private static void gaussian(float a[][],
	                             int index[]) {
		int n = index.length;
		float c[] = new float[n];
		// Initialize the index
		for (int i = 0; i < n; ++i) {
			index[i] = i;
		}
		// Find the rescaling factors, one from each row
		for (int i = 0; i < n; ++i){
			float c1 = 0;
			for (int j = 0; j < n; ++j){
				float c0 = Math.abs(a[i][j]);
				if (c0 > c1) {
					c1 = c0;
				}
			}
			c[i] = c1;
		}
		// Search the pivoting element from each column
		int k = 0;
		for (int j = 0; j < n - 1; ++j){
			float pi1 = 0;
			for (int i = j; i < n; ++i){
				float pi0 = Math.abs(a[index[i]][j]);
				pi0 /= c[index[i]];
				if (pi0 > pi1) {

					pi1 = pi0;
					k = i;
				}
			}
			// Interchange rows according to the pivoting order
			int itmp = index[j];
			index[j] = index[k];
			index[k] = itmp;
			for (int i = j + 1; i < n; ++i){
				float pj = a[index[i]][j] / a[index[j]][j];
				// Record pivoting ratios below the diagonal
				a[index[i]][j] = pj;

				// Modify other elements accordingly
				for (int l = j + 1; l < n; ++l){
					a[index[i]][l] -= pj * a[index[j]][l];
				}
			}
		}
	}