various comment changes

2 files changed, 237 insertions, 253 deletions

diff --git a/unsupported/Eigen/FFT b/unsupported/Eigen/FFT
index 3d852f5a2..31d8c74c5 100644
--- a/unsupported/Eigen/FFT
+++ b/unsupported/Eigen/FFT
@@ -1,5 +1,5 @@
 // This file is part of Eigen, a lightweight C++ template library
-// for linear algebra. Eigen itself is part of the KDE project.
+// for linear algebra. 
 //
 // Copyright (C) 2009 Mark Borgerding mark a borgerding net
 //
@@ -29,14 +29,14 @@
 #include "src/FFT/ei_kissfft_impl.h"
 #define DEFAULT_FFT_IMPL ei_kissfft_impl
 
-// FFTW: faster, GPL-not LGPL, bigger code size
+// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size
 #ifdef FFTW_PATIENT  // definition of FFTW_PATIENT indicates the caller has included fftw3.h, we can use FFTW routines
 // TODO 
 // #include "src/FFT/ei_fftw_impl.h"
 // #define DEFAULT_FFT_IMPL ei_fftw_impl
 #endif
 
-// intel Math Kernel Library: fastest, commerical
+// intel Math Kernel Library: fastest, commerical -- incompatible with Eigen in GPL form
 #ifdef _MKL_DFTI_H_ // mkl_dfti.h has been included, we can use MKL FFT routines
 // TODO 
 // #include "src/FFT/ei_imkl_impl.h"
diff --git a/unsupported/Eigen/src/FFT/ei_kissfft_impl.h b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
index 453c7f6da..91fa5ca18 100644
--- a/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
+++ b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
@@ -1,5 +1,5 @@
 // This file is part of Eigen, a lightweight C++ template library
-// for linear algebra. Eigen itself is part of the KDE project.
+// for linear algebra.
 //
 // Copyright (C) 2009 Mark Borgerding mark a borgerding net
 //
@@ -28,252 +28,255 @@
 
 namespace Eigen {
 
+  // 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;
-    bool m_inverse;
-
-    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 conjugate()
+    struct ei_kiss_cpx_fft
     {
-      m_inverse = !m_inverse;
-      for ( size_t i=0;i<m_twiddles.size() ;++i)
-        m_twiddles[i] = conj( m_twiddles[i] );
-    }
+      typedef _Scalar Scalar;
+      typedef std::complex<Scalar> Complex;
+      std::vector<Complex> m_twiddles;
+      std::vector<int> m_stageRadix;
+      std::vector<int> m_stageRemainder;
+      bool m_inverse;
 
-    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) {
+      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 conjugate()
+      {
+        m_inverse = !m_inverse;
+        for ( size_t i=0;i<m_twiddles.size() ;++i)
+          m_twiddles[i] = conj( m_twiddles[i] );
+      }
+
+      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);
+        }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 4: p = 2; break;
-            case 2: p = 3; break;
-            default: p += 2; break;
+            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;
           }
-          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);
-      }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;
+      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 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 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];
+        }
       }
-    }
 
-    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];
+      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);
       }
-    }
 
-    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);
-    }
-
-    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())
+      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())
               );
 
-        scratch[12] = Complex(
-            -(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
-            (scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
-            );
+          *Fout1 = scratch[5] - scratch[6];
+          *Fout4 = scratch[5] + scratch[6];
 
-        *Fout2=scratch[11]+scratch[12];
-        *Fout3=scratch[11]-scratch[12];
+          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())
+                );
 
-        ++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
-      }
-    }
-
-    /* perform the butterfly for one stage of a mixed radix FFT */
-    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 = (Complex*)alloca(p*sizeof(Complex) );
-
-      for ( u=0; u<m; ++u ) {
-        k=u;
-        for ( q1=0 ; q1<p ; ++q1 ) {
-          scratchbuf[q1] = Fout[ k  ];
-          k += m;
+          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;
         }
+      }
 
-        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;
+      /* perform the butterfly for one stage of a mixed radix FFT */
+      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 = (Complex*)alloca(p*sizeof(Complex) );
+
+        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;
           }
-          k += m;
         }
       }
-    }
-  };
+    };
 
   template <typename _Scalar>
-  struct ei_kissfft_impl
-  {
+    struct ei_kissfft_impl
+    {
       typedef _Scalar Scalar;
       typedef std::complex<Scalar> Complex;
 
@@ -284,10 +287,10 @@ namespace Eigen {
       }
 
       template <typename _Src>
-      void fwd( Complex * dst,const _Src *src,int nfft)
-      {
-        get_plan(nfft,false).work(0, dst, src, 1,1);
-      }
+        void fwd( Complex * dst,const _Src *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
@@ -363,11 +366,10 @@ namespace Eigen {
         }
       }
 
-  private:
-
+      private:
       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_scratchBuf;
@@ -376,25 +378,7 @@ namespace Eigen {
 
       PlanData & get_plan(int nfft,bool inverse)
       {
-        /*  TODO: figure out why this does not work (g++ 4.3.2)
-         * for some reason this does not work
-         *
-         PlanMap::iterator it;
-         it = m_plans.find( PlanKey(nfft,inverse) );
-         if (it == m_plans.end() ) {
-        // create new entry
-        it = m_plans.insert( make_pair( PlanKey(nfft,inverse) , PlanData() ) );
-        MapIt it2 = m_plans.find( PlanKey(nfft,!inverse) );
-        if (it2 != m_plans.end() ) {
-        it->second = it2.second;
-        it->second.conjugate();
-        }else{
-        it->second.make_twiddles(nfft,inverse);
-        it->second.factorize(nfft);
-        }
-        }
-        return it->second;
-        */
+        // 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);
@@ -421,5 +405,5 @@ namespace Eigen {
         for (int k=0;k<n;++k)
           dst[k] *= s;
       }
-  };
+    };
 }