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 * 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
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 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
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 * See the License for the specific language governing permissions and
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package org.apache.commons.math3.complex;

import java.io.Serializable;

import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.MathIllegalStateException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.ZeroException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.FastMath;

A helper class for the computation and caching of the n-th roots of unity. 
Since:
3.0/**
 * A helper class for the computation and caching of the {@code n}-th roots of
 * unity.
 *
 * @since 3.0
 */
public class RootsOfUnity implements Serializable {

    
Serializable version id. /** Serializable version id. */
    private static final long serialVersionUID = 20120201L;

    
Number of roots of unity. /** Number of roots of unity. */
    private int omegaCount;

    
Real part of the roots. /** Real part of the roots. */
    private double[] omegaReal;

    
Imaginary part of the n-th roots of unity, for positive values of n. In this array, the roots are stored in counter-clockwise order. /**
     * Imaginary part of the {@code n}-th roots of unity, for positive values
     * of {@code n}. In this array, the roots are stored in counter-clockwise
     * order.
     */
    private double[] omegaImaginaryCounterClockwise;

    
Imaginary part of the n-th roots of unity, for negative values of n. In this array, the roots are stored in clockwise order. /**
     * Imaginary part of the {@code n}-th roots of unity, for negative values
     * of {@code n}. In this array, the roots are stored in clockwise order.
     */
    private double[] omegaImaginaryClockwise;

    
true if computeRoots(int) was called with a positive value of its argument n. In this case, counter-clockwise ordering of the roots of unity should be used. /**
     * {@code true} if {@link #computeRoots(int)} was called with a positive
     * value of its argument {@code n}. In this case, counter-clockwise ordering
     * of the roots of unity should be used.
     */
    private boolean isCounterClockWise;

    
Build an engine for computing the n-th roots of unity. /**
     * Build an engine for computing the {@code n}-th roots of unity.
     */
    public RootsOfUnity() {

        omegaCount = 0;
        omegaReal = null;
        omegaImaginaryCounterClockwise = null;
        omegaImaginaryClockwise = null;
        isCounterClockWise = true;
    }

    
Returns true if computeRoots(int) was called with a positive value of its argument n. If true, then counter-clockwise ordering of the roots of unity should be used. 
Throws:
MathIllegalStateException – if no roots of unity have been computed
yet
Returns:
true if the roots of unity are stored in counter-clockwise order/**
     * Returns {@code true} if {@link #computeRoots(int)} was called with a
     * positive value of its argument {@code n}. If {@code true}, then
     * counter-clockwise ordering of the roots of unity should be used.
     *
     * @return {@code true} if the roots of unity are stored in
     * counter-clockwise order
     * @throws MathIllegalStateException if no roots of unity have been computed
     * yet
     */
    public synchronized boolean isCounterClockWise()
            throws MathIllegalStateException {

        if (omegaCount == 0) {
            throw new MathIllegalStateException(
                    LocalizedFormats.ROOTS_OF_UNITY_NOT_COMPUTED_YET);
        }
        return isCounterClockWise;
    }

    
 Computes the n-th roots of unity. The roots are stored in omega[], such that omega[k] = w ^ k, where k = 0, ..., n - 1, w = exp(2 * pi * i / n) and i = sqrt(-1). 
 Note that n can be positive of negative 

abs(n) is always the number of roots of unity.
If n > 0, then the roots are stored in counter-clockwise order.
If n < 0, then the roots are stored in clockwise order.


Params:
n – the (signed) number of roots of unity to be computed
Throws:
ZeroException – if n = 0/**
     * <p>
     * Computes the {@code n}-th roots of unity. The roots are stored in
     * {@code omega[]}, such that {@code omega[k] = w ^ k}, where
     * {@code k = 0, ..., n - 1}, {@code w = exp(2 * pi * i / n)} and
     * {@code i = sqrt(-1)}.
     * </p>
     * <p>
     * Note that {@code n} can be positive of negative
     * </p>
     * <ul>
     * <li>{@code abs(n)} is always the number of roots of unity.</li>
     * <li>If {@code n > 0}, then the roots are stored in counter-clockwise order.</li>
     * <li>If {@code n < 0}, then the roots are stored in clockwise order.</p>
     * </ul>
     *
     * @param n the (signed) number of roots of unity to be computed
     * @throws ZeroException if {@code n = 0}
     */
    public synchronized void computeRoots(int n) throws ZeroException {

        if (n == 0) {
            throw new ZeroException(
                    LocalizedFormats.CANNOT_COMPUTE_0TH_ROOT_OF_UNITY);
        }

        isCounterClockWise = n > 0;

        // avoid repetitive calculations
        final int absN = FastMath.abs(n);

        if (absN == omegaCount) {
            return;
        }

        // calculate everything from scratch
        final double t = 2.0 * FastMath.PI / absN;
        final double cosT = FastMath.cos(t);
        final double sinT = FastMath.sin(t);
        omegaReal = new double[absN];
        omegaImaginaryCounterClockwise = new double[absN];
        omegaImaginaryClockwise = new double[absN];
        omegaReal[0] = 1.0;
        omegaImaginaryCounterClockwise[0] = 0.0;
        omegaImaginaryClockwise[0] = 0.0;
        for (int i = 1; i < absN; i++) {
            omegaReal[i] = omegaReal[i - 1] * cosT -
                    omegaImaginaryCounterClockwise[i - 1] * sinT;
            omegaImaginaryCounterClockwise[i] = omegaReal[i - 1] * sinT +
                    omegaImaginaryCounterClockwise[i - 1] * cosT;
            omegaImaginaryClockwise[i] = -omegaImaginaryCounterClockwise[i];
        }
        omegaCount = absN;
    }

    
Get the real part of the k-th n-th root of unity. 
Params:
k – index of the n-th root of unity
Throws:
MathIllegalStateException – if no roots of unity have been
computed yet
MathIllegalArgumentException – if k is out of range
Returns:
real part of the k-th n-th root of unity/**
     * Get the real part of the {@code k}-th {@code n}-th root of unity.
     *
     * @param k index of the {@code n}-th root of unity
     * @return real part of the {@code k}-th {@code n}-th root of unity
     * @throws MathIllegalStateException if no roots of unity have been
     * computed yet
     * @throws MathIllegalArgumentException if {@code k} is out of range
     */
    public synchronized double getReal(int k)
            throws MathIllegalStateException, MathIllegalArgumentException {

        if (omegaCount == 0) {
            throw new MathIllegalStateException(
                    LocalizedFormats.ROOTS_OF_UNITY_NOT_COMPUTED_YET);
        }
        if ((k < 0) || (k >= omegaCount)) {
            throw new OutOfRangeException(
                    LocalizedFormats.OUT_OF_RANGE_ROOT_OF_UNITY_INDEX,
                    Integer.valueOf(k),
                    Integer.valueOf(0),
                    Integer.valueOf(omegaCount - 1));
        }

        return omegaReal[k];
    }

    
Get the imaginary part of the k-th n-th root of unity. 
Params:
k – index of the n-th root of unity
Throws:
MathIllegalStateException – if no roots of unity have been
computed yet
OutOfRangeException – if k is out of range
Returns:
imaginary part of the k-th n-th root of unity/**
     * Get the imaginary part of the {@code k}-th {@code n}-th root of unity.
     *
     * @param k index of the {@code n}-th root of unity
     * @return imaginary part of the {@code k}-th {@code n}-th root of unity
     * @throws MathIllegalStateException if no roots of unity have been
     * computed yet
     * @throws OutOfRangeException if {@code k} is out of range
     */
    public synchronized double getImaginary(int k)
            throws MathIllegalStateException, OutOfRangeException {

        if (omegaCount == 0) {
            throw new MathIllegalStateException(
                    LocalizedFormats.ROOTS_OF_UNITY_NOT_COMPUTED_YET);
        }
        if ((k < 0) || (k >= omegaCount)) {
            throw new OutOfRangeException(
                    LocalizedFormats.OUT_OF_RANGE_ROOT_OF_UNITY_INDEX,
                    Integer.valueOf(k),
                    Integer.valueOf(0),
                    Integer.valueOf(omegaCount - 1));
        }

        return isCounterClockWise ? omegaImaginaryCounterClockwise[k] :
            omegaImaginaryClockwise[k];
    }

    
Returns the number of roots of unity currently stored. If computeRoots(int) was called with n, then this method returns abs(n). If no roots of unity have been computed yet, this method returns 0. 
Returns:
the number of roots of unity currently stored/**
     * Returns the number of roots of unity currently stored. If
     * {@link #computeRoots(int)} was called with {@code n}, then this method
     * returns {@code abs(n)}. If no roots of unity have been computed yet, this
     * method returns 0.
     *
     * @return the number of roots of unity currently stored
     */
    public synchronized int getNumberOfRoots() {
        return omegaCount;
    }
}