    001    /*
    002     * Licensed to the Apache Software Foundation (ASF) under one or more
    003     * contributor license agreements.  See the NOTICE file distributed with
    004     * this work for additional information regarding copyright ownership.
    005     * The ASF licenses this file to You under the Apache License, Version 2.0
    006     * (the "License"); you may not use this file except in compliance with
    007     * the License.  You may obtain a copy of the License at
    008     *
    009     *      http://www.apache.org/licenses/LICENSE-2.0
    010     *
    011     * Unless required by applicable law or agreed to in writing, software
    012     * distributed under the License is distributed on an "AS IS" BASIS,
    013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    014     * See the License for the specific language governing permissions and
    015     * limitations under the License.
    016     */
    017    package org.apache.commons.math3.transform;
    018
    019    /**
    020     * This enumeration defines the various types of normalizations that can be
    021     * applied to discrete sine transforms (DST). The exact definition of these
    022     * normalizations is detailed below.
    023     *
    024     * @see FastSineTransformer
    025     * @version $Id: DstNormalization.java 1385310 2012-09-16 16:32:10Z tn $
    026     * @since 3.0
    027     */
    028    public enum DstNormalization {
    029        /**
    030         * Should be passed to the constructor of {@link FastSineTransformer} to
    031         * use the <em>standard</em> normalization convention. The standard DST-I
    032         * normalization convention is defined as follows
    033         * <ul>
    034         * <li>forward transform: y<sub>n</sub> = &sum;<sub>k=0</sub><sup>N-1</sup>
    035         * x<sub>k</sub> sin(&pi; nk / N),</li>
    036         * <li>inverse transform: x<sub>k</sub> = (2 / N)
    037         * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> sin(&pi; nk / N),</li>
    038         * </ul>
    039         * where N is the size of the data sample, and x<sub>0</sub> = 0.
    040         */
    041        STANDARD_DST_I,
    042
    043        /**
    044         * Should be passed to the constructor of {@link FastSineTransformer} to
    045         * use the <em>orthogonal</em> normalization convention. The orthogonal
    046         * DCT-I normalization convention is defined as follows
    047         * <ul>
    048         * <li>Forward transform: y<sub>n</sub> = &radic;(2 / N)
    049         * &sum;<sub>k=0</sub><sup>N-1</sup> x<sub>k</sub> sin(&pi; nk / N),</li>
    050         * <li>Inverse transform: x<sub>k</sub> = &radic;(2 / N)
    051         * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> sin(&pi; nk / N),</li>
    052         * </ul>
    053         * which makes the transform orthogonal. N is the size of the data sample,
    054         * and x<sub>0</sub> = 0.
    055         */
    056        ORTHOGONAL_DST_I
    057    }