如何使用 Java 中的 Apache Commons Math 库找到矩阵的逆矩阵？

Question

I'm trying to find the inverse of a matrix using the Apache Commons Math Library.

Below is my attempt at doing just that:

BigReal[][] leftMatrixData = new BigReal[][] {
    { new BigReal(1), new BigReal(0), new BigReal(0), new BigReal(0) },
    { new BigReal(1), new BigReal(0), new BigReal(1), new BigReal(0) },
    { new BigReal(1), new BigReal(1), new BigReal(0), new BigReal(0) },
    { new BigReal(1), new BigReal(1), new BigReal(1), new BigReal(1) },
};

FieldMatrix<BigReal> leftMatrix = MatrixUtils.createFieldMatrix(leftMatrixData);
FieldMatrix<BigReal> leftMatrixInverse = new FieldLUDecomposition<>(leftMatrix)
    .getSolver()
    .getInverse();

When I run this, I get the following error:

org.apache.commons.math3.exception.MathArithmeticException: zero not allowed here

    at org.apache.commons.math3.util.BigReal.divide(BigReal.java:255)
    at org.apache.commons.math3.util.BigReal.divide(BigReal.java:39)
    at org.apache.commons.math3.linear.FieldLUDecomposition.<init>(FieldLUDecomposition.java:160)

When I go to line 160 of FieldLUDecomposition.java per the above error message, I see that the library thinks this matrix is Singular ie it thinks it has no inverse:

public T getDeterminant() {
    if (this.singular) { <---- this is line 160
        return (FieldElement)this.field.getZero();
    } else {
        int m = this.pivot.length;
        T determinant = this.even ? (FieldElement)this.field.getOne() : (FieldElement)((FieldElement)this.field.getZero()).subtract(this.field.getOne());

However, doing a quick check on WolframAlpha shows that this matrix has a non-zero determinant and indeed has an inverse:

So the question is - what am I doing wrong and how do I find the inverse of my matrix? Am I using the wrong solver?

Answer 1

Below is based on apache common math 3.6.1

A ticket is raised concerning this issue, I submitted a patch to fix the problem and the fix version will be 4.0 (not yet released as of 2021-07-19)

The reason of issue is equals method in BigReal

    @Override
    public boolean equals(Object other) {
        if (this == other){
            return true;
        }

        if (other instanceof BigReal){
            return d.equals(((BigReal) other).d);
        }
        return false;
    }

where d is BigDecimal , the backing value of BigReal . This cause equals comparison return undesired result when two BigReal has d with same value but different scale , and cause error when initializing FieldLUDecomposition . For BigDecimal we should check

    return d.compareTo((BigReal) other) == 0;

instead.

Solution:

1. Check if workaround section (Copy BigReal as local class and change equals ) helps.
2. Wait for version 4.0 release.
3. If double value matrix is acceptable, Use RealMatrix instead, and MatrixUtils provide handy inverse method

import org.apache.commons.math3.linear.MatrixUtils;
import org.apache.commons.math3.linear.RealMatrix;

public class CalculateInverse {
    public static void main(String[] args) {
        double[][] matrixData = new double[][]{
                {1, 0, 0, 0},
                {1, 0, 1, 0},
                {1, 1, 0, 0},
                {1, 1, 1, 1}
        };
        RealMatrix matrix = MatrixUtils.createRealMatrix(matrixData);
        RealMatrix inverse = MatrixUtils.inverse(matrix);
        System.out.println(inverse);
    }
}