Detailed explanation of mathematical functions and algorithms used in Commons Math

Commons Math (referred to as CM) is an open source Java library that provides many commonly used mathematical functions and algorithms, which are widely used in mathematics, science and engineering calculations.This article will introduce the mathematical functions and algorithms commonly used in the Commons Math, and provide the corresponding Java code example. 1. Mathematical function 1. Absolute value function ABS () This function is used to calculate the absolute value of the given value. Example code: double result1 = Math.abs(-5.2); int result2 = Math.abs(10); 2. Power function POW () This function is used to calculate the index power of the given bottom number. Example code: double result1 = math.pow (2, 3); // Calculate the 3 power of 2 double result2 = math.pow (10, -2); // Calculate the negative 2 times of 10 3. Fang Root Function SQRT () This function is used to calculate the square root of the given value. Example code: double result1 = math.sqrt (16); // Calculate the square root of 16 double result2 = math.sqrt (2.7); // Calculate the square root of 2.7 4. Matrix Log () This function is used to calculate the number of pairs of the given bottom number. Example code: double result1 = math.log (10); // Calculate the number of 10 pairs of 10 at the bottom of E double result2 = math.log10 (100); // Calculate the number of 100 pairs of 100 bottom 100 5. Take the entire function Round () This function is used to enter the given value to the closest integer. Example code: long result1 = math.round (5.7); // into 5.7 four and five into 6 long result2 = math.round (-3.2); // into -3.2 four houses and five into -3 2. Common algorithms 1. Linear regression Commons Math provides a class for performing linear regression. It can fit the linear model based on the given data set and calculate the slope and interception of the regression equation. Example code: SimpleRegression regression = new SimpleRegression(); regression.addData(1, 2); regression.addData(2, 3); regression.addData(3, 4); double slope = regression.getslope (); // Get the slope of the regression equation double intercept = regression.getIntercept (); // Get the interception of the regression equation 2. Insert Commons Math provides a variety of interpolation algorithms, which can estimate the unknown value in the middle according to the given discrete data point. Example code: LinearInterpolator interpolator = new LinearInterpolator(); UnivariateFunction function = interpolator.interpolate( new double[]{1, 2, 3}, new double[]{4, 5, 6}); double result = function.value (1.5); // Estimated the y value corresponding to x = 1.5 3. Numerical points Commons Math provides a variety of numerical accumulation algorithms that can be used to calculate the score value of the function in the given range. Example code: UnivariateFunction function = new UnivariateFunction() { public double value(double x) { return x * x; } }; UnivariateIntegrator integrator = new SimpsonIntegrator(); double result = Integrator.integraate (100, Function, 0, 1); // Calculate the points of x^2 on 0 to 1 4. Probability distribution Commons Math provides a variety of common probability distribution implementation, including normal distribution, Patson distribution, etc., which can be used to calculate the probability density function, cumulative distribution function, etc. Example code: NormalDistribution distribution = new NormalDistribution(0, 1); double pdf = distility.denSity (0); // Calculate the probability density value of x = 0 under normal distribution of standards double CDF = distribution.cumulativeProbility (1); // Calculate the cumulative probability value of x ≤1 under the normal distribution of the standard normal distribution under normal distribution 3. Summary This article introduces the mathematical functions and algorithms often used in Commons Math, covering algorithms such as absolute value, power function, square root function, pairing function, rectification function, and linear regression, interpolation, numerical integration and probability distribution.By using Commons Math in the project, developers can easily perform various mathematical computing and statistical analysis, and improve development efficiency.