[MATH-1617] FieldLUDecomposition with BigReal throw divide by zero error

• Type: Bug
• Status: Resolved
• Priority: Major
• Resolution: Fixed
• Affects Version/s: 3.6.1
• Fix Version/s: 4.0
• Assignee: Unassigned
• Reporter: Ng Tsz Sum
• Created: 18/Jul/21 11:49
• Updated: 30/Jul/21 02:10
• Resolved: 18/Jul/21 16:41

Description

From https://stackoverflow.com/questions/68427448/how-to-find-the-inverse-of-a-matrix-using-apache-commons-math-library-in-java/68427869?noredirect=1#comment120932354_68427869

Reproducible example

import org.apache.commons.math3.linear.FieldLUDecomposition;
import org.apache.commons.math3.linear.FieldMatrix;
import org.apache.commons.math3.linear.MatrixUtils;
import org.apache.commons.math3.util.BigReal;

public class REPREX {
    public static void main(String[] args) {
        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();
//  Exception in thread "main" 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)
//	  at stackoverflow.math.matrix.REPREX.main(REPREX.java:18)
    }
}

Possible reason:

In FieldLUDecomposition line 130-133

                if (lu[nonZero][col].equals(field.getZero())) {
                    // try to select a better permutation choice
                    ++nonZero;
                }

Which produce incorrect result when lu[nonZeror][col] the BigDecimal val has different scale
to field.getZero() scale. as the BigReal#equals is comparing using BigDecimal#equals

Workaround

I tried to copy class BigReal and BigRealField to FixBigReal and FixBigRealField and replace all BigReal to FixBigReal inside. Then override FixBIgReal#equals and {{FixBIgReal#hashcode }}as

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

        if (other instanceof FixBigReal) {
            return d.compareTo(((FixBigReal) other).d) == 0;
        }
        return false;
    }
...
    @Override
    public int hashCode() {
        return Double.hashCode(d.doubleValue());
    }

Then the below program will not throw error

import org.apache.commons.math3.linear.FieldLUDecomposition;
import org.apache.commons.math3.linear.FieldMatrix;
import org.apache.commons.math3.linear.MatrixUtils;
import org.apache.commons.math3.util.BigReal;

public class MVE {
    public static void main(String[] args) {
        FixBigReal[][] leftMatrixData = new FixBigReal[][]{
                {new FixBigReal(1), new FixBigReal(0), new FixBigReal(0), new FixBigReal(0)},
                {new FixBigReal(1), new FixBigReal(0), new FixBigReal(1), new FixBigReal(0)},
                {new FixBigReal(1), new FixBigReal(1), new FixBigReal(0), new FixBigReal(0)},
                {new FixBigReal(1), new FixBigReal(1), new FixBigReal(1), new FixBigReal(1)},
        };

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