java - 计算函数的偏导数

Question

我需要计算用户指定函数的一阶导数。程序从文件中读取函数作为字符串，然后需要计算一个变量的导数。函数有更多的变量，可以是线性的也可以是非线性的。最简单的方法是什么？

可以调用 MATLAB(也许)吗？

程序没有任何互联网访问权限。

Answer 1

您可以使用符号代数库，例如 javacalculus .

import java.util.Scanner;
import javacalculus.core.CALC;
import javacalculus.core.CalcParser;
import javacalculus.evaluator.CalcSUB;
import javacalculus.struct.CalcDouble;
import javacalculus.struct.CalcObject;
import javacalculus.struct.CalcSymbol;

public class Demo
{
    public static void main(String[] args) throws Exception
    {
        Scanner in = new Scanner(System.in);

        System.out.println("Enter expression:");
        String expression = in.nextLine();
        // javacalculus uses uppercase function names
        expression = expression.replace("sin", "SIN");
        expression = expression.replace("cos", "COS");

        System.out.println("Differentiate with respect to:");
        String variable = in.nextLine();

        // differentiate
        String command = "DIFF(" + expression + ", " + variable + ")";
        CalcParser parser = new CalcParser();
        CalcObject parsed = parser.parse(command);
        CalcObject result = parsed.evaluate();

        // compute numerical value
        result = subst(result, "a1", 0.0);
        result = subst(result, "a2", 10.0);
        result = CALC.SYM_EVAL(result);

        System.out.println("Result:");
        System.out.println(result);
    }

    static CalcObject subst(CalcObject input, String var, double number)
    {
        CalcSymbol symbol = new CalcSymbol(var);
        CalcDouble value = new CalcDouble(number);
        return CalcSUB.numericSubstitute(input, symbol, value);
    }
}

示例输入和输出:

Enter expression:
sin(a1) * 4 * a2 + (a1 + 1)^2
Differentiate with respect to:
a1
Result:
42