurtosis(); // Kurtosis,峰度
SumOfSquares sumOfSquares = new SumOfSquares(); // 平方和
StandardDeviation StandardDeviation = new StandardDeviation();//標准差
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);
}
}
Commons Math 的詳細介紹：請點這裡
Commons Math 的下載地址：請點這裡
