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/*******************************************************************************
 * Copyright (c) 2010 Haifeng Li
 *   
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *  
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *******************************************************************************/

/**
 * Distance and metric measures. A distance function maps pairs of
 * points into the nonnegative reals and has to satisfy
 * 
 *  non-negativity: d(x, y) ≥ 0
 * 
 isolation: d(x, y) = 0 if and only if x = y
 * 
 symmetry: d(x, y) = d(x, y)
 * .
 * Note that a distance function is not required to satisfy triangular
 * inequality |x - y| + |y - z| ≥ |x - z|, which is necessary for a metric.
 * 
 * @author Haifeng Li
 */
package smile.math.distance;