Performs Gauss-Jordan reduction on a matrix using field arithmetic. - Java java.lang

Java examples for java.lang:Math Algorithm

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Description

Performs Gauss-Jordan reduction on a matrix using field arithmetic.

Demo Code



public class Main{
    /**//www.j  a  v a  2s  .  co  m
     * Performs Gauss-Jordan reduction on a matrix using field arithmetic.
     */
    public static void rowReduce(int[][] matrix, Field field) {
        int width = matrix[0].length;
        int height = matrix.length;
        if (width != height + 1) {
            throw new IllegalArgumentException(
                    "Matrix is not in the proper form.");
        }

        // Elimination step
        for (int column = 0; column < height; column++) {
            //Ensure that the element of this column in the diagonal is nonzero
            if (matrix[column][column] == 0) {
                for (int row = column + 1; row < height; row++) {
                    if (matrix[row][column] != 0) {
                        rowSwap(matrix, column, row);
                        break;
                    }
                }
            }

            int diagElement = matrix[column][column];
            if (diagElement != 0) {
                rowScale(matrix, column, field.reciprocal(diagElement),
                        field);

                for (int row = column + 1; row < height; row++) {
                    rowAddMultiple(matrix, row, column,
                            field.negate(matrix[row][column]), field);
                }
            }
        }

        // Back-substitution step
        for (int column = height - 1; column > 0; column--) {
            for (int row = 0; row < column; row++) {
                rowAddMultiple(matrix, row, column,
                        field.negate(matrix[row][column]), field);
            }
        }
    }
    /**
     * Swaps rows <code>ra</code> and <code>rb</code>.
     */
    public static void rowSwap(int[][] matrix, int ra, int rb) {
        int[] temp = matrix[ra];
        matrix[ra] = matrix[rb];
        matrix[rb] = temp;
    }
    /**
     * Multiplies every element in row <code>r</code> by a scalar <code>s</code>.
     */
    public static void rowScale(int[][] matrix, int r, int s, Field field) {
        int width = matrix[0].length;
        for (int column = 0; column < width; column++) {
            matrix[r][column] = field.mul(matrix[r][column], s);
        }
    }
    /**
     * Adds <code>s</code> times row <code>rs</code> to row <code>rd</code>.
     */
    public static void rowAddMultiple(int[][] matrix, int rd, int rs,
            int s, Field field) {
        int width = matrix[0].length;
        for (int column = 0; column < width; column++) {
            matrix[rd][column] = field.add(matrix[rd][column],
                    field.mul(matrix[rs][column], s));
        }
    }
}

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