mirror of
https://github.com/apache/commons-math.git
synced 2025-02-13 13:35:56 +00:00
Moved private class o.a.c.m.transform.FastFourierTransformer.RootsOfUnity to o.a.c.m.complex.RootsOfUnity (MATH-677).
git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1237544 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Sebastien Brisard
parent
271bbc9eb6
commit
74813500be
196
src/main/java/org/apache/commons/math/complex/RootsOfUnity.java
Normal file
196
src/main/java/org/apache/commons/math/complex/RootsOfUnity.java
Normal file
@ -0,0 +1,196 @@
|
|||||||
|
/*
|
||||||
|
* 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.math.complex;
|
||||||
|
|
||||||
|
import java.io.Serializable;
|
||||||
|
|
||||||
|
import org.apache.commons.math.exception.MathIllegalArgumentException;
|
||||||
|
import org.apache.commons.math.exception.MathIllegalStateException;
|
||||||
|
import org.apache.commons.math.exception.OutOfRangeException;
|
||||||
|
import org.apache.commons.math.exception.ZeroException;
|
||||||
|
import org.apache.commons.math.exception.util.LocalizedFormats;
|
||||||
|
import org.apache.commons.math.util.FastMath;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* A helper class for the computation and caching of the {@code n}<sup>th</sup>
|
||||||
|
* roots of unity.
|
||||||
|
*
|
||||||
|
* @version $Id$
|
||||||
|
* @since 3.0
|
||||||
|
*/
|
||||||
|
public class RootsOfUnity implements Serializable {
|
||||||
|
|
||||||
|
/** Serializable version id. */
|
||||||
|
private static final long serialVersionUID = 6404784357747329667L;
|
||||||
|
|
||||||
|
/** Number of roots of unity. */
|
||||||
|
private int omegaCount;
|
||||||
|
|
||||||
|
/** Real part of the roots. */
|
||||||
|
private double[] omegaReal;
|
||||||
|
|
||||||
|
/** Imaginary part of the roots for forward transform. */
|
||||||
|
private double[] omegaImaginaryForward;
|
||||||
|
|
||||||
|
/** Imaginary part of the roots for reverse transform. */
|
||||||
|
private double[] omegaImaginaryInverse;
|
||||||
|
|
||||||
|
/** Forward/reverse indicator. */
|
||||||
|
private boolean isForward;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Build an engine for computing the {@code n}<sup>th</sup> roots of
|
||||||
|
* unity.
|
||||||
|
*/
|
||||||
|
public RootsOfUnity() {
|
||||||
|
|
||||||
|
omegaCount = 0;
|
||||||
|
omegaReal = null;
|
||||||
|
omegaImaginaryForward = null;
|
||||||
|
omegaImaginaryInverse = null;
|
||||||
|
isForward = true;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Check if computation has been done for forward or reverse transform.
|
||||||
|
*
|
||||||
|
* @return {@code true} if computation has been done for forward transform
|
||||||
|
* @throws MathIllegalStateException if no roots of unity have been computed
|
||||||
|
* yet
|
||||||
|
*/
|
||||||
|
public synchronized boolean isForward()
|
||||||
|
throws MathIllegalStateException {
|
||||||
|
|
||||||
|
if (omegaCount == 0) {
|
||||||
|
throw new MathIllegalStateException(
|
||||||
|
LocalizedFormats.ROOTS_OF_UNITY_NOT_COMPUTED_YET);
|
||||||
|
}
|
||||||
|
return isForward;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* <p>
|
||||||
|
* Computes the {@code n}<sup>th</sup> 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 π i / n)} and
|
||||||
|
* {@code i = sqrt(-1)}.
|
||||||
|
* </p>
|
||||||
|
* <p>
|
||||||
|
* Note that {@code n} is positive for forward transform and negative
|
||||||
|
* for inverse transform.
|
||||||
|
* </p>
|
||||||
|
*
|
||||||
|
* @param n number of roots of unity to compute, positive for forward
|
||||||
|
* transform, negative for inverse transform
|
||||||
|
* @throws ZeroException if {@code n = 0}
|
||||||
|
*/
|
||||||
|
public synchronized void computeOmega(int n) throws ZeroException {
|
||||||
|
|
||||||
|
if (n == 0) {
|
||||||
|
throw new ZeroException(
|
||||||
|
LocalizedFormats.CANNOT_COMPUTE_0TH_ROOT_OF_UNITY);
|
||||||
|
}
|
||||||
|
|
||||||
|
isForward = n > 0;
|
||||||
|
|
||||||
|
// avoid repetitive calculations
|
||||||
|
final int absN = FastMath.abs(n);
|
||||||
|
|
||||||
|
if (absN == omegaCount) {
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
// calculate everything from scratch, for both forward and inverse
|
||||||
|
// versions
|
||||||
|
final double t = 2.0 * FastMath.PI / absN;
|
||||||
|
final double cosT = FastMath.cos(t);
|
||||||
|
final double sinT = FastMath.sin(t);
|
||||||
|
omegaReal = new double[absN];
|
||||||
|
omegaImaginaryForward = new double[absN];
|
||||||
|
omegaImaginaryInverse = new double[absN];
|
||||||
|
omegaReal[0] = 1.0;
|
||||||
|
omegaImaginaryForward[0] = 0.0;
|
||||||
|
omegaImaginaryInverse[0] = 0.0;
|
||||||
|
for (int i = 1; i < absN; i++) {
|
||||||
|
omegaReal[i] = omegaReal[i - 1] * cosT +
|
||||||
|
omegaImaginaryForward[i - 1] * sinT;
|
||||||
|
omegaImaginaryForward[i] = omegaImaginaryForward[i - 1] * cosT -
|
||||||
|
omegaReal[i - 1] * sinT;
|
||||||
|
omegaImaginaryInverse[i] = -omegaImaginaryForward[i];
|
||||||
|
}
|
||||||
|
omegaCount = absN;
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Get the real part of the {@code k}<sup>th</sup>
|
||||||
|
* {@code n}<sup>th</sup> root of unity.
|
||||||
|
*
|
||||||
|
* @param k index of the {@code n}<sup>th</sup> root of unity
|
||||||
|
* @return real part of the {@code k}<sup>th</sup>
|
||||||
|
* {@code n}<sup>th</sup> 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 getOmegaReal(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 {@code k}<sup>th</sup>
|
||||||
|
* {@code n}<sup>th</sup> root of unity.
|
||||||
|
*
|
||||||
|
* @param k index of the {@code n}<sup>th</sup> root of unity
|
||||||
|
* @return imaginary part of the {@code k}<sup>th</sup>
|
||||||
|
* {@code n}<sup>th</sup> 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 getOmegaImaginary(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 isForward ? omegaImaginaryForward[k] :
|
||||||
|
omegaImaginaryInverse[k];
|
||||||
|
}
|
||||||
|
}
|
||||||
@ -22,11 +22,9 @@ import java.lang.reflect.Array;
|
|||||||
import org.apache.commons.math.analysis.FunctionUtils;
|
import org.apache.commons.math.analysis.FunctionUtils;
|
||||||
import org.apache.commons.math.analysis.UnivariateFunction;
|
import org.apache.commons.math.analysis.UnivariateFunction;
|
||||||
import org.apache.commons.math.complex.Complex;
|
import org.apache.commons.math.complex.Complex;
|
||||||
|
import org.apache.commons.math.complex.RootsOfUnity;
|
||||||
import org.apache.commons.math.exception.DimensionMismatchException;
|
import org.apache.commons.math.exception.DimensionMismatchException;
|
||||||
import org.apache.commons.math.exception.MathIllegalArgumentException;
|
import org.apache.commons.math.exception.MathIllegalArgumentException;
|
||||||
import org.apache.commons.math.exception.MathIllegalStateException;
|
|
||||||
import org.apache.commons.math.exception.OutOfRangeException;
|
|
||||||
import org.apache.commons.math.exception.ZeroException;
|
|
||||||
import org.apache.commons.math.exception.util.LocalizedFormats;
|
import org.apache.commons.math.exception.util.LocalizedFormats;
|
||||||
import org.apache.commons.math.util.ArithmeticUtils;
|
import org.apache.commons.math.util.ArithmeticUtils;
|
||||||
import org.apache.commons.math.util.FastMath;
|
import org.apache.commons.math.util.FastMath;
|
||||||
@ -638,172 +636,4 @@ public class FastFourierTransformer implements Serializable {
|
|||||||
}
|
}
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Computes the {@code n}<sup>th</sup> roots of unity. A cache of already
|
|
||||||
* computed values is maintained.
|
|
||||||
*/
|
|
||||||
private static class RootsOfUnity implements Serializable {
|
|
||||||
|
|
||||||
/** Serializable version id. */
|
|
||||||
private static final long serialVersionUID = 6404784357747329667L;
|
|
||||||
|
|
||||||
/** Number of roots of unity. */
|
|
||||||
private int omegaCount;
|
|
||||||
|
|
||||||
/** Real part of the roots. */
|
|
||||||
private double[] omegaReal;
|
|
||||||
|
|
||||||
/** Imaginary part of the roots for forward transform. */
|
|
||||||
private double[] omegaImaginaryForward;
|
|
||||||
|
|
||||||
/** Imaginary part of the roots for reverse transform. */
|
|
||||||
private double[] omegaImaginaryInverse;
|
|
||||||
|
|
||||||
/** Forward/reverse indicator. */
|
|
||||||
private boolean isForward;
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Build an engine for computing the {@code n}<sup>th</sup> roots of
|
|
||||||
* unity.
|
|
||||||
*/
|
|
||||||
public RootsOfUnity() {
|
|
||||||
|
|
||||||
omegaCount = 0;
|
|
||||||
omegaReal = null;
|
|
||||||
omegaImaginaryForward = null;
|
|
||||||
omegaImaginaryInverse = null;
|
|
||||||
isForward = true;
|
|
||||||
}
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Check if computation has been done for forward or reverse transform.
|
|
||||||
*
|
|
||||||
* @return {@code true} if computation has been done for forward transform
|
|
||||||
* @throws MathIllegalStateException if no roots of unity have been computed
|
|
||||||
* yet
|
|
||||||
*/
|
|
||||||
public synchronized boolean isForward()
|
|
||||||
throws MathIllegalStateException {
|
|
||||||
|
|
||||||
if (omegaCount == 0) {
|
|
||||||
throw new MathIllegalStateException(
|
|
||||||
LocalizedFormats.ROOTS_OF_UNITY_NOT_COMPUTED_YET);
|
|
||||||
}
|
|
||||||
return isForward;
|
|
||||||
}
|
|
||||||
|
|
||||||
/**
|
|
||||||
* <p>
|
|
||||||
* Computes the {@code n}<sup>th</sup> 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 π i / n)} and
|
|
||||||
* {@code i = sqrt(-1)}.
|
|
||||||
* </p>
|
|
||||||
* <p>
|
|
||||||
* Note that {@code n} is positive for forward transform and negative
|
|
||||||
* for inverse transform.
|
|
||||||
* </p>
|
|
||||||
*
|
|
||||||
* @param n number of roots of unity to compute, positive for forward
|
|
||||||
* transform, negative for inverse transform
|
|
||||||
* @throws ZeroException if {@code n = 0}
|
|
||||||
*/
|
|
||||||
public synchronized void computeOmega(int n) throws ZeroException {
|
|
||||||
|
|
||||||
if (n == 0) {
|
|
||||||
throw new ZeroException(
|
|
||||||
LocalizedFormats.CANNOT_COMPUTE_0TH_ROOT_OF_UNITY);
|
|
||||||
}
|
|
||||||
|
|
||||||
isForward = n > 0;
|
|
||||||
|
|
||||||
// avoid repetitive calculations
|
|
||||||
final int absN = FastMath.abs(n);
|
|
||||||
|
|
||||||
if (absN == omegaCount) {
|
|
||||||
return;
|
|
||||||
}
|
|
||||||
|
|
||||||
// calculate everything from scratch, for both forward and inverse
|
|
||||||
// versions
|
|
||||||
final double t = 2.0 * FastMath.PI / absN;
|
|
||||||
final double cosT = FastMath.cos(t);
|
|
||||||
final double sinT = FastMath.sin(t);
|
|
||||||
omegaReal = new double[absN];
|
|
||||||
omegaImaginaryForward = new double[absN];
|
|
||||||
omegaImaginaryInverse = new double[absN];
|
|
||||||
omegaReal[0] = 1.0;
|
|
||||||
omegaImaginaryForward[0] = 0.0;
|
|
||||||
omegaImaginaryInverse[0] = 0.0;
|
|
||||||
for (int i = 1; i < absN; i++) {
|
|
||||||
omegaReal[i] = omegaReal[i - 1] * cosT +
|
|
||||||
omegaImaginaryForward[i - 1] * sinT;
|
|
||||||
omegaImaginaryForward[i] = omegaImaginaryForward[i - 1] * cosT -
|
|
||||||
omegaReal[i - 1] * sinT;
|
|
||||||
omegaImaginaryInverse[i] = -omegaImaginaryForward[i];
|
|
||||||
}
|
|
||||||
omegaCount = absN;
|
|
||||||
}
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Get the real part of the {@code k}<sup>th</sup>
|
|
||||||
* {@code n}<sup>th</sup> root of unity.
|
|
||||||
*
|
|
||||||
* @param k index of the {@code n}<sup>th</sup> root of unity
|
|
||||||
* @return real part of the {@code k}<sup>th</sup>
|
|
||||||
* {@code n}<sup>th</sup> 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 getOmegaReal(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 {@code k}<sup>th</sup>
|
|
||||||
* {@code n}<sup>th</sup> root of unity.
|
|
||||||
*
|
|
||||||
* @param k index of the {@code n}<sup>th</sup> root of unity
|
|
||||||
* @return imaginary part of the {@code k}<sup>th</sup>
|
|
||||||
* {@code n}<sup>th</sup> 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 getOmegaImaginary(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 isForward ? omegaImaginaryForward[k] :
|
|
||||||
omegaImaginaryInverse[k];
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
}
|
||||||
|
|||||||
Loading…
x
Reference in New Issue
Block a user