/*************************************************************************
Internal subroutine. Never call it directly!
-- ALGLIB --
Copyright 01.06.2009 by Bochkanov Sergey
*************************************************************************/
public static void fftr1dinvinternaleven(ref double[] a,
int n,
ref double[] buf,
ftbase.ftplan plan)
{
double x = 0;
double y = 0;
double t = 0;
int i = 0;
int n2 = 0;
ap.assert(n>0 & n%2==0, "FFTR1DInvInternalEven: incorrect N!");
//
// Special cases:
// * N=2
//
// After this block we assume that N is strictly greater than 2
//
if( n==2 )
{
x = 0.5*(a[0]+a[1]);
y = 0.5*(a[0]-a[1]);
a[0] = x;
a[1] = y;
return;
}
//
// inverse real FFT is reduced to the inverse real FHT,
// which is reduced to the forward real FHT,
// which is reduced to the forward real FFT.
//
// Don't worry, it is really compact and efficient reduction :)
//
n2 = n/2;
buf[0] = a[0];
for(i=1; i<=n2-1; i++)
{
x = a[2*i+0];
y = a[2*i+1];
buf[i] = x-y;
buf[n-i] = x+y;
}
buf[n2] = a[1];
fftr1dinternaleven(ref buf, n, ref a, plan);
a[0] = buf[0]/n;
t = (double)1/(double)n;
for(i=1; i<=n2-1; i++)
{
x = buf[2*i+0];
y = buf[2*i+1];
a[i] = t*(x-y);
a[n-i] = t*(x+y);
}
a[n2] = buf[1]/n;
}
/*************************************************************************
Internal subroutine. Never call it directly!
-- ALGLIB --
Copyright 01.06.2009 by Bochkanov Sergey
*************************************************************************/
public static void fftr1dinternaleven(ref double[] a,
int n,
ref double[] buf,
ftbase.ftplan plan)
{
double x = 0;
double y = 0;
int i = 0;
int n2 = 0;
int idx = 0;
complex hn = 0;
complex hmnc = 0;
complex v = 0;
int i_ = 0;
ap.assert(n>0 & n%2==0, "FFTR1DEvenInplace: incorrect N!");
//
// Special cases:
// * N=2
//
// After this block we assume that N is strictly greater than 2
//
if( n==2 )
{
x = a[0]+a[1];
y = a[0]-a[1];
a[0] = x;
a[1] = y;
return;
}
//
// even-size real FFT, use reduction to the complex task
//
n2 = n/2;
for(i_=0; i_<=n-1;i_++)
{
buf[i_] = a[i_];
}
ftbase.ftbaseexecuteplan(ref buf, 0, n2, plan);
a[0] = buf[0]+buf[1];
for(i=1; i<=n2-1; i++)
{
idx = 2*(i%n2);
hn.x = buf[idx+0];
hn.y = buf[idx+1];
idx = 2*(n2-i);
hmnc.x = buf[idx+0];
hmnc.y = -buf[idx+1];
v.x = -Math.Sin(-(2*Math.PI*i/n));
v.y = Math.Cos(-(2*Math.PI*i/n));
v = hn+hmnc-v*(hn-hmnc);
a[2*i+0] = 0.5*v.x;
a[2*i+1] = 0.5*v.y;
}
a[1] = buf[0]-buf[1];
}