FastSineTransformer.java
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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
*
* https://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.
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/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.transform;
import java.io.Serializable;
import org.hipparchus.analysis.FunctionUtils;
import org.hipparchus.analysis.UnivariateFunction;
import org.hipparchus.complex.Complex;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.util.ArithmeticUtils;
import org.hipparchus.util.FastMath;
/**
* Implements the Fast Sine Transform for transformation of one-dimensional real
* data sets. For reference, see James S. Walker, <em>Fast Fourier
* Transforms</em>, chapter 3 (ISBN 0849371635).
* <p>
* There are several variants of the discrete sine transform. The present
* implementation corresponds to DST-I, with various normalization conventions,
* which are specified by the parameter {@link DstNormalization}.
* <strong>It should be noted that regardless to the convention, the first
* element of the dataset to be transformed must be zero.</strong>
* <p>
* DST-I is equivalent to DFT of an <em>odd extension</em> of the data series.
* More precisely, if x<sub>0</sub>, …, x<sub>N-1</sub> is the data set
* to be sine transformed, the extended data set x<sub>0</sub><sup>#</sup>,
* …, x<sub>2N-1</sub><sup>#</sup> is defined as follows
* <ul>
* <li>x<sub>0</sub><sup>#</sup> = x<sub>0</sub> = 0,</li>
* <li>x<sub>k</sub><sup>#</sup> = x<sub>k</sub> if 1 ≤ k < N,</li>
* <li>x<sub>N</sub><sup>#</sup> = 0,</li>
* <li>x<sub>k</sub><sup>#</sup> = -x<sub>2N-k</sub> if N + 1 ≤ k <
* 2N.</li>
* </ul>
* <p>
* Then, the standard DST-I y<sub>0</sub>, …, y<sub>N-1</sub> of the real
* data set x<sub>0</sub>, …, x<sub>N-1</sub> is equal to <em>half</em>
* of i (the pure imaginary number) times the N first elements of the DFT of the
* extended data set x<sub>0</sub><sup>#</sup>, …,
* x<sub>2N-1</sub><sup>#</sup> <br>
* y<sub>n</sub> = (i / 2) ∑<sub>k=0</sub><sup>2N-1</sup>
* x<sub>k</sub><sup>#</sup> exp[-2πi nk / (2N)]
* k = 0, …, N-1.
* <p>
* The present implementation of the discrete sine transform as a fast sine
* transform requires the length of the data to be a power of two. Besides,
* it implicitly assumes that the sampled function is odd. In particular, the
* first element of the data set must be 0, which is enforced in
* {@link #transform(UnivariateFunction, double, double, int, TransformType)},
* after sampling.
*
*/
public class FastSineTransformer implements RealTransformer, Serializable {
/** Serializable version identifier. */
static final long serialVersionUID = 20120211L;
/** The type of DST to be performed. */
private final DstNormalization normalization;
/**
* Creates a new instance of this class, with various normalization conventions.
*
* @param normalization the type of normalization to be applied to the transformed data
*/
public FastSineTransformer(final DstNormalization normalization) {
this.normalization = normalization;
}
/**
* {@inheritDoc}
*
* The first element of the specified data set is required to be {@code 0}.
*
* @throws MathIllegalArgumentException if the length of the data array is
* not a power of two, or the first element of the data array is not zero
*/
@Override
public double[] transform(final double[] f, final TransformType type) {
if (normalization == DstNormalization.ORTHOGONAL_DST_I) {
final double s = FastMath.sqrt(2.0 / f.length);
return TransformUtils.scaleArray(fst(f), s);
}
if (type == TransformType.FORWARD) {
return fst(f);
}
final double s = 2.0 / f.length;
return TransformUtils.scaleArray(fst(f), s);
}
/**
* {@inheritDoc}
*
* This implementation enforces {@code f(x) = 0.0} at {@code x = 0.0}.
*
* @throws org.hipparchus.exception.MathIllegalArgumentException
* if the lower bound is greater than, or equal to the upper bound
* @throws org.hipparchus.exception.MathIllegalArgumentException
* if the number of sample points is negative
* @throws MathIllegalArgumentException if the number of sample points is not a power of two
*/
@Override
public double[] transform(final UnivariateFunction f,
final double min, final double max, final int n,
final TransformType type) {
final double[] data = FunctionUtils.sample(f, min, max, n);
data[0] = 0.0;
return transform(data, type);
}
/**
* Perform the FST algorithm (including inverse). The first element of the
* data set is required to be {@code 0}.
*
* @param f the real data array to be transformed
* @return the real transformed array
* @throws MathIllegalArgumentException if the length of the data array is
* not a power of two, or the first element of the data array is not zero
*/
protected double[] fst(double[] f) throws MathIllegalArgumentException {
final double[] transformed = new double[f.length];
if (!ArithmeticUtils.isPowerOfTwo(f.length)) {
throw new MathIllegalArgumentException(
LocalizedFFTFormats.NOT_POWER_OF_TWO_CONSIDER_PADDING,
Integer.valueOf(f.length));
}
if (f[0] != 0.0) {
throw new MathIllegalArgumentException(
LocalizedFFTFormats.FIRST_ELEMENT_NOT_ZERO,
Double.valueOf(f[0]));
}
final int n = f.length;
if (n == 1) { // trivial case
transformed[0] = 0.0;
return transformed;
}
// construct a new array and perform FFT on it
final double[] x = new double[n];
x[0] = 0.0;
x[n >> 1] = 2.0 * f[n >> 1];
for (int i = 1; i < (n >> 1); i++) {
final double a = FastMath.sin(i * FastMath.PI / n) * (f[i] + f[n - i]);
final double b = 0.5 * (f[i] - f[n - i]);
x[i] = a + b;
x[n - i] = a - b;
}
FastFourierTransformer transformer;
transformer = new FastFourierTransformer(DftNormalization.STANDARD);
Complex[] y = transformer.transform(x, TransformType.FORWARD);
// reconstruct the FST result for the original array
transformed[0] = 0.0;
transformed[1] = 0.5 * y[0].getReal();
for (int i = 1; i < (n >> 1); i++) {
transformed[2 * i] = -y[i].getImaginary();
transformed[2 * i + 1] = y[i].getReal() + transformed[2 * i - 1];
}
return transformed;
}
}