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);
}
}
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;
}
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++; }
}
//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;
}
//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;
}