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* merge

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* remove a ctor in QuaternionBase as it gives a strange error with GCC 4.4.2.
This commit is contained in:
Benoit Jacob
2009-11-09 09:08:03 -05:00
parent 4b366b07be 670651e2e0
commit 92749eed11
32 changed files with 1055 additions and 710 deletions
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2
unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
View File

@@ -29,7 +29,7 @@ namespace Eigen {
template<typename A, typename B>
struct ei_make_coherent_impl {
static void run(A& a, B& b) {}
static void run(A&, B&) {}
};
// resize a to match b is a.size()==0, and conversely.

128
unsupported/Eigen/src/AutoDiff/AutoDiffVector.h
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@@ -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;
};
}

17
unsupported/Eigen/src/FFT/ei_fftw_impl.h
View File

@@ -166,6 +166,7 @@
m_plans.clear();
}
// complex-to-complex forward FFT
inline
void fwd( Complex * dst,const Complex *src,int nfft)
{
@@ -177,9 +178,6 @@
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);
int nhbins=(nfft>>1)+1;
for (int k=nhbins;k < nfft; ++k )
dst[k] = conj(dst[nfft-k]);
}
// inverse complex-to-complex
@@ -187,12 +185,6 @@
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 );
//TODO move scaling to Eigen::FFT
// scaling
Scalar s = Scalar(1.)/nfft;
for (int k=0;k<nfft;++k)
dst[k] *= s;
}
// half-complex to scalar
@@ -200,11 +192,6 @@
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 );
//TODO move scaling to Eigen::FFT
Scalar s = Scalar(1.)/nfft;
for (int k=0;k<nfft;++k)
dst[k] *= s;
}
protected:
@@ -222,3 +209,5 @@
return m_plans[key];
}
};
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

706
unsupported/Eigen/src/FFT/ei_kissfft_impl.h
View File

@@ -27,388 +27,384 @@
// 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
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)
{
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;
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 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>
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;
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);
}
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];
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{
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);
// 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;
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;
}
// 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;
}
}
/* 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
inline
void bfly2( Complex * Fout, const size_t fstride, int m)
{
typedef _Scalar Scalar;
typedef std::complex<Scalar> Complex;
void clear()
{
m_plans.clear();
m_realTwiddles.clear();
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;
}
}
template <typename _Src>
inline
void fwd( Complex * dst,const _Src *src,int nfft)
{
get_plan(nfft,false).work(0, dst, src, 1,1);
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;
}
// 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
get_plan(nfft,false).work(0, dst, src, 1,1);
}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);
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;
}
// place conjugate-symmetric half at the end for completeness
// TODO: make this configurable ( opt-out )
for ( k=1;k < ncfft ; ++k )
dst[nfft-k] = conj(dst[k]);
dst[0] = dc;
dst[ncfft] = nyquist;
k += m;
}
}
}
};
// inverse complex-to-complex
inline
void inv(Complex * dst,const Complex *src,int nfft)
{
get_plan(nfft,true).work(0, dst, src, 1,1);
scale(dst, nfft, Scalar(1)/nfft );
}
template <typename _Scalar>
struct ei_kissfft_impl
{
typedef _Scalar Scalar;
typedef std::complex<Scalar> Complex;
// half-complex to scalar
inline
void inv( Scalar * dst,const Complex * src,int nfft)
{
if (nfft&3) {
m_tmpBuf.resize(nfft);
inv(&m_tmpBuf[0],src,nfft);
for (int k=0;k<nfft;++k)
dst[k] = m_tmpBuf[k].real();
}else{
// optimized version for multiple of 4
int ncfft = nfft>>1;
int ncfft2 = nfft>>2;
Complex * rtw = real_twiddles(ncfft2);
m_tmpBuf.resize(ncfft);
m_tmpBuf[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_tmpBuf[k] = fek + fok;
m_tmpBuf[ncfft-k] = conj(fek - fok);
}
scale(&m_tmpBuf[0], ncfft, Scalar(1)/nfft );
get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf[0], 1,1);
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;
}
}
protected:
typedef ei_kiss_cpx_fft<Scalar> PlanData;
typedef std::map<int,PlanData> PlanMap;
// inverse complex-to-complex
inline
void inv(Complex * dst,const Complex *src,int nfft)
{
get_plan(nfft,true).work(0, dst, src, 1,1);
}
PlanMap m_plans;
std::map<int, std::vector<Complex> > m_realTwiddles;
std::vector<Complex> m_tmpBuf;
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);
// 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);
}
return pd;
get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf1[0], 1,1);
}
}
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];
}
protected:
typedef ei_kiss_cpx_fft<Scalar> PlanData;
typedef std::map<int,PlanData> PlanMap;
// TODO move scaling up into Eigen::FFT
inline
void scale(Complex *dst,int n,Scalar s)
{
for (int k=0;k<n;++k)
dst[k] *= s;
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: */