打印出来：没有解决方案，在Java中使用Apache的多个解决方案

Question

我有这个代码可以解决4x4线性方程。  当线性方程没有解或者有多个解时，我怎么能打印出来。而不是打印错误？

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();

    }
}

当我在这段代码中写下这样的矩阵：

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

此代码打印：

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)

因为上面的矩阵有多个解决方案，或者没有解决方案

Answer 1

您可以要求决定因素https://en.wikipedia.org/wiki/Determinant

“当且仅当其行列式为非零时，线性方程组才有一个独特的非平凡解。如果该行列式为零，那么系统要么没有非平凡解，要么无数个解。” / p>

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)));
}