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Thomas Capricelli
2009-11-08 22:27:32 +01:00
parent 456f7d094d aa0974286f
commit 751a333491
65 changed files with 2753 additions and 476 deletions
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229
unsupported/Eigen/Complex Normal file
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#ifndef EIGEN_COMPLEX_H
#define EIGEN_COMPLEX_H
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
// Eigen::Complex reuses as much as possible from std::complex
// and allows easy conversion to and from, even at the pointer level.
#include <complex>
namespace Eigen {
template <typename _NativeData,typename _PunnedData>
struct castable_pointer
{
castable_pointer(_NativeData * ptr) : _ptr(ptr) { }
operator _NativeData * () {return _ptr;}
operator _PunnedData * () {return reinterpret_cast<_PunnedData*>(_ptr);}
operator const _NativeData * () const {return _ptr;}
operator const _PunnedData * () const {return reinterpret_cast<_PunnedData*>(_ptr);}
private:
_NativeData * _ptr;
};
template <typename _NativeData,typename _PunnedData>
struct const_castable_pointer
{
const_castable_pointer(_NativeData * ptr) : _ptr(ptr) { }
operator const _NativeData * () const {return _ptr;}
operator const _PunnedData * () const {return reinterpret_cast<_PunnedData*>(_ptr);}
private:
_NativeData * _ptr;
};
template <typename T>
struct Complex
{
typedef typename std::complex<T> StandardComplex;
typedef T value_type;
// constructors
Complex() {}
Complex(const T& re, const T& im = T()) : _re(re),_im(im) { }
Complex(const Complex&other ): _re(other.real()) ,_im(other.imag()) {}
template<class X>
Complex(const Complex<X>&other): _re(other.real()) ,_im(other.imag()) {}
template<class X>
Complex(const std::complex<X>&other): _re(other.real()) ,_im(other.imag()) {}
// allow binary access to the object as a std::complex
typedef castable_pointer< Complex<T>, StandardComplex > pointer_type;
typedef const_castable_pointer< Complex<T>, StandardComplex > const_pointer_type;
inline
pointer_type operator & () {return pointer_type(this);}
inline
const_pointer_type operator & () const {return const_pointer_type(this);}
inline
operator StandardComplex () const {return std_type();}
inline
operator StandardComplex & () {return std_type();}
inline
const StandardComplex & std_type() const {return *reinterpret_cast<const StandardComplex*>(this);}
inline
StandardComplex & std_type() {return *reinterpret_cast<StandardComplex*>(this);}
// every sort of accessor and mutator that has ever been in fashion.
// For a brief history, search for "std::complex over-encapsulated"
// http://www.open-std.org/jtc1/sc22/wg21/docs/lwg-defects.html#387
inline
const T & real() const {return _re;}
inline
const T & imag() const {return _im;}
inline
T & real() {return _re;}
inline
T & imag() {return _im;}
inline
T & real(const T & x) {return _re=x;}
inline
T & imag(const T & x) {return _im=x;}
inline
void set_real(const T & x) {_re = x;}
inline
void set_imag(const T & x) {_im = x;}
// *** complex member functions: ***
inline
Complex<T>& operator= (const T& val) { _re=val;_im=0;return *this; }
inline
Complex<T>& operator+= (const T& val) {_re+=val;return *this;}
inline
Complex<T>& operator-= (const T& val) {_re-=val;return *this;}
inline
Complex<T>& operator*= (const T& val) {_re*=val;_im*=val;return *this; }
inline
Complex<T>& operator/= (const T& val) {_re/=val;_im/=val;return *this; }
inline
Complex& operator= (const Complex& rhs) {_re=rhs._re;_im=rhs._im;return *this;}
inline
Complex& operator= (const StandardComplex& rhs) {_re=rhs.real();_im=rhs.imag();return *this;}
template<class X> Complex<T>& operator= (const Complex<X>& rhs) { _re=rhs._re;_im=rhs._im;return *this;}
template<class X> Complex<T>& operator+= (const Complex<X>& rhs) { _re+=rhs._re;_im+=rhs._im;return *this;}
template<class X> Complex<T>& operator-= (const Complex<X>& rhs) { _re-=rhs._re;_im-=rhs._im;return *this;}
template<class X> Complex<T>& operator*= (const Complex<X>& rhs) { this->std_type() *= rhs.std_type(); return *this; }
template<class X> Complex<T>& operator/= (const Complex<X>& rhs) { this->std_type() /= rhs.std_type(); return *this; }
private:
T _re;
T _im;
};
//template <typename T> T ei_to_std( const T & x) {return x;}
template <typename T>
std::complex<T> ei_to_std( const Complex<T> & x) {return x.std_type();}
// 26.2.6 operators
template<class T> Complex<T> operator+(const Complex<T>& rhs) {return rhs;}
template<class T> Complex<T> operator-(const Complex<T>& rhs) {return -ei_to_std(rhs);}
template<class T> Complex<T> operator+(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) + ei_to_std(rhs);}
template<class T> Complex<T> operator-(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) - ei_to_std(rhs);}
template<class T> Complex<T> operator*(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) * ei_to_std(rhs);}
template<class T> Complex<T> operator/(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) / ei_to_std(rhs);}
template<class T> bool operator==(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) == ei_to_std(rhs);}
template<class T> bool operator!=(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) != ei_to_std(rhs);}
template<class T> Complex<T> operator+(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) + ei_to_std(rhs); }
template<class T> Complex<T> operator-(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) - ei_to_std(rhs); }
template<class T> Complex<T> operator*(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) * ei_to_std(rhs); }
template<class T> Complex<T> operator/(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) / ei_to_std(rhs); }
template<class T> bool operator==(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) == ei_to_std(rhs); }
template<class T> bool operator!=(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) != ei_to_std(rhs); }
template<class T> Complex<T> operator+(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) + ei_to_std(rhs); }
template<class T> Complex<T> operator-(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) - ei_to_std(rhs); }
template<class T> Complex<T> operator*(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) * ei_to_std(rhs); }
template<class T> Complex<T> operator/(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) / ei_to_std(rhs); }
template<class T> bool operator==(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) == ei_to_std(rhs); }
template<class T> bool operator!=(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) != ei_to_std(rhs); }
template<class T, class charT, class traits>
std::basic_istream<charT,traits>&
operator>> (std::basic_istream<charT,traits>& istr, Complex<T>& rhs)
{
return istr >> rhs.std_type();
}
template<class T, class charT, class traits>
std::basic_ostream<charT,traits>&
operator<< (std::basic_ostream<charT,traits>& ostr, const Complex<T>& rhs)
{
return ostr << rhs.std_type();
}
// 26.2.7 values:
template<class T> T real(const Complex<T>&x) {return real(ei_to_std(x));}
template<class T> T abs(const Complex<T>&x) {return abs(ei_to_std(x));}
template<class T> T arg(const Complex<T>&x) {return arg(ei_to_std(x));}
template<class T> T norm(const Complex<T>&x) {return norm(ei_to_std(x));}
template<class T> Complex<T> conj(const Complex<T>&x) { return conj(ei_to_std(x));}
template<class T> Complex<T> polar(const T& x, const T&y) {return polar(ei_to_std(x),ei_to_std(y));}
// 26.2.8 transcendentals:
template<class T> Complex<T> cos (const Complex<T>&x){return cos(ei_to_std(x));}
template<class T> Complex<T> cosh (const Complex<T>&x){return cosh(ei_to_std(x));}
template<class T> Complex<T> exp (const Complex<T>&x){return exp(ei_to_std(x));}
template<class T> Complex<T> log (const Complex<T>&x){return log(ei_to_std(x));}
template<class T> Complex<T> log10 (const Complex<T>&x){return log10(ei_to_std(x));}
template<class T> Complex<T> pow(const Complex<T>&x, int p) {return pow(ei_to_std(x),p);}
template<class T> Complex<T> pow(const Complex<T>&x, const T&p) {return pow(ei_to_std(x),ei_to_std(p));}
template<class T> Complex<T> pow(const Complex<T>&x, const Complex<T>&p) {return pow(ei_to_std(x),ei_to_std(p));}
template<class T> Complex<T> pow(const T&x, const Complex<T>&p) {return pow(ei_to_std(x),ei_to_std(p));}
template<class T> Complex<T> sin (const Complex<T>&x){return sin(ei_to_std(x));}
template<class T> Complex<T> sinh (const Complex<T>&x){return sinh(ei_to_std(x));}
template<class T> Complex<T> sqrt (const Complex<T>&x){return sqrt(ei_to_std(x));}
template<class T> Complex<T> tan (const Complex<T>&x){return tan(ei_to_std(x));}
template<class T> Complex<T> tanh (const Complex<T>&x){return tanh(ei_to_std(x));}
template<typename _Real> struct NumTraits<Complex<_Real> >
{
typedef _Real Real;
typedef Complex<_Real> FloatingPoint;
enum {
IsComplex = 1,
HasFloatingPoint = NumTraits<Real>::HasFloatingPoint,
ReadCost = 2,
AddCost = 2 * NumTraits<Real>::AddCost,
MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
};
};
}
#endif
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

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unsupported/Eigen/FFT Normal file
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@@ -0,0 +1,208 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_FFT_H
#define EIGEN_FFT_H
#include <complex>
#include <vector>
#include <map>
#include <Eigen/Core>
#ifdef EIGEN_FFTW_DEFAULT
// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size
# include <fftw3.h>
namespace Eigen {
# include "src/FFT/ei_fftw_impl.h"
//template <typename T> typedef struct ei_fftw_impl default_fft_impl; this does not work
template <typename T> struct default_fft_impl : public ei_fftw_impl<T> {};
}
#elif defined EIGEN_MKL_DEFAULT
// TODO
// intel Math Kernel Library: fastest, commercial -- may be incompatible with Eigen in GPL form
namespace Eigen {
# include "src/FFT/ei_imklfft_impl.h"
template <typename T> struct default_fft_impl : public ei_imklfft_impl {};
}
#else
// ei_kissfft_impl: small, free, reasonably efficient default, derived from kissfft
//
namespace Eigen {
# include "src/FFT/ei_kissfft_impl.h"
template <typename T>
struct default_fft_impl : public ei_kissfft_impl<T> {};
}
#endif
namespace Eigen {
template <typename _Scalar,
typename _Impl=default_fft_impl<_Scalar> >
class FFT
{
public:
typedef _Impl impl_type;
typedef typename impl_type::Scalar Scalar;
typedef typename impl_type::Complex Complex;
enum Flag {
Default=0, // goof proof
Unscaled=1,
HalfSpectrum=2,
// SomeOtherSpeedOptimization=4
Speedy=32767
};
FFT( const impl_type & impl=impl_type() , Flag flags=Default ) :m_impl(impl),m_flag(flags) { }
inline
bool HasFlag(Flag f) const { return (m_flag & (int)f) == f;}
inline
void SetFlag(Flag f) { m_flag |= (int)f;}
inline
void ClearFlag(Flag f) { m_flag &= (~(int)f);}
inline
void fwd( Complex * dst, const Scalar * src, int nfft)
{
m_impl.fwd(dst,src,nfft);
if ( HasFlag(HalfSpectrum) == false)
ReflectSpectrum(dst,nfft);
}
inline
void fwd( Complex * dst, const Complex * src, int nfft)
{
m_impl.fwd(dst,src,nfft);
}
template <typename _Input>
inline
void fwd( std::vector<Complex> & dst, const std::vector<_Input> & src)
{
if ( NumTraits<_Input>::IsComplex == 0 && HasFlag(HalfSpectrum) )
dst.resize( (src.size()>>1)+1);
else
dst.resize(src.size());
fwd(&dst[0],&src[0],src.size());
}
template<typename InputDerived, typename ComplexDerived>
inline
void fwd( MatrixBase<ComplexDerived> & dst, const MatrixBase<InputDerived> & src)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(InputDerived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,InputDerived) // size at compile-time
EIGEN_STATIC_ASSERT((ei_is_same_type<typename ComplexDerived::Scalar, Complex>::ret),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
EIGEN_STATIC_ASSERT(int(InputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
if ( NumTraits< typename InputDerived::Scalar >::IsComplex == 0 && HasFlag(HalfSpectrum) )
dst.derived().resize( (src.size()>>1)+1);
else
dst.derived().resize(src.size());
fwd( &dst[0],&src[0],src.size() );
}
inline
void inv( Complex * dst, const Complex * src, int nfft)
{
m_impl.inv( dst,src,nfft );
if ( HasFlag( Unscaled ) == false)
scale(dst,1./nfft,nfft);
}
inline
void inv( Scalar * dst, const Complex * src, int nfft)
{
m_impl.inv( dst,src,nfft );
if ( HasFlag( Unscaled ) == false)
scale(dst,1./nfft,nfft);
}
template<typename OutputDerived, typename ComplexDerived>
inline
void inv( MatrixBase<OutputDerived> & dst, const MatrixBase<ComplexDerived> & src)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(OutputDerived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,OutputDerived) // size at compile-time
EIGEN_STATIC_ASSERT((ei_is_same_type<typename ComplexDerived::Scalar, Complex>::ret),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
EIGEN_STATIC_ASSERT(int(OutputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
int nfft = src.size();
int nout = HasFlag(HalfSpectrum) ? ((nfft>>1)+1) : nfft;
dst.derived().resize( nout );
inv( &dst[0],&src[0],src.size() );
}
template <typename _Output>
inline
void inv( std::vector<_Output> & dst, const std::vector<Complex> & src)
{
if ( NumTraits<_Output>::IsComplex == 0 && HasFlag(HalfSpectrum) )
dst.resize( 2*(src.size()-1) );
else
dst.resize( src.size() );
inv( &dst[0],&src[0],dst.size() );
}
// TODO: multi-dimensional FFTs
// TODO: handle Eigen MatrixBase
// ---> i added fwd and inv specializations above + unit test, is this enough? (bjacob)
inline
impl_type & impl() {return m_impl;}
private:
template <typename _It,typename _Val>
inline
void scale(_It x,_Val s,int nx)
{
for (int k=0;k<nx;++k)
*x++ *= s;
}
inline
void ReflectSpectrum(Complex * freq,int nfft)
{
// create the implicit right-half spectrum (conjugate-mirror of the left-half)
int nhbins=(nfft>>1)+1;
for (int k=nhbins;k < nfft; ++k )
freq[k] = conj(freq[nfft-k]);
}
impl_type m_impl;
int m_flag;
};
}
#endif
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

25
unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h
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@@ -46,13 +46,16 @@ public:
InputsAtCompileTime = Functor::InputsAtCompileTime,
ValuesAtCompileTime = Functor::ValuesAtCompileTime
};
typedef typename Functor::InputType InputType;
typedef typename Functor::ValueType ValueType;
typedef typename Functor::JacobianType JacobianType;
typedef typename JacobianType::Scalar Scalar;
typedef Matrix<Scalar,InputsAtCompileTime,1> DerivativeType;
typedef AutoDiffScalar<DerivativeType> ActiveScalar;
typedef AutoDiffScalar<Matrix<double,InputsAtCompileTime,1> > ActiveScalar;
typedef Matrix<ActiveScalar, InputsAtCompileTime, 1> ActiveInput;
typedef Matrix<ActiveScalar, ValuesAtCompileTime, 1> ActiveValue;
@@ -69,26 +72,20 @@ public:
ActiveInput ax = x.template cast<ActiveScalar>();
ActiveValue av(jac.rows());
if(InputsAtCompileTime==Dynamic)
{
for (int j=0; j<jac.cols(); j++)
ax[j].derivatives().resize(this->inputs());
for (int j=0; j<jac.rows(); j++)
av[j].derivatives().resize(this->inputs());
}
for (int j=0; j<jac.cols(); j++)
for (int i=0; i<jac.cols(); i++)
ax[i].derivatives().coeffRef(j) = i==j ? 1 : 0;
for (int i=0; i<jac.cols(); i++)
ax[i].derivatives() = DerivativeType::Unit(this->inputs(),i);
Functor::operator()(ax, &av);
for (int i=0; i<jac.rows(); i++)
{
(*v)[i] = av[i].value();
for (int j=0; j<jac.cols(); j++)
jac.coeffRef(i,j) = av[i].derivatives().coeff(j);
jac.row(i) = av[i].derivatives();
}
}
protected:

225
unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
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@@ -27,15 +27,35 @@
namespace Eigen {
template<typename A, typename B>
struct ei_make_coherent_impl {
static void run(A& a, B& b) {}
};
// resize a to match b is a.size()==0, and conversely.
template<typename A, typename B>
void ei_make_coherent(const A& a, const B&b)
{
ei_make_coherent_impl<A,B>::run(a.const_cast_derived(), b.const_cast_derived());
}
/** \class AutoDiffScalar
* \brief A scalar type replacement with automatic differentation capability
*
* \param DerType the vector type used to store/represent the derivatives (e.g. Vector3f)
* \param _DerType the vector type used to store/represent the derivatives. The base scalar type
* as well as the number of derivatives to compute are determined from this type.
* Typical choices include, e.g., \c Vector4f for 4 derivatives, or \c VectorXf
* if the number of derivatives is not known at compile time, and/or, the number
* of derivatives is large.
* Note that _DerType can also be a reference (e.g., \c VectorXf&) to wrap a
* existing vector into an AutoDiffScalar.
* Finally, _DerType can also be any Eigen compatible expression.
*
* This class represents a scalar value while tracking its respective derivatives.
* This class represents a scalar value while tracking its respective derivatives using Eigen's expression
* template mechanism.
*
* It supports the following list of global math function:
* - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
* - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
* - ei_abs, ei_sqrt, ei_pow, ei_exp, ei_log, ei_sin, ei_cos,
* - ei_conj, ei_real, ei_imag, ei_abs2.
*
@@ -44,34 +64,35 @@ namespace Eigen {
* while derivatives are computed right away.
*
*/
template<typename DerType>
template<typename _DerType>
class AutoDiffScalar
{
public:
typedef typename ei_cleantype<_DerType>::type DerType;
typedef typename ei_traits<DerType>::Scalar Scalar;
inline AutoDiffScalar() {}
inline AutoDiffScalar(const Scalar& value)
: m_value(value)
{
if(m_derivatives.size()>0)
m_derivatives.setZero();
}
inline AutoDiffScalar(const Scalar& value, const DerType& der)
: m_value(value), m_derivatives(der)
{}
template<typename OtherDerType>
inline AutoDiffScalar(const AutoDiffScalar<OtherDerType>& other)
: m_value(other.value()), m_derivatives(other.derivatives())
{}
inline AutoDiffScalar(const AutoDiffScalar& other)
: m_value(other.value()), m_derivatives(other.derivatives())
{}
template<typename OtherDerType>
inline AutoDiffScalar& operator=(const AutoDiffScalar<OtherDerType>& other)
{
@@ -79,32 +100,49 @@ class AutoDiffScalar
m_derivatives = other.derivatives();
return *this;
}
inline AutoDiffScalar& operator=(const AutoDiffScalar& other)
{
m_value = other.value();
m_derivatives = other.derivatives();
return *this;
}
// inline operator const Scalar& () const { return m_value; }
// inline operator Scalar& () { return m_value; }
inline const Scalar& value() const { return m_value; }
inline Scalar& value() { return m_value; }
inline const DerType& derivatives() const { return m_derivatives; }
inline DerType& derivatives() { return m_derivatives; }
inline const AutoDiffScalar<DerType&> operator+(const Scalar& other) const
{
return AutoDiffScalar<DerType>(m_value + other, m_derivatives);
}
friend inline const AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b)
{
return AutoDiffScalar<DerType>(a + b.value(), b.derivatives());
}
inline AutoDiffScalar& operator+=(const Scalar& other)
{
value() += other;
return *this;
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >
inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,typename ei_cleantype<OtherDerType>::type>::Type >
operator+(const AutoDiffScalar<OtherDerType>& other) const
{
return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >(
ei_make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,typename ei_cleantype<OtherDerType>::type>::Type >(
m_value + other.value(),
m_derivatives + other.derivatives());
}
template<typename OtherDerType>
inline AutoDiffScalar&
operator+=(const AutoDiffScalar<OtherDerType>& other)
@@ -112,16 +150,17 @@ class AutoDiffScalar
(*this) = (*this) + other;
return *this;
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >
inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,typename ei_cleantype<OtherDerType>::type>::Type >
operator-(const AutoDiffScalar<OtherDerType>& other) const
{
return AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >(
ei_make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,typename ei_cleantype<OtherDerType>::type>::Type >(
m_value - other.value(),
m_derivatives - other.derivatives());
}
template<typename OtherDerType>
inline AutoDiffScalar&
operator-=(const AutoDiffScalar<OtherDerType>& other)
@@ -129,104 +168,151 @@ class AutoDiffScalar
*this = *this - other;
return *this;
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType>::Type >
operator-() const
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType>::Type >(
-m_value,
-m_derivatives);
}
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
operator*(const Scalar& other) const
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
m_value * other,
(m_derivatives * other));
}
friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
friend inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
operator*(const Scalar& other, const AutoDiffScalar& a)
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
a.value() * other,
a.derivatives() * other);
}
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
operator/(const Scalar& other) const
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
m_value / other,
(m_derivatives * (Scalar(1)/other)));
}
friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
friend inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
operator/(const Scalar& other, const AutoDiffScalar& a)
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
other / a.value(),
a.derivatives() * (-Scalar(1)/other));
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >::Type >::Type >
operator/(const AutoDiffScalar<OtherDerType>& other) const
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >(
ei_make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >::Type >::Type >(
m_value / other.value(),
((m_derivatives * other.value()).nestByValue() - (m_value * other.derivatives()).nestByValue()).nestByValue()
* (Scalar(1)/(other.value()*other.value())));
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >
inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >
operator*(const AutoDiffScalar<OtherDerType>& other) const
{
return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >(
ei_make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >(
m_value * other.value(),
(m_derivatives * other.value()).nestByValue() + (m_value * other.derivatives()).nestByValue());
}
inline AutoDiffScalar& operator*=(const Scalar& other)
{
*this = *this * other;
return *this;
}
template<typename OtherDerType>
inline AutoDiffScalar& operator*=(const AutoDiffScalar<OtherDerType>& other)
{
*this = *this * other;
return *this;
}
protected:
Scalar m_value;
DerType m_derivatives;
};
template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename B>
struct ei_make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, B> {
typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
static void run(A& a, B& b) {
if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
{
a.resize(b.size());
a.setZero();
}
}
};
template<typename A, typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>
struct ei_make_coherent_impl<A, Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
static void run(A& a, B& b) {
if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
{
b.resize(a.size());
b.setZero();
}
}
};
template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols,
typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>
struct ei_make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,
Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
static void run(A& a, B& b) {
if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
{
a.resize(b.size());
a.setZero();
}
else if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
{
b.resize(a.size());
b.setZero();
}
}
};
}
#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
template<typename DerType> \
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> > \
FUNC(const AutoDiffScalar<DerType>& x) { \
inline const Eigen::AutoDiffScalar<typename Eigen::MakeCwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType>::Type > \
FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
using namespace Eigen; \
typedef typename ei_traits<DerType>::Scalar Scalar; \
typedef AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> > ReturnType; \
typedef AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type > ReturnType; \
CODE; \
}
@@ -234,34 +320,35 @@ namespace std
{
EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs,
return ReturnType(std::abs(x.value()), x.derivatives() * (sign(x.value())));)
EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt,
Scalar sqrtx = std::sqrt(x.value());
return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos,
return ReturnType(std::cos(x.value()), x.derivatives() * (-std::sin(x.value())));)
EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin,
return ReturnType(std::sin(x.value()),x.derivatives() * std::cos(x.value()));)
EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp,
Scalar expx = std::exp(x.value());
return ReturnType(expx,x.derivatives() * expx);)
EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
return ReturnType(std::log(x.value),x.derivatives() * (Scalar(1).x.value()));)
template<typename DerType>
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> >
pow(const AutoDiffScalar<DerType>& x, typename ei_traits<DerType>::Scalar y)
inline const Eigen::AutoDiffScalar<typename Eigen::MakeCwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType>::Type >
pow(const Eigen::AutoDiffScalar<DerType>& x, typename Eigen::ei_traits<DerType>::Scalar y)
{
using namespace Eigen;
typedef typename ei_traits<DerType>::Scalar Scalar;
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
std::pow(x.value(),y),
x.derivatives() * (y * std::pow(x.value(),y-1)));
}
}
namespace Eigen {
@@ -297,7 +384,7 @@ EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
return ReturnType(ei_log(x.value),x.derivatives() * (Scalar(1).x.value()));)
template<typename DerType>
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType>::Type >
ei_pow(const AutoDiffScalar<DerType>& x, typename ei_traits<DerType>::Scalar y)
{ return std::pow(x,y);}

128
unsupported/Eigen/src/AutoDiff/AutoDiffVector.h
View File

@@ -35,7 +35,7 @@ namespace Eigen {
* This class represents a scalar value while tracking its respective derivatives.
*
* It supports the following list of global math function:
* - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
* - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
* - ei_abs, ei_sqrt, ei_pow, ei_exp, ei_log, ei_sin, ei_cos,
* - ei_conj, ei_real, ei_imag, ei_abs2.
*
@@ -48,130 +48,150 @@ template<typename ValueType, typename JacobianType>
class AutoDiffVector
{
public:
typedef typename ei_traits<ValueType>::Scalar Scalar;
//typedef typename ei_traits<ValueType>::Scalar Scalar;
typedef typename ei_traits<ValueType>::Scalar BaseScalar;
typedef AutoDiffScalar<Matrix<BaseScalar,JacobianType::RowsAtCompileTime,1> > ActiveScalar;
typedef ActiveScalar Scalar;
typedef AutoDiffScalar<typename JacobianType::ColXpr> CoeffType;
inline AutoDiffVector() {}
inline AutoDiffVector(const ValueType& values)
: m_values(values)
{
m_jacobian.setZero();
}
CoeffType operator[] (int i) { return CoeffType(m_values[i], m_jacobian.col(i)); }
const CoeffType operator[] (int i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }
CoeffType operator() (int i) { return CoeffType(m_values[i], m_jacobian.col(i)); }
const CoeffType operator() (int i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }
CoeffType coeffRef(int i) { return CoeffType(m_values[i], m_jacobian.col(i)); }
const CoeffType coeffRef(int i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }
int size() const { return m_values.size(); }
// FIXME here we could return an expression of the sum
Scalar sum() const { /*std::cerr << "sum \n\n";*/ /*std::cerr << m_jacobian.rowwise().sum() << "\n\n";*/ return Scalar(m_values.sum(), m_jacobian.rowwise().sum()); }
inline AutoDiffVector(const ValueType& values, const JacobianType& jac)
: m_values(values), m_jacobian(jac)
{}
template<typename OtherValueType, typename OtherJacobianType>
inline AutoDiffVector(const AutoDiffVector<OtherValueType, OtherJacobianType>& other)
: m_values(other.values()), m_jacobian(other.jacobian())
{}
inline AutoDiffVector(const AutoDiffVector& other)
: m_values(other.values()), m_jacobian(other.jacobian())
{}
template<typename OtherValueType, typename OtherJacobianType>
inline AutoDiffScalar& operator=(const AutoDiffVector<OtherValueType, OtherJacobianType>& other)
inline AutoDiffVector& operator=(const AutoDiffVector<OtherValueType, OtherJacobianType>& other)
{
m_values = other.values();
m_jacobian = other.jacobian();
return *this;
}
inline AutoDiffVector& operator=(const AutoDiffVector& other)
{
m_values = other.values();
m_jacobian = other.jacobian();
return *this;
}
inline const ValueType& values() const { return m_values; }
inline ValueType& values() { return m_values; }
inline const JacobianType& jacobian() const { return m_jacobian; }
inline JacobianType& jacobian() { return m_jacobian; }
template<typename OtherValueType,typename OtherJacobianType>
inline const AutoDiffVector<
CwiseBinaryOp<ei_scalar_sum_op<Scalar>,ValueType,OtherValueType> >
CwiseBinaryOp<ei_scalar_sum_op<Scalar>,JacobianType,OtherJacobianType> >
operator+(const AutoDiffScalar<OtherDerType>& other) const
typename MakeCwiseBinaryOp<ei_scalar_sum_op<BaseScalar>,ValueType,OtherValueType>::Type,
typename MakeCwiseBinaryOp<ei_scalar_sum_op<BaseScalar>,JacobianType,OtherJacobianType>::Type >
operator+(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const
{
return AutoDiffVector<
CwiseBinaryOp<ei_scalar_sum_op<Scalar>,ValueType,OtherValueType> >
CwiseBinaryOp<ei_scalar_sum_op<Scalar>,JacobianType,OtherJacobianType> >(
typename MakeCwiseBinaryOp<ei_scalar_sum_op<BaseScalar>,ValueType,OtherValueType>::Type,
typename MakeCwiseBinaryOp<ei_scalar_sum_op<BaseScalar>,JacobianType,OtherJacobianType>::Type >(
m_values + other.values(),
m_jacobian + other.jacobian());
}
template<typename OtherValueType, typename OtherJacobianType>
inline AutoDiffVector&
operator+=(const AutoDiffVector<OtherValueType,OtherDerType>& other)
operator+=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other)
{
m_values += other.values();
m_jacobian += other.jacobian();
return *this;
}
template<typename OtherValueType,typename OtherJacobianType>
inline const AutoDiffVector<
CwiseBinaryOp<ei_scalar_difference_op<Scalar>,ValueType,OtherValueType> >
CwiseBinaryOp<ei_scalar_difference_op<Scalar>,JacobianType,OtherJacobianType> >
operator-(const AutoDiffScalar<OtherDerType>& other) const
typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,ValueType,OtherValueType>::Type,
typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,JacobianType,OtherJacobianType>::Type >
operator-(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const
{
return AutoDiffVector<
CwiseBinaryOp<ei_scalar_difference_op<Scalar>,ValueType,OtherValueType> >
CwiseBinaryOp<ei_scalar_difference_op<Scalar>,JacobianType,OtherJacobianType> >(
m_values - other.values(),
m_jacobian - other.jacobian());
typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,ValueType,OtherValueType>::Type,
typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,JacobianType,OtherJacobianType>::Type >(
m_values - other.values(),
m_jacobian - other.jacobian());
}
template<typename OtherValueType, typename OtherJacobianType>
inline AutoDiffVector&
operator-=(const AutoDiffVector<OtherValueType,OtherDerType>& other)
operator-=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other)
{
m_values -= other.values();
m_jacobian -= other.jacobian();
return *this;
}
inline const AutoDiffVector<
CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, ValueType>
CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, JacobianType> >
typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, ValueType>::Type,
typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, JacobianType>::Type >
operator-() const
{
return AutoDiffVector<
CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, ValueType>
CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, JacobianType> >(
-m_values,
-m_jacobian);
typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, ValueType>::Type,
typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, JacobianType>::Type >(
-m_values,
-m_jacobian);
}
inline const AutoDiffVector<
CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, ValueType>
CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, JacobianType> >
operator*(const Scalar& other) const
typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, ValueType>::Type,
typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, JacobianType>::Type>
operator*(const BaseScalar& other) const
{
return AutoDiffVector<
CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, ValueType>
CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, JacobianType> >(
typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, ValueType>::Type,
typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, JacobianType>::Type >(
m_values * other,
(m_jacobian * other));
m_jacobian * other);
}
friend inline const AutoDiffVector<
CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, ValueType>
CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, JacobianType> >
typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, ValueType>::Type,
typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, JacobianType>::Type >
operator*(const Scalar& other, const AutoDiffVector& v)
{
return AutoDiffVector<
CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, ValueType>
CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, JacobianType> >(
typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, ValueType>::Type,
typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, JacobianType>::Type >(
v.values() * other,
v.jacobian() * other);
}
// template<typename OtherValueType,typename OtherJacobianType>
// inline const AutoDiffVector<
// CwiseBinaryOp<ei_scalar_multiple_op<Scalar>, ValueType, OtherValueType>
@@ -188,25 +208,25 @@ class AutoDiffVector
// m_values.cwise() * other.values(),
// (m_jacobian * other.values()).nestByValue() + (m_values * other.jacobian()).nestByValue());
// }
inline AutoDiffVector& operator*=(const Scalar& other)
{
m_values *= other;
m_jacobian *= other;
return *this;
}
template<typename OtherValueType,typename OtherJacobianType>
inline AutoDiffVector& operator*=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other)
{
*this = *this * other;
return *this;
}
protected:
ValueType m_values;
JacobianType m_jacobian;
};
}

213
unsupported/Eigen/src/FFT/ei_fftw_impl.h Normal file
View File

@@ -0,0 +1,213 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
// FFTW uses non-const arguments
// so we must use ugly const_cast calls for all the args it uses
//
// This should be safe as long as
// 1. we use FFTW_ESTIMATE for all our planning
// see the FFTW docs section 4.3.2 "Planner Flags"
// 2. fftw_complex is compatible with std::complex
// This assumes std::complex<T> layout is array of size 2 with real,imag
template <typename T>
inline
T * ei_fftw_cast(const T* p)
{
return const_cast<T*>( p);
}
inline
fftw_complex * ei_fftw_cast( const std::complex<double> * p)
{
return const_cast<fftw_complex*>( reinterpret_cast<const fftw_complex*>(p) );
}
inline
fftwf_complex * ei_fftw_cast( const std::complex<float> * p)
{
return const_cast<fftwf_complex*>( reinterpret_cast<const fftwf_complex*>(p) );
}
inline
fftwl_complex * ei_fftw_cast( const std::complex<long double> * p)
{
return const_cast<fftwl_complex*>( reinterpret_cast<const fftwl_complex*>(p) );
}
template <typename T>
struct ei_fftw_plan {};
template <>
struct ei_fftw_plan<float>
{
typedef float scalar_type;
typedef fftwf_complex complex_type;
fftwf_plan m_plan;
ei_fftw_plan() :m_plan(NULL) {}
~ei_fftw_plan() {if (m_plan) fftwf_destroy_plan(m_plan);}
inline
void fwd(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE);
fftwf_execute_dft( m_plan, src,dst);
}
inline
void inv(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE);
fftwf_execute_dft( m_plan, src,dst);
}
inline
void fwd(complex_type * dst,scalar_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwf_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE);
fftwf_execute_dft_r2c( m_plan,src,dst);
}
inline
void inv(scalar_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL)
m_plan = fftwf_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE);
fftwf_execute_dft_c2r( m_plan, src,dst);
}
};
template <>
struct ei_fftw_plan<double>
{
typedef double scalar_type;
typedef fftw_complex complex_type;
fftw_plan m_plan;
ei_fftw_plan() :m_plan(NULL) {}
~ei_fftw_plan() {if (m_plan) fftw_destroy_plan(m_plan);}
inline
void fwd(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE);
fftw_execute_dft( m_plan, src,dst);
}
inline
void inv(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE);
fftw_execute_dft( m_plan, src,dst);
}
inline
void fwd(complex_type * dst,scalar_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftw_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE);
fftw_execute_dft_r2c( m_plan,src,dst);
}
inline
void inv(scalar_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL)
m_plan = fftw_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE);
fftw_execute_dft_c2r( m_plan, src,dst);
}
};
template <>
struct ei_fftw_plan<long double>
{
typedef long double scalar_type;
typedef fftwl_complex complex_type;
fftwl_plan m_plan;
ei_fftw_plan() :m_plan(NULL) {}
~ei_fftw_plan() {if (m_plan) fftwl_destroy_plan(m_plan);}
inline
void fwd(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE);
fftwl_execute_dft( m_plan, src,dst);
}
inline
void inv(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE);
fftwl_execute_dft( m_plan, src,dst);
}
inline
void fwd(complex_type * dst,scalar_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwl_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE);
fftwl_execute_dft_r2c( m_plan,src,dst);
}
inline
void inv(scalar_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL)
m_plan = fftwl_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE);
fftwl_execute_dft_c2r( m_plan, src,dst);
}
};
template <typename _Scalar>
struct ei_fftw_impl
{
typedef _Scalar Scalar;
typedef std::complex<Scalar> Complex;
inline
void clear()
{
m_plans.clear();
}
// complex-to-complex forward FFT
inline
void fwd( Complex * dst,const Complex *src,int nfft)
{
get_plan(nfft,false,dst,src).fwd(ei_fftw_cast(dst), ei_fftw_cast(src),nfft );
}
// real-to-complex forward FFT
inline
void fwd( Complex * dst,const Scalar * src,int nfft)
{
get_plan(nfft,false,dst,src).fwd(ei_fftw_cast(dst), ei_fftw_cast(src) ,nfft);
}
// inverse complex-to-complex
inline
void inv(Complex * dst,const Complex *src,int nfft)
{
get_plan(nfft,true,dst,src).inv(ei_fftw_cast(dst), ei_fftw_cast(src),nfft );
}
// half-complex to scalar
inline
void inv( Scalar * dst,const Complex * src,int nfft)
{
get_plan(nfft,true,dst,src).inv(ei_fftw_cast(dst), ei_fftw_cast(src),nfft );
}
protected:
typedef ei_fftw_plan<Scalar> PlanData;
typedef std::map<int,PlanData> PlanMap;
PlanMap m_plans;
inline
PlanData & get_plan(int nfft,bool inverse,void * dst,const void * src)
{
bool inplace = (dst==src);
bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0;
int key = (nfft<<3 ) | (inverse<<2) | (inplace<<1) | aligned;
return m_plans[key];
}
};
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

410
unsupported/Eigen/src/FFT/ei_kissfft_impl.h Normal file
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@@ -0,0 +1,410 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
// This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft
// Copyright 2003-2009 Mark Borgerding
template <typename _Scalar>
struct ei_kiss_cpx_fft
{
typedef _Scalar Scalar;
typedef std::complex<Scalar> Complex;
std::vector<Complex> m_twiddles;
std::vector<int> m_stageRadix;
std::vector<int> m_stageRemainder;
std::vector<Complex> m_scratchBuf;
bool m_inverse;
inline
void make_twiddles(int nfft,bool inverse)
{
m_inverse = inverse;
m_twiddles.resize(nfft);
Scalar phinc = (inverse?2:-2)* acos( (Scalar) -1) / nfft;
for (int i=0;i<nfft;++i)
m_twiddles[i] = exp( Complex(0,i*phinc) );
}
void factorize(int nfft)
{
//start factoring out 4's, then 2's, then 3,5,7,9,...
int n= nfft;
int p=4;
do {
while (n % p) {
switch (p) {
case 4: p = 2; break;
case 2: p = 3; break;
default: p += 2; break;
}
if (p*p>n)
p=n;// impossible to have a factor > sqrt(n)
}
n /= p;
m_stageRadix.push_back(p);
m_stageRemainder.push_back(n);
if ( p > 5 )
m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic
}while(n>1);
}
template <typename _Src>
inline
void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride)
{
int p = m_stageRadix[stage];
int m = m_stageRemainder[stage];
Complex * Fout_beg = xout;
Complex * Fout_end = xout + p*m;
if (m>1) {
do{
// recursive call:
// DFT of size m*p performed by doing
// p instances of smaller DFTs of size m,
// each one takes a decimated version of the input
work(stage+1, xout , xin, fstride*p,in_stride);
xin += fstride*in_stride;
}while( (xout += m) != Fout_end );
}else{
do{
*xout = *xin;
xin += fstride*in_stride;
}while(++xout != Fout_end );
}
xout=Fout_beg;
// recombine the p smaller DFTs
switch (p) {
case 2: bfly2(xout,fstride,m); break;
case 3: bfly3(xout,fstride,m); break;
case 4: bfly4(xout,fstride,m); break;
case 5: bfly5(xout,fstride,m); break;
default: bfly_generic(xout,fstride,m,p); break;
}
}
inline
void bfly2( Complex * Fout, const size_t fstride, int m)
{
for (int k=0;k<m;++k) {
Complex t = Fout[m+k] * m_twiddles[k*fstride];
Fout[m+k] = Fout[k] - t;
Fout[k] += t;
}
}
inline
void bfly4( Complex * Fout, const size_t fstride, const size_t m)
{
Complex scratch[6];
int negative_if_inverse = m_inverse * -2 +1;
for (size_t k=0;k<m;++k) {
scratch[0] = Fout[k+m] * m_twiddles[k*fstride];
scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];
scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];
scratch[5] = Fout[k] - scratch[1];
Fout[k] += scratch[1];
scratch[3] = scratch[0] + scratch[2];
scratch[4] = scratch[0] - scratch[2];
scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
Fout[k+2*m] = Fout[k] - scratch[3];
Fout[k] += scratch[3];
Fout[k+m] = scratch[5] + scratch[4];
Fout[k+3*m] = scratch[5] - scratch[4];
}
}
inline
void bfly3( Complex * Fout, const size_t fstride, const size_t m)
{
size_t k=m;
const size_t m2 = 2*m;
Complex *tw1,*tw2;
Complex scratch[5];
Complex epi3;
epi3 = m_twiddles[fstride*m];
tw1=tw2=&m_twiddles[0];
do{
scratch[1]=Fout[m] * *tw1;
scratch[2]=Fout[m2] * *tw2;
scratch[3]=scratch[1]+scratch[2];
scratch[0]=scratch[1]-scratch[2];
tw1 += fstride;
tw2 += fstride*2;
Fout[m] = Complex( Fout->real() - .5*scratch[3].real() , Fout->imag() - .5*scratch[3].imag() );
scratch[0] *= epi3.imag();
*Fout += scratch[3];
Fout[m2] = Complex( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );
++Fout;
}while(--k);
}
inline
void bfly5( Complex * Fout, const size_t fstride, const size_t m)
{
Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
size_t u;
Complex scratch[13];
Complex * twiddles = &m_twiddles[0];
Complex *tw;
Complex ya,yb;
ya = twiddles[fstride*m];
yb = twiddles[fstride*2*m];
Fout0=Fout;
Fout1=Fout0+m;
Fout2=Fout0+2*m;
Fout3=Fout0+3*m;
Fout4=Fout0+4*m;
tw=twiddles;
for ( u=0; u<m; ++u ) {
scratch[0] = *Fout0;
scratch[1] = *Fout1 * tw[u*fstride];
scratch[2] = *Fout2 * tw[2*u*fstride];
scratch[3] = *Fout3 * tw[3*u*fstride];
scratch[4] = *Fout4 * tw[4*u*fstride];
scratch[7] = scratch[1] + scratch[4];
scratch[10] = scratch[1] - scratch[4];
scratch[8] = scratch[2] + scratch[3];
scratch[9] = scratch[2] - scratch[3];
*Fout0 += scratch[7];
*Fout0 += scratch[8];
scratch[5] = scratch[0] + Complex(
(scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),
(scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())
);
scratch[6] = Complex(
(scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),
-(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())
);
*Fout1 = scratch[5] - scratch[6];
*Fout4 = scratch[5] + scratch[6];
scratch[11] = scratch[0] +
Complex(
(scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),
(scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())
);
scratch[12] = Complex(
-(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
(scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
);
*Fout2=scratch[11]+scratch[12];
*Fout3=scratch[11]-scratch[12];
++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
}
}
/* perform the butterfly for one stage of a mixed radix FFT */
inline
void bfly_generic(
Complex * Fout,
const size_t fstride,
int m,
int p
)
{
int u,k,q1,q;
Complex * twiddles = &m_twiddles[0];
Complex t;
int Norig = m_twiddles.size();
Complex * scratchbuf = &m_scratchBuf[0];
for ( u=0; u<m; ++u ) {
k=u;
for ( q1=0 ; q1<p ; ++q1 ) {
scratchbuf[q1] = Fout[ k ];
k += m;
}
k=u;
for ( q1=0 ; q1<p ; ++q1 ) {
int twidx=0;
Fout[ k ] = scratchbuf[0];
for (q=1;q<p;++q ) {
twidx += fstride * k;
if (twidx>=Norig) twidx-=Norig;
t=scratchbuf[q] * twiddles[twidx];
Fout[ k ] += t;
}
k += m;
}
}
}
};
template <typename _Scalar>
struct ei_kissfft_impl
{
typedef _Scalar Scalar;
typedef std::complex<Scalar> Complex;
void clear()
{
m_plans.clear();
m_realTwiddles.clear();
}
inline
void fwd( Complex * dst,const Complex *src,int nfft)
{
get_plan(nfft,false).work(0, dst, src, 1,1);
}
// real-to-complex forward FFT
// perform two FFTs of src even and src odd
// then twiddle to recombine them into the half-spectrum format
// then fill in the conjugate symmetric half
inline
void fwd( Complex * dst,const Scalar * src,int nfft)
{
if ( nfft&3 ) {
// use generic mode for odd
m_tmpBuf1.resize(nfft);
get_plan(nfft,false).work(0, &m_tmpBuf1[0], src, 1,1);
std::copy(m_tmpBuf1.begin(),m_tmpBuf1.begin()+(nfft>>1)+1,dst );
}else{
int ncfft = nfft>>1;
int ncfft2 = nfft>>2;
Complex * rtw = real_twiddles(ncfft2);
// use optimized mode for even real
fwd( dst, reinterpret_cast<const Complex*> (src), ncfft);
Complex dc = dst[0].real() + dst[0].imag();
Complex nyquist = dst[0].real() - dst[0].imag();
int k;
for ( k=1;k <= ncfft2 ; ++k ) {
Complex fpk = dst[k];
Complex fpnk = conj(dst[ncfft-k]);
Complex f1k = fpk + fpnk;
Complex f2k = fpk - fpnk;
Complex tw= f2k * rtw[k-1];
dst[k] = (f1k + tw) * Scalar(.5);
dst[ncfft-k] = conj(f1k -tw)*Scalar(.5);
}
dst[0] = dc;
dst[ncfft] = nyquist;
}
}
// inverse complex-to-complex
inline
void inv(Complex * dst,const Complex *src,int nfft)
{
get_plan(nfft,true).work(0, dst, src, 1,1);
}
// half-complex to scalar
inline
void inv( Scalar * dst,const Complex * src,int nfft)
{
if (nfft&3) {
m_tmpBuf1.resize(nfft);
m_tmpBuf2.resize(nfft);
std::copy(src,src+(nfft>>1)+1,m_tmpBuf1.begin() );
for (int k=1;k<(nfft>>1)+1;++k)
m_tmpBuf1[nfft-k] = conj(m_tmpBuf1[k]);
inv(&m_tmpBuf2[0],&m_tmpBuf1[0],nfft);
for (int k=0;k<nfft;++k)
dst[k] = m_tmpBuf2[k].real();
}else{
// optimized version for multiple of 4
int ncfft = nfft>>1;
int ncfft2 = nfft>>2;
Complex * rtw = real_twiddles(ncfft2);
m_tmpBuf1.resize(ncfft);
m_tmpBuf1[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() );
for (int k = 1; k <= ncfft / 2; ++k) {
Complex fk = src[k];
Complex fnkc = conj(src[ncfft-k]);
Complex fek = fk + fnkc;
Complex tmp = fk - fnkc;
Complex fok = tmp * conj(rtw[k-1]);
m_tmpBuf1[k] = fek + fok;
m_tmpBuf1[ncfft-k] = conj(fek - fok);
}
get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf1[0], 1,1);
}
}
protected:
typedef ei_kiss_cpx_fft<Scalar> PlanData;
typedef std::map<int,PlanData> PlanMap;
PlanMap m_plans;
std::map<int, std::vector<Complex> > m_realTwiddles;
std::vector<Complex> m_tmpBuf1;
std::vector<Complex> m_tmpBuf2;
inline
int PlanKey(int nfft,bool isinverse) const { return (nfft<<1) | isinverse; }
inline
PlanData & get_plan(int nfft,bool inverse)
{
// TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles
PlanData & pd = m_plans[ PlanKey(nfft,inverse) ];
if ( pd.m_twiddles.size() == 0 ) {
pd.make_twiddles(nfft,inverse);
pd.factorize(nfft);
}
return pd;
}
inline
Complex * real_twiddles(int ncfft2)
{
std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
if ( (int)twidref.size() != ncfft2 ) {
twidref.resize(ncfft2);
int ncfft= ncfft2<<1;
Scalar pi = acos( Scalar(-1) );
for (int k=1;k<=ncfft2;++k)
twidref[k-1] = exp( Complex(0,-pi * ((double) (k) / ncfft + .5) ) );
}
return &twidref[0];
}
};
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

117
unsupported/doc/examples/FFT.cpp Normal file
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@@ -0,0 +1,117 @@
// To use the simple FFT implementation
// g++ -o demofft -I.. -Wall -O3 FFT.cpp
// To use the FFTW implementation
// g++ -o demofft -I.. -DUSE_FFTW -Wall -O3 FFT.cpp -lfftw3 -lfftw3f -lfftw3l
#ifdef USE_FFTW
#include <fftw3.h>
#endif
#include <vector>
#include <complex>
#include <algorithm>
#include <iterator>
#include <Eigen/Core>
#include <unsupported/Eigen/FFT>
using namespace std;
using namespace Eigen;
template <typename T>
T mag2(T a)
{
return a*a;
}
template <typename T>
T mag2(std::complex<T> a)
{
return norm(a);
}
template <typename T>
T mag2(const std::vector<T> & vec)
{
T out=0;
for (size_t k=0;k<vec.size();++k)
out += mag2(vec[k]);
return out;
}
template <typename T>
T mag2(const std::vector<std::complex<T> > & vec)
{
T out=0;
for (size_t k=0;k<vec.size();++k)
out += mag2(vec[k]);
return out;
}
template <typename T>
vector<T> operator-(const vector<T> & a,const vector<T> & b )
{
vector<T> c(a);
for (size_t k=0;k<b.size();++k)
c[k] -= b[k];
return c;
}
template <typename T>
void RandomFill(std::vector<T> & vec)
{
for (size_t k=0;k<vec.size();++k)
vec[k] = T( rand() )/T(RAND_MAX) - .5;
}
template <typename T>
void RandomFill(std::vector<std::complex<T> > & vec)
{
for (size_t k=0;k<vec.size();++k)
vec[k] = std::complex<T> ( T( rand() )/T(RAND_MAX) - .5, T( rand() )/T(RAND_MAX) - .5);
}
template <typename T_time,typename T_freq>
void fwd_inv(size_t nfft)
{
typedef typename NumTraits<T_freq>::Real Scalar;
vector<T_time> timebuf(nfft);
RandomFill(timebuf);
vector<T_freq> freqbuf;
static FFT<Scalar> fft;
fft.fwd(freqbuf,timebuf);
vector<T_time> timebuf2;
fft.inv(timebuf2,freqbuf);
long double rmse = mag2(timebuf - timebuf2) / mag2(timebuf);
cout << "roundtrip rmse: " << rmse << endl;
}
template <typename T_scalar>
void two_demos(int nfft)
{
cout << " scalar ";
fwd_inv<T_scalar,std::complex<T_scalar> >(nfft);
cout << " complex ";
fwd_inv<std::complex<T_scalar>,std::complex<T_scalar> >(nfft);
}
void demo_all_types(int nfft)
{
cout << "nfft=" << nfft << endl;
cout << " float" << endl;
two_demos<float>(nfft);
cout << " double" << endl;
two_demos<double>(nfft);
cout << " long double" << endl;
two_demos<long double>(nfft);
}
int main()
{
demo_all_types( 2*3*4*5*7 );
demo_all_types( 2*9*16*25 );
demo_all_types( 1024 );
return 0;
}

8
unsupported/test/CMakeLists.txt
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@@ -21,3 +21,11 @@ ei_add_test(autodiff)
ei_add_test(BVH)
#ei_add_test(matrixExponential)
ei_add_test(alignedvector3)
ei_add_test(FFT)
find_package(FFTW)
if(FFTW_FOUND)
ei_add_test(FFTW "-DEIGEN_FFTW_DEFAULT " "-lfftw3 -lfftw3f -lfftw3l" )
endif(FFTW_FOUND)
ei_add_test(Complex)

77
unsupported/test/Complex.cpp Normal file
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@@ -0,0 +1,77 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifdef EIGEN_TEST_FUNC
# include "main.h"
#else
# include <iostream>
# define CALL_SUBTEST(x) x
# define VERIFY(x) x
# define test_Complex main
#endif
#include <unsupported/Eigen/Complex>
#include <vector>
using namespace std;
using namespace Eigen;
template <typename T>
void take_std( std::complex<T> * dst, int n )
{
cout << dst[n-1] << endl;
}
template <typename T>
void syntax()
{
// this works fine
Matrix< Complex<T>, 9, 1> a;
std::complex<T> * pa = &a[0];
Complex<T> * pa2 = &a[0];
take_std( pa,9);
// this does not work, but I wish it would
// take_std(&a[0];)
// this does
take_std( (std::complex<T> *)&a[0],9);
// this does not work, but it would be really nice
//vector< Complex<T> > a;
// (on my gcc 4.4.1 )
// std::vector assumes operator& returns a POD pointer
// this works fine
Complex<T> b[9];
std::complex<T> * pb = &b[0]; // this works fine
take_std( pb,9);
}
void test_Complex()
{
CALL_SUBTEST( syntax<float>() );
CALL_SUBTEST( syntax<double>() );
CALL_SUBTEST( syntax<long double>() );
}

235
unsupported/test/FFT.cpp Normal file
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@@ -0,0 +1,235 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <unsupported/Eigen/FFT>
using namespace std;
float norm(float x) {return x*x;}
double norm(double x) {return x*x;}
long double norm(long double x) {return x*x;}
template < typename T>
complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
complex<long double> promote(float x) { return complex<long double>( x); }
complex<long double> promote(double x) { return complex<long double>( x); }
complex<long double> promote(long double x) { return complex<long double>( x); }
template <typename VectorType1,typename VectorType2>
long double fft_rmse( const VectorType1 & fftbuf,const VectorType2 & timebuf)
{
long double totalpower=0;
long double difpower=0;
cerr <<"idx\ttruth\t\tvalue\t|dif|=\n";
for (size_t k0=0;k0<size_t(fftbuf.size());++k0) {
complex<long double> acc = 0;
long double phinc = -2.*k0* M_PIl / timebuf.size();
for (size_t k1=0;k1<size_t(timebuf.size());++k1) {
acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
}
totalpower += norm(acc);
complex<long double> x = promote(fftbuf[k0]);
complex<long double> dif = acc - x;
difpower += norm(dif);
cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(norm(dif)) << endl;
}
cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
return sqrt(difpower/totalpower);
}
template <typename VectorType1,typename VectorType2>
long double dif_rmse( const VectorType1& buf1,const VectorType2& buf2)
{
long double totalpower=0;
long double difpower=0;
size_t n = min( buf1.size(),buf2.size() );
for (size_t k=0;k<n;++k) {
totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.;
difpower += norm(buf1[k] - buf2[k]);
}
return sqrt(difpower/totalpower);
}
enum { StdVectorContainer, EigenVectorContainer };
template<int Container, typename Scalar> struct VectorType;
template<typename Scalar> struct VectorType<StdVectorContainer,Scalar>
{
typedef vector<Scalar> type;
};
template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar>
{
typedef Matrix<Scalar,Dynamic,1> type;
};
template <int Container, typename T>
void test_scalar_generic(int nfft)
{
typedef typename FFT<T>::Complex Complex;
typedef typename FFT<T>::Scalar Scalar;
typedef typename VectorType<Container,Scalar>::type ScalarVector;
typedef typename VectorType<Container,Complex>::type ComplexVector;
FFT<T> fft;
ScalarVector inbuf(nfft);
ComplexVector outbuf;
for (int k=0;k<nfft;++k)
inbuf[k]= (T)(rand()/(double)RAND_MAX - .5);
// make sure it DOESN'T give the right full spectrum answer
// if we've asked for half-spectrum
fft.SetFlag(fft.HalfSpectrum );
fft.fwd( outbuf,inbuf);
VERIFY(outbuf.size() == (nfft>>1)+1);
VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
fft.ClearFlag(fft.HalfSpectrum );
fft.fwd( outbuf,inbuf);
VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
ScalarVector buf3;
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
// verify that the Unscaled flag takes effect
ComplexVector buf4;
fft.SetFlag(fft.Unscaled);
fft.inv( buf4 , outbuf);
for (int k=0;k<nfft;++k)
buf4[k] *= T(1./nfft);
VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check
// verify that ClearFlag works
fft.ClearFlag(fft.Unscaled);
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
}
template <typename T>
void test_scalar(int nfft)
{
test_scalar_generic<StdVectorContainer,T>(nfft);
test_scalar_generic<EigenVectorContainer,T>(nfft);
}
template <int Container, typename T>
void test_complex_generic(int nfft)
{
typedef typename FFT<T>::Complex Complex;
typedef typename VectorType<Container,Complex>::type ComplexVector;
FFT<T> fft;
ComplexVector inbuf(nfft);
ComplexVector outbuf;
ComplexVector buf3;
for (int k=0;k<nfft;++k)
inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
fft.fwd( outbuf , inbuf);
VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
// verify that the Unscaled flag takes effect
ComplexVector buf4;
fft.SetFlag(fft.Unscaled);
fft.inv( buf4 , outbuf);
for (int k=0;k<nfft;++k)
buf4[k] *= T(1./nfft);
VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check
// verify that ClearFlag works
fft.ClearFlag(fft.Unscaled);
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
}
template <typename T>
void test_complex(int nfft)
{
test_complex_generic<StdVectorContainer,T>(nfft);
test_complex_generic<EigenVectorContainer,T>(nfft);
}
void test_FFT()
{
CALL_SUBTEST( test_complex<float>(32) );
CALL_SUBTEST( test_complex<double>(32) );
CALL_SUBTEST( test_complex<long double>(32) );
CALL_SUBTEST( test_complex<float>(256) );
CALL_SUBTEST( test_complex<double>(256) );
CALL_SUBTEST( test_complex<long double>(256) );
CALL_SUBTEST( test_complex<float>(3*8) );
CALL_SUBTEST( test_complex<double>(3*8) );
CALL_SUBTEST( test_complex<long double>(3*8) );
CALL_SUBTEST( test_complex<float>(5*32) );
CALL_SUBTEST( test_complex<double>(5*32) );
CALL_SUBTEST( test_complex<long double>(5*32) );
CALL_SUBTEST( test_complex<float>(2*3*4) );
CALL_SUBTEST( test_complex<double>(2*3*4) );
CALL_SUBTEST( test_complex<long double>(2*3*4) );
CALL_SUBTEST( test_complex<float>(2*3*4*5) );
CALL_SUBTEST( test_complex<double>(2*3*4*5) );
CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
CALL_SUBTEST( test_complex<float>(2*3*4*5*7) );
CALL_SUBTEST( test_complex<double>(2*3*4*5*7) );
CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<float>(32) );
CALL_SUBTEST( test_scalar<double>(32) );
CALL_SUBTEST( test_scalar<long double>(32) );
CALL_SUBTEST( test_scalar<float>(45) );
CALL_SUBTEST( test_scalar<double>(45) );
CALL_SUBTEST( test_scalar<long double>(45) );
CALL_SUBTEST( test_scalar<float>(50) );
CALL_SUBTEST( test_scalar<double>(50) );
CALL_SUBTEST( test_scalar<long double>(50) );
CALL_SUBTEST( test_scalar<float>(256) );
CALL_SUBTEST( test_scalar<double>(256) );
CALL_SUBTEST( test_scalar<long double>(256) );
CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
}

136
unsupported/test/FFTW.cpp Normal file
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@@ -0,0 +1,136 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <fftw3.h>
#include <unsupported/Eigen/FFT>
using namespace std;
float norm(float x) {return x*x;}
double norm(double x) {return x*x;}
long double norm(long double x) {return x*x;}
template < typename T>
complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
complex<long double> promote(float x) { return complex<long double>( x); }
complex<long double> promote(double x) { return complex<long double>( x); }
complex<long double> promote(long double x) { return complex<long double>( x); }
template <typename T1,typename T2>
long double fft_rmse( const vector<T1> & fftbuf,const vector<T2> & timebuf)
{
long double totalpower=0;
long double difpower=0;
cerr <<"idx\ttruth\t\tvalue\t|dif|=\n";
for (size_t k0=0;k0<fftbuf.size();++k0) {
complex<long double> acc = 0;
long double phinc = -2.*k0* M_PIl / timebuf.size();
for (size_t k1=0;k1<timebuf.size();++k1) {
acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
}
totalpower += norm(acc);
complex<long double> x = promote(fftbuf[k0]);
complex<long double> dif = acc - x;
difpower += norm(dif);
cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(norm(dif)) << endl;
}
cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
return sqrt(difpower/totalpower);
}
template <typename T1,typename T2>
long double dif_rmse( const vector<T1> buf1,const vector<T2> buf2)
{
long double totalpower=0;
long double difpower=0;
size_t n = min( buf1.size(),buf2.size() );
for (size_t k=0;k<n;++k) {
totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.;
difpower += norm(buf1[k] - buf2[k]);
}
return sqrt(difpower/totalpower);
}
template <class T>
void test_scalar(int nfft)
{
typedef typename Eigen::FFT<T>::Complex Complex;
typedef typename Eigen::FFT<T>::Scalar Scalar;
FFT<T> fft;
vector<Scalar> inbuf(nfft);
vector<Complex> outbuf;
for (int k=0;k<nfft;++k)
inbuf[k]= (T)(rand()/(double)RAND_MAX - .5);
fft.fwd( outbuf,inbuf);
VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
vector<Scalar> buf3;
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
}
template <class T>
void test_complex(int nfft)
{
typedef typename Eigen::FFT<T>::Complex Complex;
FFT<T> fft;
vector<Complex> inbuf(nfft);
vector<Complex> outbuf;
vector<Complex> buf3;
for (int k=0;k<nfft;++k)
inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
fft.fwd( outbuf , inbuf);
VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
}
void test_FFTW()
{
CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) ); CALL_SUBTEST( test_complex<long double>(32) );
CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) ); CALL_SUBTEST( test_complex<long double>(256) );
CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) ); CALL_SUBTEST( test_complex<long double>(3*8) );
CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) ); CALL_SUBTEST( test_complex<long double>(5*32) );
CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) ); CALL_SUBTEST( test_complex<long double>(2*3*4) );
CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) ); CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) ); CALL_SUBTEST( test_scalar<long double>(32) );
CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) ); CALL_SUBTEST( test_scalar<long double>(45) );
CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) ); CALL_SUBTEST( test_scalar<long double>(50) );
CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) ); CALL_SUBTEST( test_scalar<long double>(256) );
CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
}

8
unsupported/test/autodiff.cpp
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@@ -46,12 +46,12 @@ struct TestFunc1
typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
int m_inputs, m_values;
TestFunc1() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
TestFunc1(int inputs, int values) : m_inputs(inputs), m_values(values) {}
int inputs() const { return m_inputs; }
int values() const { return m_values; }
@@ -142,7 +142,7 @@ void test_autodiff_scalar()
std::cerr << foo<AutoDiffScalar<Vector2f> >(ax,ay).value() << " <> "
<< foo<AutoDiffScalar<Vector2f> >(ax,ay).derivatives().transpose() << "\n\n";
}
void test_autodiff_jacobian()
{
for(int i = 0; i < g_repeat; i++) {