/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You 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.
 */
package org.apache.commons.math3.transform;

/**
 * This enumeration defines the various types of normalizations that can be applied to discrete
 * cosine transforms (DCT). The exact definition of these normalizations is detailed below.
 *
 * @see FastCosineTransformer
 * @since 3.0
 */
public enum DctNormalization {
    /**
     * Should be passed to the constructor of {@link FastCosineTransformer} to use the
     * <em>standard</em> normalization convention. The standard DCT-I normalization convention is
     * defined as follows
     *
     * <ul>
     *   <li>forward transform: y<sub>n</sub> = (1/2) [x<sub>0</sub> +
     *       (-1)<sup>n</sup>x<sub>N-1</sub>] + &sum;<sub>k=1</sub><sup>N-2</sup> x<sub>k</sub>
     *       cos[&pi; nk / (N - 1)],
     *   <li>inverse transform: x<sub>k</sub> = [1 / (N - 1)] [y<sub>0</sub> +
     *       (-1)<sup>k</sup>y<sub>N-1</sub>] + [2 / (N - 1)] &sum;<sub>n=1</sub><sup>N-2</sup>
     *       y<sub>n</sub> cos[&pi; nk / (N - 1)],
     * </ul>
     *
     * where N is the size of the data sample.
     */
    STANDARD_DCT_I,

    /**
     * Should be passed to the constructor of {@link FastCosineTransformer} to use the
     * <em>orthogonal</em> normalization convention. The orthogonal DCT-I normalization convention
     * is defined as follows
     *
     * <ul>
     *   <li>forward transform: y<sub>n</sub> = [2(N - 1)]<sup>-1/2</sup> [x<sub>0</sub> +
     *       (-1)<sup>n</sup>x<sub>N-1</sub>] + [2 / (N - 1)]<sup>1/2</sup>
     *       &sum;<sub>k=1</sub><sup>N-2</sup> x<sub>k</sub> cos[&pi; nk / (N - 1)],
     *   <li>inverse transform: x<sub>k</sub> = [2(N - 1)]<sup>-1/2</sup> [y<sub>0</sub> +
     *       (-1)<sup>k</sup>y<sub>N-1</sub>] + [2 / (N - 1)]<sup>1/2</sup>
     *       &sum;<sub>n=1</sub><sup>N-2</sup> y<sub>n</sub> cos[&pi; nk / (N - 1)],
     * </ul>
     *
     * which makes the transform orthogonal. N is the size of the data sample.
     */
    ORTHOGONAL_DCT_I;
}