//=============================================================
// Fast Fourier transform of DPoly to CDPoly
static CDPoly PolyFFT(const DPoly & p)
{
size_t n = p.Degree();
size_t nl = log2(n);
size_t j, k, m, m2, s;
DComplex wm, w, t, u;
CDPoly a = BitRevCopy(p);
m = 2;
m2 = 1;
for (s = 0; s < nl; ++s)
{
wm = exp(PI2I / double(m));
w = DComplex(1.0);
for (j = 0; j <= (m2 - 1); ++j)
{
for (k = j; k <= n - 1; k += m)
{
t = w * a[k + m2];
u = a[k];
a[k] = u + t;
a[k + m2] = u - t;
}
w *= wm;
}
m <<= 1;
m2 <<= 1;
}
return a;
}
void
// Translate the PSF to be for source at (x0,y0);
// ??need a sign flip here?
kTable::Translate(double x0, double y0) {
// convert to phases:
x0*=dk; y0*=dk;
// too big will just be wrapping around:
if (x0 > PI || y0 > PI) throw FFTOutofRange();
DComplex I(0.,1.);
DComplex dxphase=exp(DComplex(0.,x0));
DComplex dyphase=exp(DComplex(0.,y0));
DComplex phase(1.,0.);
DComplex yphase=1.;
DComplex z;
DComplex *zptr=array;
for (int i=0; i< N/2; i++) {
phase = yphase;
for (int j=0; j<= N/2 ; j++) {
z = *zptr;
*zptr = phase * z;
phase *= dxphase;
zptr++;
}
yphase *= dyphase;
}
// wrap to the negative ky's
yphase = exp(I*((-N/2)*y0));
for (int i=-N/2; i< 0; i++) {
phase = yphase;
for (int j=0; j<= N/2 ; j++) {
z = *zptr;
*zptr = phase* z;
phase *= dxphase;
zptr++;
}
yphase *= dyphase;
}
return;
}
//=============================================================
// performs a reverse-bit copy of a DPoly into a new CDPoly
static CDPoly BitRevCopy(const DPoly & p)
{
size_t n = p.Degree();
size_t b = log2(n);
CDPoly a(n);
for (size_t k = 0; k < n; ++k)
a[FlipBits(k,b)] = DComplex(p.Get(k));
return a;
}
