Exemple #1
0
void RealFFT(const ColumnVector& U, ColumnVector& X, ColumnVector& Y)
{
   // Fourier transform of a real series
   Tracer trace("RealFFT");
   REPORT
   const int n = U.Nrows();                     // length of arrays
   const int n2 = n / 2;
   if (n != 2 * n2)
      Throw(ProgramException("Vector length not multiple of 2", U));
   ColumnVector A(n2), B(n2);
   Real* a = A.Store(); Real* b = B.Store(); Real* u = U.Store(); int i = n2;
   while (i--) { *a++ = *u++; *b++ = *u++; }
   FFT(A,B,A,B);
   int n21 = n2 + 1;
   X.ReSize(n21); Y.ReSize(n21);
   i = n2 - 1;
   a = A.Store(); b = B.Store();              // first els of A and B
   Real* an = a + i; Real* bn = b + i;        // last els of A and B
   Real* x = X.Store(); Real* y = Y.Store();  // first els of X and Y
   Real* xn = x + n2; Real* yn = y + n2;      // last els of X and Y

   *x++ = *a + *b; *y++ = 0.0;                // first complex element
   *xn-- = *a++ - *b++; *yn-- = 0.0;          // last complex element

   int j = -1; i = n2/2;
   while (i--)
   {
      Real c,s; cossin(j--,n,c,s);
      Real am = *a - *an; Real ap = *a++ + *an--;
      Real bm = *b - *bn; Real bp = *b++ + *bn--;
      Real samcbp = s * am + c * bp; Real sbpcam = s * bp - c * am;
      *x++  =  0.5 * ( ap + samcbp); *y++  =  0.5 * ( bm + sbpcam);
      *xn-- =  0.5 * ( ap - samcbp); *yn-- =  0.5 * (-bm + sbpcam);
   }
}
Exemple #2
0
void FFT(const ColumnVector& U, const ColumnVector& V,
   ColumnVector& X, ColumnVector& Y)
{
   // from Carl de Boor (1980), Siam J Sci Stat Comput, 1 173-8
   // but first try Sande and Gentleman
   Tracer trace("FFT");
   REPORT
   const int n = U.Nrows();                     // length of arrays
   if (n != V.Nrows() || n == 0)
      Throw(ProgramException("Vector lengths unequal or zero", U, V));
   if (n == 1) { REPORT X = U; Y = V; return; }

   // see if we can use the newfft routine
   if (!FFT_Controller::OnlyOldFFT && FFT_Controller::CanFactor(n))
   {
      REPORT
      X = U; Y = V;
      if ( FFT_Controller::ar_1d_ft(n,X.Store(),Y.Store()) ) return;
   }

   ColumnVector B = V;
   ColumnVector A = U;
   X.ReSize(n); Y.ReSize(n);
   const int nextmx = 8;
#ifndef ATandT
   int prime[8] = { 2,3,5,7,11,13,17,19 };
#else
   int prime[8];
   prime[0]=2; prime[1]=3; prime[2]=5; prime[3]=7;
   prime[4]=11; prime[5]=13; prime[6]=17; prime[7]=19;
#endif
   int after = 1; int before = n; int next = 0; bool inzee = true;
   int now = 0; int b1;             // initialised to keep gnu happy

   do
   {
      for (;;)
      {
     if (next < nextmx) { REPORT now = prime[next]; }
     b1 = before / now;  if (b1 * now == before) { REPORT break; }
     next++; now += 2;
      }
      before = b1;

      if (inzee) { REPORT fftstep(A, B, X, Y, after, now, before); }
      else { REPORT fftstep(X, Y, A, B, after, now, before); }

      inzee = !inzee; after *= now;
   }
Exemple #3
0
void RealFFTI(const ColumnVector& A, const ColumnVector& B, ColumnVector& U)
{
   // inverse of a Fourier transform of a real series
   Tracer trace("RealFFTI");
   REPORT
   const int n21 = A.Nrows();                     // length of arrays
   if (n21 != B.Nrows() || n21 == 0)
      Throw(ProgramException("Vector lengths unequal or zero", A, B));
   const int n2 = n21 - 1;  const int n = 2 * n2;  int i = n2 - 1;

   ColumnVector X(n2), Y(n2);
   Real* a = A.Store(); Real* b = B.Store();  // first els of A and B
   Real* an = a + n2;   Real* bn = b + n2;    // last els of A and B
   Real* x = X.Store(); Real* y = Y.Store();  // first els of X and Y
   Real* xn = x + i;    Real* yn = y + i;     // last els of X and Y

   Real hn = 0.5 / n2;
   *x++  = hn * (*a + *an);  *y++  = - hn * (*a - *an);
   a++; an--; b++; bn--;
   int j = -1;  i = n2/2;
   while (i--)
   {
      Real c,s; cossin(j--,n,c,s);
      Real am = *a - *an; Real ap = *a++ + *an--;
      Real bm = *b - *bn; Real bp = *b++ + *bn--;
      Real samcbp = s * am - c * bp; Real sbpcam = s * bp + c * am;
      *x++  =  hn * ( ap + samcbp); *y++  =  - hn * ( bm + sbpcam);
      *xn-- =  hn * ( ap - samcbp); *yn-- =  - hn * (-bm + sbpcam);
   }
   FFT(X,Y,X,Y);             // have done inverting elsewhere
   U.ReSize(n); i = n2;
   x = X.Store(); y = Y.Store(); Real* u = U.Store();
   while (i--) { *u++ = *x++; *u++ = - *y++; }
}
Exemple #4
0
//Predict on a chunk of data.
ReturnMatrix SOGP::predictM(const Matrix& in, ColumnVector &sigconf,bool conf){
  //printf("SOGP::Predicting on %d points\n",in.Ncols());
  Matrix out(alpha.Ncols(),in.Ncols());
  sigconf.ReSize(in.Ncols());
  for(int c=1;c<=in.Ncols();c++)
    out.Column(c) = predict(in.Column(c),sigconf(c),conf);
  out.Release();
  return out;
}
static void SlowFT(const ColumnVector& a, const ColumnVector&b,
   ColumnVector& x, ColumnVector& y)
{
   int n = a.Nrows();
   x.ReSize(n); y.ReSize(n);
   Real f = 6.2831853071795864769/n;
   for (int j=1; j<=n; j++)
   {
      Real sumx = 0.0; Real sumy = 0.0;
      for (int k=1; k<=n; k++)
      {
	 Real theta = - (j-1) * (k-1) * f;
	 Real c = cos(theta); Real s = sin(theta);
	 sumx += c * a(k) - s * b(k); sumy += s * a(k) + c * b(k);
      }
      x(j) = sumx; y(j) = sumy;
   }
}
static void SlowDTT_II(const ColumnVector& a, ColumnVector& c, ColumnVector& s)
{
   int n = a.Nrows(); c.ReSize(n); s.ReSize(n);
   Real f = 6.2831853071795864769 / (4*n);
   int k;

   for (k=1; k<=n; k++)
   {
      Real sum = 0.0;
      const int k1 = k-1;              // otherwise Visual C++ 5 fails
      for (int j=1; j<=n; j++) sum += cos(k1 * (2*j-1) * f) * a(j);
      c(k) = sum;
   }

   for (k=1; k<=n; k++)
   {
      Real sum = 0.0;
      for (int j=1; j<=n; j++) sum += sin(k * (2*j-1) * f) * a(j);
      s(k) = sum;
   }
}
static void SlowDTT(const ColumnVector& a, ColumnVector& c, ColumnVector& s)
{
   int n1 = a.Nrows(); int n = n1 - 1;
   c.ReSize(n1); s.ReSize(n1);
   Real f = 6.2831853071795864769 / (2*n);
   int k;

   int sign = 1;
   for (k=1; k<=n1; k++)
   {
      Real sum = 0.0;
      for (int j=2; j<=n; j++) sum += cos((j-1) * (k-1) * f) * a(j);
      c(k) = sum + (a(1) + sign * a(n1)) / 2.0;
      sign = -sign;
   }

   for (k=2; k<=n; k++)
   {
      Real sum = 0.0;
      for (int j=2; j<=n; j++) sum += sin((j-1) * (k-1) * f) * a(j);
      s(k) = sum;
   }
   s(1) = s(n1) = 0;
}
Exemple #8
0
//Predict the output and uncertainty for this input.
ReturnMatrix SOGP::predict(const ColumnVector& in, double &sigma,bool conf){
  double kstar = m_params.m_kernel->kstar(in);
  ColumnVector k=m_params.m_kernel->kernelM(in,BV);

  ColumnVector out;
  if(current_size==0){
    sigma = kstar+m_params.s20;
    //We don't actually know the correct output dimensionality
    //So return nothing.
    out.ReSize(0);
  }
  else{
    out=(k.t()*alpha).t();//Page 33
    sigma=m_params.s20 + kstar + (k.t()*C*k).AsScalar();//Ibid..needs s2 from page 19
  }
  
  if(sigma<0){//Numerical instability?
    printf("SOGP:: sigma (%lf) < 0!\n",sigma);
    sigma=0;
  }

  //Switch to a confidence (0-100)
  if(conf){
    //Normalize to one
    sigma /= kstar+m_params.s20;
    //switch diretion
    sigma = 1-sigma;
    //and times 100;
    sigma *=100;
    //sigma = (1-sigma)*100;
  }
  else
    sigma=sqrt(sigma);
    
  out.Release();
  return out;

}
bool SpectClust::MaxEigen(const Matrix &M, double &maxValue, ColumnVector &MaxVec, int maxIterations) {
  double maxDelta = 1e-6;
  bool converged = false;
  int i = 0;
  int nRows = M.Ncols();
  if(M.Ncols() != M.Nrows()) 
    Err::errAbort("MaxEigen() - Can't get eigen values of non square matrices.");
  if(M.Ncols() <= 0) 
    Err::errAbort("MaxEigen() - Must have positive number of rows and columns.");
  ColumnVector V(M.Ncols());
  V = 1.0 / M.Nrows(); // any vector really...
  V = V / Norm1(V);
  MaxVec.ReSize(M.Ncols());
  for(i = 0; i < maxIterations; ++i) {
    //    MaxVec = M * V;
    multByMatrix(MaxVec, V, M);
    double delta = 0;
    double norm = sqrt(SumSquare(MaxVec));
    for(int vIx = 0; vIx < nRows; vIx++) {
      MaxVec.element(vIx) = MaxVec.element(vIx) / norm; // scale so we don't get too big.
    }
    for(int rowIx = 0; rowIx < nRows; rowIx++) {
      delta += fabs((double)MaxVec.element(rowIx) - V.element(rowIx));
    }
    if(delta < maxDelta)  
      break; // we've already converged to eigen vector.
    V = MaxVec;
  }
  if(i < maxIterations) {
    converged = true;
  }
  // calculate approximate max eigen value using Rayleigh quotient (x'*M*x/x'*x).
  Matrix num = (MaxVec.t() * M * MaxVec);
  Matrix denom =  (MaxVec.t() * MaxVec);
  maxValue = num.element(0,0) / denom.element(0,0);
  return converged;
}