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fourier_ndim.h
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fourier_ndim.h
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void fourn(Doub *data, VecInt_I &nn, const Int isign) {
Int idim,i1,i2,i3,i2rev,i3rev,ip1,ip2,ip3,ifp1,ifp2;
Int ibit,k1,k2,n,nprev,nrem,ntot=1,ndim=nn.size();
Doub tempi,tempr,theta,wi,wpi,wpr,wr,wtemp;
for (idim=0;idim<ndim;idim++) ntot *= nn[idim];
if (ntot<2 || ntot&(ntot-1)) throw("must have powers of 2 in fourn");
nprev=1;
for (idim=ndim-1;idim>=0;idim--) {
n=nn[idim];
nrem=ntot/(n*nprev);
ip1=nprev << 1;
ip2=ip1*n;
ip3=ip2*nrem;
i2rev=0;
for (i2=0;i2<ip2;i2+=ip1) {
if (i2 < i2rev) {
for (i1=i2;i1<i2+ip1-1;i1+=2) {
for (i3=i1;i3<ip3;i3+=ip2) {
i3rev=i2rev+i3-i2;
SWAP(data[i3],data[i3rev]);
SWAP(data[i3+1],data[i3rev+1]);
}
}
}
ibit=ip2 >> 1;
while (ibit >= ip1 && i2rev+1 > ibit) {
i2rev -= ibit;
ibit >>= 1;
}
i2rev += ibit;
}
ifp1=ip1;
while (ifp1 < ip2) {
ifp2=ifp1 << 1;
theta=isign*6.28318530717959/(ifp2/ip1);
wtemp=sin(0.5*theta);
wpr= -2.0*wtemp*wtemp;
wpi=sin(theta);
wr=1.0;
wi=0.0;
for (i3=0;i3<ifp1;i3+=ip1) {
for (i1=i3;i1<i3+ip1-1;i1+=2) {
for (i2=i1;i2<ip3;i2+=ifp2) {
k1=i2;
k2=k1+ifp1;
tempr=wr*data[k2]-wi*data[k2+1];
tempi=wr*data[k2+1]+wi*data[k2];
data[k2]=data[k1]-tempr;
data[k2+1]=data[k1+1]-tempi;
data[k1] += tempr;
data[k1+1] += tempi;
}
}
wr=(wtemp=wr)*wpr-wi*wpi+wr;
wi=wi*wpr+wtemp*wpi+wi;
}
ifp1=ifp2;
}
nprev *= n;
}
}
void fourn(VecDoub_IO &data, VecInt_I &nn, const Int isign) {
fourn(&data[0],nn,isign);
}
void rlft3(Doub *data, Doub *speq, const Int isign,
const Int nn1, const Int nn2, const Int nn3) {
Int i1,i2,i3,j1,j2,j3,k1,k2,k3,k4;
Doub theta,wi,wpi,wpr,wr,wtemp;
Doub c1,c2,h1r,h1i,h2r,h2i;
VecInt nn(3);
VecDoubp spq(nn1);
for (i1=0;i1<nn1;i1++) spq[i1] = speq + 2*nn2*i1;
c1 = 0.5;
c2 = -0.5*isign;
theta = isign*(6.28318530717959/nn3);
wtemp = sin(0.5*theta);
wpr = -2.0*wtemp*wtemp;
wpi = sin(theta);
nn[0] = nn1;
nn[1] = nn2;
nn[2] = nn3 >> 1;
if (isign == 1) {
fourn(data,nn,isign);
k1=0;
for (i1=0;i1<nn1;i1++)
for (i2=0,j2=0;i2<nn2;i2++,k1+=nn3) {
spq[i1][j2++]=data[k1];
spq[i1][j2++]=data[k1+1];
}
}
for (i1=0;i1<nn1;i1++) {
j1=(i1 != 0 ? nn1-i1 : 0);
wr=1.0;
wi=0.0;
for (i3=0;i3<=(nn3>>1);i3+=2) {
k1=i1*nn2*nn3;
k3=j1*nn2*nn3;
for (i2=0;i2<nn2;i2++,k1+=nn3) {
if (i3 == 0) {
j2=(i2 != 0 ? ((nn2-i2)<<1) : 0);
h1r=c1*(data[k1]+spq[j1][j2]);
h1i=c1*(data[k1+1]-spq[j1][j2+1]);
h2i=c2*(data[k1]-spq[j1][j2]);
h2r= -c2*(data[k1+1]+spq[j1][j2+1]);
data[k1]=h1r+h2r;
data[k1+1]=h1i+h2i;
spq[j1][j2]=h1r-h2r;
spq[j1][j2+1]=h2i-h1i;
} else {
j2=(i2 != 0 ? nn2-i2 : 0);
j3=nn3-i3;
k2=k1+i3;
k4=k3+j2*nn3+j3;
h1r=c1*(data[k2]+data[k4]);
h1i=c1*(data[k2+1]-data[k4+1]);
h2i=c2*(data[k2]-data[k4]);
h2r= -c2*(data[k2+1]+data[k4+1]);
data[k2]=h1r+wr*h2r-wi*h2i;
data[k2+1]=h1i+wr*h2i+wi*h2r;
data[k4]=h1r-wr*h2r+wi*h2i;
data[k4+1]= -h1i+wr*h2i+wi*h2r;
}
}
wr=(wtemp=wr)*wpr-wi*wpi+wr;
wi=wi*wpr+wtemp*wpi+wi;
}
}
if (isign == -1) fourn(data,nn,isign);
}
void rlft3(Mat3DDoub_IO &data, MatDoub_IO &speq, const Int isign) {
if (speq.nrows() != data.dim1() || speq.ncols() != 2*data.dim2())
throw("bad dims in rlft3");
rlft3(&data[0][0][0],&speq[0][0],isign,data.dim1(),data.dim2(),data.dim3());
}
void rlft3(MatDoub_IO &data, VecDoub_IO &speq, const Int isign) {
if (speq.size() != 2*data.nrows()) throw("bad dims in rlft3");
rlft3(&data[0][0],&speq[0],isign,1,data.nrows(),data.ncols());
}