SweepCWLH.java

package jaea.optimization.sampling;

/**
 * Function to create Latin-hyper cube sampling with objective to maximize the
 * sparseness between samples (i.e. defined as MIN distance)
 * 
 * @author Le Minh Nghia, NTU-Singapore
 * 
 */
public class SweepCWLH {
	SimpleLH sLHGen = new SimpleLH();

	/**
	 * Main function
	 * 
	 * @param N
	 *            Number of samples
	 * @param dim
	 *            Number of dimensions
	 * @return Matrix of sampling: each row is the indices of discretized
	 *         'hypersquare'
	 */
	public int[][] getSweepCWLH(int N, int dim) {
		int[] distInfo = new int[3];
		// First generate initial matrix
		int[][] LH = sLHGen.getSimpleLH(N, dim);
		int i, j;
		// Create square matrix
		int[][] SQR = new int[N][N];
		for (i = 1; i <= N; i++)
			for (j = i; j <= N; j++) {
				if (i != j) {
					int x = (i - j) * (i - j);
					SQR[i - 1][j - 1] = x;
					SQR[j - 1][i - 1] = x;
				} else
					SQR[i - 1][i - 1] = 0;
			}
		// Get min distance
		distInfo = calMinDist(LH, SQR);
		System.out.println("Initial min dist: " + distInfo[2]);
		// Then maximize the MIN-Distance
		// Sweep column-wise
		for (i = 0; i < dim; i++) {
			int bestR1 = 0, bestR2 = 0;
			int r1, r2;
			int temp;
			int[] distInfoTmp = new int[3];
			boolean improved = false;
			// Sweep through each row (r1,r2)
			for (r1 = 0; r1 < N - 1; r1++)
				for (r2 = r1 + 1; r2 < N; r2++) {
					// Swap 2 elements at row r1, r2
					temp = LH[r1][i];
					LH[r1][i] = LH[r2][i];
					LH[r2][i] = temp;
					// Calculate new min distance
					distInfoTmp = calMinDist(LH, SQR);
					// Check if min is maximum, then store r1,r2
					if (distInfoTmp[2] > distInfo[2]) {
						bestR1 = r1;
						bestR2 = r2;
						improved = true;
					}
					// Swap back rows r1,r2
					temp = LH[r1][i];
					LH[r1][i] = LH[r2][i];
					LH[r2][i] = temp;
				}
			// Swap bestR1, bestR2
			if (improved) {
				temp = LH[bestR1][i];
				LH[bestR1][i] = LH[bestR2][i];
				LH[bestR2][i] = temp;
				distInfo = calMinDist(LH, SQR);
			}
		}
		System.out.println("Initial min dist: " + distInfo[2]);
		return LH;
	}

	/**
	 * 
	 * @param LH
	 * @param SQR
	 *            : squared array a(i,j) = (i-j)^2
	 * @return
	 */
	private int[] calMinDist(int[][] LH, int[][] SQR) {
		// res in order Point1 - Point 2 - Distance
		int[] res = new int[3];
		int N = LH.length;
		int i, j;
		int minDist = Integer.MAX_VALUE;
		int r1 = 0, r2 = 0;
		// Get minimum distance d(xi,xj)
		for (i = 0; i < N - 1; i++)
			for (j = i + 1; j < N; j++) {
				int a = calDistance(LH[i], LH[j], SQR);
				if (minDist > a) {
					minDist = a;
					r1 = i;
					r2 = j;
				}
			}
		// System.out.println(r1 + ", " + r2);
		res[0] = r1;
		res[1] = r2;
		res[2] = minDist;
		return res;
	}

	private int calDistance(int[] u, int[] v, int[][] SQR) {
		int res = 0;
		for (int i = 0; i < u.length; i++)
			res += SQR[u[i] - 1][v[i] - 1];
		return res;
	}

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int N = 10;
		int dim = 3;
		SweepCWLH LHGen = new SweepCWLH();
		int[][] aLH = LHGen.getSweepCWLH(N, dim);
		for (int r = 0; r < N; r++) {
			for (int c = 0; c < dim; c++)
				System.out.print(aLH[r][c] + " ");
			System.out.println();
		}
	}
}