/*
 * 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 standard normalization convention.  The standard
     * DCT-I normalization convention is defined as follows
     * 

     * 
forward transform:
     * yn = (1/2) [x0 + (-1)nxN-1]
     * + ∑k=1N-2
     * xk cos[π nk / (N - 1)],
     * 
inverse transform:
     * xk = [1 / (N - 1)] [y0
     * + (-1)kyN-1]
     * + [2 / (N - 1)] ∑n=1N-2
     * yn cos[π nk / (N - 1)],
     * 
     * where N is the size of the data sample.
     */
    STANDARD_DCT_I,

    /**
     * Should be passed to the constructor of {@link FastCosineTransformer}
     * to use the orthogonal normalization convention. The orthogonal
     * DCT-I normalization convention is defined as follows
     * 

     * 
forward transform:
     * yn = [2(N - 1)]-1/2 [x0
     * + (-1)nxN-1]
     * + [2 / (N - 1)]1/2 ∑k=1N-2
     * xk cos[π nk / (N - 1)],
     * 
inverse transform:
     * xk = [2(N - 1)]-1/2 [y0
     * + (-1)kyN-1]
     * + [2 / (N - 1)]1/2 ∑n=1N-2
     * yn cos[π nk / (N - 1)],
     * 
     * which makes the transform orthogonal. N is the size of the data sample.
     */
    ORTHOGONAL_DCT_I;
}