打印出來：沒有解決方案，在java中使用Apache的多種解決方案

Question

我有這段代碼可以解決 4x4 線性方程。 當線性方程沒有解或有多個解時，我如何打印出來。 而不是打印錯誤？

public class OvaWork 
{


    void fourthEquationSolver()
    {
        //Creating  Arrays Representing Equations
        double[][] lhsArray = {{8,1,10,1}, {2,1,5,4}, {1,5,3,2}, {9,8,4,6}};
        double[] rhsArray = {14,22,38,44};
        //Creating Matrix Objects with arrays
        Matrix lhs = new Matrix(lhsArray);
        Matrix rhs = new Matrix(rhsArray, 4);
        //Calculate Solved Matrix
        Matrix ans = lhs.solve(rhs);
        //Printing Answers
        System.out.println("x1 = " + (ans.get(0, 0)));
        System.out.println("x2 = " + (ans.get(1, 0)));
        System.out.println("X3 = " + (ans.get(2, 0)));
        System.out.println("X4 = " + (ans.get(3, 0)));
    }



    public static void main(String[] args) 
    {
        OvaWork equation = new OvaWork();

    }
}

當我寫入此代碼時，像這樣的矩陣：

1,1,1,1=14
2,2,2,2=22
3,3,3,3=38
4,4,4,4=44

此代碼打印：

Exception in thread "main" java.lang.RuntimeException: Matrix is singular.
    at Jama.LUDecomposition.solve(LUDecomposition.java:282)
    at Jama.Matrix.solve(Matrix.java:815)
    at OvaWork.fourthEquationSolver(OvaWork.java:20)
    at OvaWork.main(OvaWork.java:106)

因為上面的矩陣有或多個解，或沒有解

Answer 1

您可以要求行列式https://en.wikipedia.org/wiki/Determinant

“一個線性方程組有一個唯一的非平凡解，當且僅當它的行列式不為零。如果這個行列式為零，那么系統要么沒有非平凡解，要么有無限多個解。”

http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/system/system.html

if (lhs.det() == 0) {
    System.out.println("No solution or infinite number of solutions");
} else {
    Matrix ans = lhs.solve(rhs);
    //Printing Answers
    System.out.println("x1 = " + (ans.get(0, 0)));
    System.out.println("x2 = " + (ans.get(1, 0)));
    System.out.println("X3 = " + (ans.get(2, 0)));
    System.out.println("X4 = " + (ans.get(3, 0)));
}