transforms.h
Go to the documentation of this file.
#ifndef TRANSFORMS_H
#define TRANSFORMS_H
#include <itpp/base/vec.h>
#include <itpp/base/mat.h>
#include <itpp/base/matfunc.h>
#include <itpp/itexports.h>
namespace itpp
{
ITPP_EXPORT bool have_fourier_transforms();
ITPP_EXPORT void fft(const cvec &in, cvec &out);
ITPP_EXPORT cvec fft(const cvec &in);
ITPP_EXPORT cvec fft(const cvec &in, const int N);
ITPP_EXPORT void ifft(const cvec &in, cvec &out);
ITPP_EXPORT cvec ifft(const cvec &in);
ITPP_EXPORT cvec ifft(const cvec &in, const int N);
ITPP_EXPORT void fft_real(const vec& in, cvec &out);
ITPP_EXPORT cvec fft_real(const vec& in);
ITPP_EXPORT cvec fft_real(const vec &in, const int N);
ITPP_EXPORT void ifft_real(const cvec &in, vec &out);
ITPP_EXPORT vec ifft_real(const cvec &in);
ITPP_EXPORT vec ifft_real(const cvec &in, const int N);
ITPP_EXPORT bool have_cosine_transforms();
ITPP_EXPORT void dct(const vec &in, vec &out);
ITPP_EXPORT vec dct(const vec &in);
ITPP_EXPORT vec dct(const vec &in, const int N);
ITPP_EXPORT void idct(const vec &in, vec &out);
ITPP_EXPORT vec idct(const vec &in);
ITPP_EXPORT vec idct(const vec &in, const int N);
template <class T> Vec<T> dht(const Vec<T> &v);
template <class T> void dht(const Vec<T> &vin, Vec<T> &vout);
template <class T> void self_dht(Vec<T> &v);
template <class T> Vec<T> dwht(const Vec<T> &v);
template <class T> void dwht(const Vec<T> &vin, Vec<T> &vout);
template <class T> void self_dwht(Vec<T> &v);
template <class T> Mat<T> dht2(const Mat<T> &m);
template <class T> Mat<T> dwht2(const Mat<T> &m);
template <class T>
Vec<T> dht(const Vec<T> &v)
{
Vec<T> ret(v.size());
dht(v, ret);
return ret;
}
template <class T>
void bitrv(Vec<T> &out)
{
int N = out.size();
int j = 0;
int N1 = N - 1;
for(int i = 0; i < N1; ++i) {
if(i < j) {
T temp = out[j];
out[j] = out[i];
out[i] = temp;
}
int K = N / 2;
while(K <= j) {
j -= K;
K /= 2;
}
j += K;
}
}
template <class T>
void dht(const Vec<T> &vin, Vec<T> &vout)
{
int N = vin.size();
int m = levels2bits(N);
it_assert_debug((1 << m) == N, "dht(): The vector size must be a power of two");
vout.set_size(N);
// This step is separated because it copies vin to vout
for(int ib = 0; ib < N; ib += 2) {
vout(ib) = vin(ib) + vin(ib + 1);
vout(ib + 1) = vin(ib) - vin(ib + 1);
}
N /= 2;
int l = 2;
for(int i = 1; i < m; ++i) {
N /= 2;
int ib = 0;
for(int k = 0; k < N; ++k) {
for(int j = 0; j < l; ++j) {
T t = vout(ib + j);
vout(ib + j) += vout(ib + j + l);
vout(ib + j + l) = t - vout(ib + j + l);
}
ib += 2 * l;
}
l *= 2;
}
vout /= static_cast<T>(std::sqrt(static_cast<double>(vin.size())));
}
template <class T>
void self_dht(Vec<T> &v)
{
int N = v.size();
int m = levels2bits(N);
it_assert_debug((1 << m) == N, "self_dht(): The vector size must be a power "
"of two");
int l = 1;
for(int i = 0; i < m; ++i) {
N /= 2;
int ib = 0;
for(int k = 0; k < N; ++k) {
for(int j = 0; j < l; ++j) {
T t = v(ib + j);
v(ib + j) += v(ib + j + l);
v(ib + j + l) = t - v(ib + j + l);
}
ib += 2 * l;
}
l *= 2;
}
v /= static_cast<T>(std::sqrt(static_cast<double>(v.size())));
}
template <class T>
Vec<T> dwht(const Vec<T> &v)
{
Vec<T> ret(v.size());
dwht(v, ret);
return ret;
}
template <class T>
void dwht(const Vec<T> &vin, Vec<T> &vout)
{
dht(vin, vout);
bitrv(vout);
}
template <class T>
void self_dwht(Vec<T> &v)
{
self_dht(v);
bitrv(v);
}
template <class T>
Mat<T> dht2(const Mat<T> &m)
{
Mat<T> ret(m.rows(), m.cols());
Vec<T> v;
for(int i = 0; i < m.rows(); ++i) {
v = m.get_row(i);
self_dht(v);
ret.set_row(i, v);
}
for(int i = 0; i < m.cols(); ++i) {
v = ret.get_col(i);
self_dht(v);
ret.set_col(i, v);
}
return transpose(ret);
}
template <class T>
Mat<T> dwht2(const Mat<T> &m)
{
Mat<T> ret(m.rows(), m.cols());
Vec<T> v;
for(int i = 0; i < m.rows(); ++i) {
v = m.get_row(i);
self_dwht(v);
ret.set_row(i, v);
}
for(int i = 0; i < m.cols(); ++i) {
v = ret.get_col(i);
self_dwht(v);
ret.set_col(i, v);
}
return transpose(ret);
}
// ----------------------------------------------------------------------
// Instantiations
// ----------------------------------------------------------------------
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT vec dht(const vec &v);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT cvec dht(const cvec &v);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT void dht(const vec &vin, vec &vout);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT void dht(const cvec &vin, cvec &vout);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT void self_dht(vec &v);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT void self_dht(cvec &v);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT vec dwht(const vec &v);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT cvec dwht(const cvec &v);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT void dwht(const vec &vin, vec &vout);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT void dwht(const cvec &vin, cvec &vout);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT void self_dwht(vec &v);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT void self_dwht(cvec &v);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT mat dht2(const mat &m);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT cmat dht2(const cmat &m);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT mat dwht2(const mat &m);
ITPP_EXPORT_TEMPLATE template ITPP_EXPORT cmat dwht2(const cmat &m);
} // namespace itpp
#endif // #ifndef TRANSFORMS_H
matfunc.h
Various functions on vectors and matrices - header file.
itpp::Mat::cols
int cols() const
The number of columns.
Definition: mat.h:235
itpp::Mat::rows
int rows() const
The number of rows.
Definition: mat.h:237
itpp::Mat< T >
itpp::idct
ITPP_EXPORT void idct(const vec &in, vec &out)
Inverse Discrete Cosine Transform (IDCT)
itpp::ifft
ITPP_EXPORT void ifft(const cvec &in, cvec &out)
Inverse Fast Fourier Transform.
itpp::fft_real
ITPP_EXPORT void fft_real(const vec &in, cvec &out)
Real Fast Fourier Transform.
itpp::have_cosine_transforms
ITPP_EXPORT bool have_cosine_transforms()
Run-time test if library is built with cosine transforms enabled.
itpp::Vec::set_size
void set_size(int size, bool copy=false)
Set length of vector. if copy = true then keeping the old values.
Definition: vec.h:663
itpp::fft
ITPP_EXPORT void fft(const cvec &in, cvec &out)
Fast Fourier Transform.
itpp::ifft_real
ITPP_EXPORT void ifft_real(const cvec &in, vec &out)
Inverse Real Fast Fourier Transform.
it_assert_debug
#define it_assert_debug(t, s)
Abort if t is not true and NDEBUG is not defined.
Definition: itassert.h:107
itpp::self_dwht
void self_dwht(Vec< T > &v)
Fast Walsh Hadamard Transform - memory efficient (result in v)
Definition: transforms.h:349
itpp::Mat::get_row
Vec< Num_T > get_row(int r) const
Get row r.
Definition: mat.h:852
itpp::bitrv
void bitrv(Vec< T > &out)
Bit reverse.
Definition: transforms.h:252
itpp::dht2
Mat< T > dht2(const Mat< T > &m)
Fast 2D Hadamard Transform.
Definition: transforms.h:356
itpp::have_fourier_transforms
ITPP_EXPORT bool have_fourier_transforms()
Run-time test if library is built with Fast Fourier Transforms enabled.
mat.h
Matrix Class Definitions.
itpp::dwht
Vec< T > dwht(const Vec< T > &v)
Fast Walsh Hadamard Transform.
Definition: transforms.h:333
itpp
itpp namespace
Definition: itmex.h:36
itpp::Vec::size
int size() const
The size of the vector.
Definition: vec.h:271
itpp::self_dht
void self_dht(Vec< T > &v)
Fast Hadamard Transform - memory efficient. Stores the result in v.
Definition: transforms.h:307
itpp::transpose
void transpose(const Mat< T > &m, Mat< T > &out)
Transposition of the matrix m returning the transposed matrix in out.
Definition: matfunc.h:308
itpp::sqrt
vec sqrt(const vec &x)
Square root of the elements.
Definition: elem_math.h:123
itpp::Vec< T >
itpp::dwht2
Mat< T > dwht2(const Mat< T > &m)
Fast 2D Walsh Hadamard Transform.
Definition: transforms.h:376
itpp::dct
ITPP_EXPORT void dct(const vec &in, vec &out)
Discrete Cosine Transform (DCT)
itpp::Mat::get_col
Vec< Num_T > get_col(int c) const
Get column c.
Definition: mat.h:889
itpp::levels2bits
int levels2bits(int n)
Calculate the number of bits needed to represent n different values (levels).
Definition: log_exp.h:92
vec.h
Templated Vector Class Definitions.
itpp::dht
Vec< T > dht(const Vec< T > &v)
Fast Hadamard Transform.
Definition: transforms.h:243

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