universal.MMatrix.java Source code

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Here is the source code for universal.MMatrix.java

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/*
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package universal;

import java.util.*;
import java.lang.Math;
import org.apache.commons.math3.fraction.Fraction;
import org.apache.commons.math3.fraction.FractionConversionException;

/**
 *
 * @author Doreen
 */
class MMatrix {
    LinkedList<LinkedList<Fraction>> matrix;
    int numRows;
    int numCols;

    static class Coordinate {
        int row;
        int col;

        Coordinate(int r, int c) {
            row = r;
            col = c;
        }

        public String toString() {
            return "(" + row + ", " + col + ")";
        }
    }

    MMatrix(double[][] m) {
        numRows = m.length;
        numCols = m[0].length;
        matrix = new LinkedList<LinkedList<Fraction>>();

        for (int i = 0; i < numRows; i++) {
            matrix.add(new LinkedList<Fraction>());
            for (int j = 0; j < numCols; j++) {
                try {
                    matrix.get(i).add(new Fraction(m[i][j]));
                } catch (FractionConversionException e) {
                    System.err.println("Fraction could not be converted from double by apache commons . . .");
                }
            }
        }
    }

    public void Interchange(Coordinate a, Coordinate b) {
        LinkedList<Fraction> temp = matrix.get(a.row);
        matrix.set(a.row, matrix.get(b.row));
        matrix.set(b.row, temp);

        int t = a.row;
        a.row = b.row;
        b.row = t;
    }

    public void Scale(Coordinate x, Fraction d) {
        LinkedList<Fraction> row = matrix.get(x.row);
        for (int i = 0; i < numCols; i++) {
            row.set(i, row.get(i).multiply(d));
        }
    }

    public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
        LinkedList<Fraction> row = matrix.get(to.row);
        LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
        for (int i = 0; i < numCols; i++) {
            row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
        }
    }

    public void RREF() {
        Coordinate pivot = new Coordinate(0, 0);

        int submatrix = 0;
        for (int x = 0; x < numCols; x++) {
            pivot = new Coordinate(pivot.row, x);
            //Step 1
            //Begin with the leftmost nonzero column. This is a pivot column. The pivot position is at the top.
            for (int i = x; i < numCols; i++) {
                if (isColumnZeroes(pivot) == false) {
                    break;
                } else {
                    pivot.col = i;
                }
            }
            //Step 2
            //Select a nonzero entry in the pivot column with the highest absolute value as a pivot. 
            pivot = findPivot(pivot);

            if (getCoordinate(pivot).doubleValue() == 0.0) {
                pivot.row++;
                continue;
            }

            //If necessary, interchange rows to move this entry into the pivot position.
            //move this row to the top of the submatrix
            if (pivot.row != submatrix) {
                Interchange(new Coordinate(submatrix, pivot.col), pivot);
            }

            //Force pivot to be 1
            if (getCoordinate(pivot).doubleValue() != 1) {
                /*
                System.out.println(getCoordinate(pivot));
                System.out.println(pivot);
                System.out.println(matrix);
                */
                Fraction scalar = getCoordinate(pivot).reciprocal();
                Scale(pivot, scalar);
            }
            //Step 3
            //Use row replacement operations to create zeroes in all positions below the pivot.
            //belowPivot = belowPivot + (Pivot * -belowPivot)
            for (int i = pivot.row; i < numRows; i++) {
                if (i == pivot.row) {
                    continue;
                }
                Coordinate belowPivot = new Coordinate(i, pivot.col);
                Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
                MultiplyAndAdd(belowPivot, pivot, complement);
            }
            //Step 5
            //Beginning with the rightmost pivot and working upward and to the left, create zeroes above each pivot.
            //If a pivot is not 1, make it 1 by a scaling operation.
            //Use row replacement operations to create zeroes in all positions above the pivot
            for (int i = pivot.row; i >= 0; i--) {
                if (i == pivot.row) {
                    if (getCoordinate(pivot).doubleValue() != 1.0) {
                        Scale(pivot, getCoordinate(pivot).reciprocal());
                    }
                    continue;
                }
                if (i == pivot.row) {
                    continue;
                }

                Coordinate abovePivot = new Coordinate(i, pivot.col);
                Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
                MultiplyAndAdd(abovePivot, pivot, complement);
            }
            //Step 4
            //Ignore the row containing the pivot position and cover all rows, if any, above it.
            //Apply steps 1-3 to the remaining submatrix. Repeat until there are no more nonzero entries.
            if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row + 1, pivot.col))) {
                break;
            }

            submatrix++;
            pivot.row++;
        }
    }

    public boolean isColumnZeroes(Coordinate a) {
        for (int i = 0; i < numRows; i++) {
            if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
                return false;
            }
        }

        return true;
    }

    public boolean isRowZeroes(Coordinate a) {
        for (int i = 0; i < numCols; i++) {
            if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
                return false;
            }
        }

        return true;
    }

    public Coordinate findPivot(Coordinate a) {
        int first_row = a.row;
        Coordinate pivot = new Coordinate(a.row, a.col);
        Coordinate current = new Coordinate(a.row, a.col);

        for (int i = a.row; i < (numRows - first_row); i++) {
            current.row = i;
            if (getCoordinate(current).doubleValue() == 1.0) {
                Interchange(current, a);
            }
        }

        current.row = a.row;
        for (int i = current.row; i < (numRows - first_row); i++) {
            current.row = i;
            if (getCoordinate(current).doubleValue() != 0) {
                pivot.row = i;
                break;
            }
        }

        return pivot;
    }

    public Fraction getCoordinate(Coordinate a) {
        return matrix.get(a.row).get(a.col);
    }

    public String toString() {
        return matrix.toString().replace("], ", "]\n");
    }
}