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111 lines
2.9 KiB
111 lines
2.9 KiB
#pragma once
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#include <includes.hpp>
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#include "striding_iterator.hpp"
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#include "periodic_iterator.hpp"
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static double const evn_coef[] = {
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(1.0 + std::sqrt(3.0))/(std::sqrt(32.0)),
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(3.0 + std::sqrt(3.0))/(std::sqrt(32.0)),
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(3.0 - std::sqrt(3.0))/(std::sqrt(32.0)),
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(1.0 - std::sqrt(3.0))/(std::sqrt(32.0))
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};
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static double const odd_coef[] = {
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evn_coef[3],
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-evn_coef[2],
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evn_coef[1],
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-evn_coef[0]
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};
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// Apply the matrix Wn with the DAUB4 coefficients
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// Assumes input to be periodic
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template <typename Iterator>
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void wavelet_mul(Iterator begin, Iterator end){
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auto mul = end - begin;
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std::vector<double> out(mul, 0.0);
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for(int i = 0; i < mul; i += 2){
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out[i] = std::inner_product(evn_coef, evn_coef+4, periodic(begin, end) + i, 0.0);
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out[i+1] = std::inner_product(odd_coef, odd_coef+4, periodic(begin, end) + i, 0.0);
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}
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for(int i = 0; i < mul; ++i){
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*begin++ = out[i];
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}
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}
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template <typename Iterator>
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void wavelet_inv(Iterator begin, Iterator end){
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auto mul = end - begin;
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std::vector<double> out(mul, 0.0);
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Iterator bc = begin;
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for(int i = 0; i < mul; i += 2, begin += 2){
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Iterator b2 = begin + 1;
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for(int j = 0; j < 4; ++j){
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out[(i+j) % mul] += *begin * evn_coef[j] + *b2 * odd_coef[j];
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}
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}
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for(int i = 0; i < mul; ++i){
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*bc++ = out[i];
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}
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}
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// Shuffle works with an extra copy, might be inefficient, but it is at least correct ;)
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// It applies the even-odd-sort matrix Sn
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template <typename Iterator>
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void shuffle(Iterator begin, Iterator end){
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typedef typename std::iterator_traits<Iterator>::value_type value_type;
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auto s = end - begin;
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assert(s % 2 == 0);
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std::vector<value_type> v(s);
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std::copy(strided(begin , 2), strided(end , 2), v.begin());
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std::copy(strided(begin+1, 2), strided(end+1, 2), v.begin() + s/2);
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std::copy(v.begin(), v.end(), begin);
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}
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template <typename Iterator>
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void unshuffle(Iterator begin, Iterator end){
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typedef typename std::iterator_traits<Iterator>::value_type value_type;
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auto s = end - begin;
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assert(s % 2 == 0);
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std::vector<value_type> v(s);
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std::copy(begin, begin + s/2, strided(v.begin(), 2));
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std::copy(begin + s/2, end, strided(v.begin()+1, 2));
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std::copy(v.begin(), v.end(), begin);
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}
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// Combines the matrix Wn and Sn recusrively
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// Only works for inputs of size 2^m
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template <typename Iterator>
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void wavelet(Iterator begin, Iterator end){
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auto s = end - begin;
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assert(s >= 4);
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for(int i = s; i >= 4; i >>= 1){
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// half interval
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end = begin + i;
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assert(is_pow_of_two(end - begin));
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// multiply with Wn
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wavelet_mul(begin, end);
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// then with Sn
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shuffle(begin, end);
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}
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}
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template <typename Iterator>
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void unwavelet(Iterator begin, Iterator end){
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auto s = end - begin;
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assert(s >= 4);
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for(int i = 4; i <= s; i <<= 1){
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// double interval
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end = begin + i;
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assert(is_pow_of_two(end - begin));
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// unshuffle: Sn^-1
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unshuffle(begin, end);
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// then Wn^-1
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wavelet_inv(begin, end);
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}
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}
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