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# RG_SZFFT -- Compute the size of the required FFT given the dimension of the
# image the window size and the fact that the FFT must be a power of 2.
int procedure rg_szfft (npts, window)
int npts #I the number of points in the data
int window #I the width of the valid cross correlation
int nfft, pow2
begin
nfft = npts + window / 2
pow2 = 2
while (pow2 < nfft)
pow2 = pow2 * 2
return (pow2)
end
# RG_RLOAD -- Procedure to load a real array into the real part of a complex
# array.
procedure rg_rload (buf, ncols, nlines, fft, nxfft, nyfft)
real buf[ARB] #I the input data buffer
int ncols, nlines #I the size of the input buffer
real fft[ARB] #O the out array to be fft'd
int nxfft, nyfft #I the dimensions of the fft
int i, dindex, findex
begin
# Load the reference and image data.
dindex = 1
findex = 1
do i = 1, nlines {
call rg_rweave (buf[dindex], fft[findex], ncols)
dindex = dindex + ncols
findex = findex + 2 * nxfft
}
end
# RG_ILOAD -- Procedure to load a real array into the complex part of a complex
# array.
procedure rg_iload (buf, ncols, nlines, fft, nxfft, nyfft)
real buf[ARB] #I the input data buffer
int ncols, nlines #I the size of the input buffer
real fft[ARB] #O the output array to be fft'd
int nxfft, nyfft #I the dimensions of the fft
int i, dindex, findex
begin
# Load the reference and image data.
dindex = 1
findex = 1
do i = 1, nlines {
call rg_iweave (buf[dindex], fft[findex], ncols)
dindex = dindex + ncols
findex = findex + 2 * nxfft
}
end
# RG_RWEAVE -- Weave a real array into the real part of a complex array.
# The output array must be twice as long as the input array.
procedure rg_rweave (a, b, npts)
real a[ARB] #I input array
real b[ARB] #O output array
int npts #I the number of data points
int i
begin
do i = 1, npts
b[2*i-1] = a[i]
end
# RG_IWEAVE -- Weave a real array into the complex part of a complex array.
# The output array must be twice as long as the input array.
procedure rg_iweave (a, b, npts)
real a[ARB] #I the input array
real b[ARB] #O the output array
int npts #I the number of data points
int i
begin
do i = 1, npts
b[2*i] = a[i]
end
# RG_FOURN -- Replaces datas by its n-dimensional discreter Fourier transform,
# if isign is input as 1. NN is an integer array of length ndim containing
# the lengths of each dimension (number of complex values), which must all
# be powers of 2. Data is a real array of length twice the product of these
# lengths, in which the data are stored as in a multidimensional complex
# Fortran array. If isign is input as -1, data is replaced by its inverse
# transform times the product of the lengths of all dimensions.
procedure rg_fourn (data, nn, ndim, isign)
real data[ARB] #I/O input data and output fft
int nn[ndim] #I array of dimension lengths
int ndim #I number of dimensions
int isign #I forward or inverse transform
int idim, i1, i2, i3, ip1, ip2, ip3, ifp1, ifp2, i2rev, i3rev, k1, k2
int ntot, nprev, n, nrem, pibit
double wr, wi, wpr, wpi, wtemp, theta
real tempr, tempi
begin
ntot = 1
do idim = 1, ndim
ntot = ntot * nn[idim]
nprev = 1
do idim = 1, ndim {
n = nn[idim]
nrem = ntot / (n * nprev)
ip1 = 2 * nprev
ip2 = ip1 * n
ip3 = ip2 * nrem
i2rev = 1
do i2 = 1, ip2, ip1 {
if (i2 < i2rev) {
do i1 = i2, i2 + ip1 - 2, 2 {
do i3 = i1, ip3, ip2 {
i3rev = i2rev + i3 - i2
tempr = data [i3]
tempi = data[i3+1]
data[i3] = data[i3rev]
data[i3+1] = data[i3rev+1]
data[i3rev] = tempr
data[i3rev+1] = tempi
}
}
}
pibit = ip2 / 2
while ((pibit >= ip1) && (i2rev > pibit)) {
i2rev = i2rev - pibit
pibit = pibit / 2
}
i2rev = i2rev + pibit
}
ifp1 = ip1
while (ifp1 < ip2) {
ifp2 = 2 * ifp1
theta = isign * 6.28318530717959d0 / (ifp2 / ip1)
wpr = - 2.0d0 * dsin (0.5d0 * theta) ** 2
wpi = dsin (theta)
wr = 1.0d0
wi = 0.0d0
do i3 = 1, ifp1, ip1 {
do i1 = i3, i3 + ip1 - 2, 2 {
do i2 = i1, ip3, ifp2 {
k1 = i2
k2 = k1 + ifp1
tempr = sngl (wr) * data[k2] - sngl (wi) *
data[k2+1]
tempi = sngl (wr) * data[k2+1] + sngl (wi) *
data[k2]
data[k2] = data[k1] - tempr
data[k2+1] = data[k1+1] - tempi
data[k1] = data[k1] + tempr
data[k1+1] = data[k1+1] + tempi
}
}
wtemp = wr
wr = wr * wpr - wi * wpi + wr
wi = wi * wpr + wtemp * wpi + wi
}
ifp1 = ifp2
}
nprev = n * nprev
}
end
# RG_FSHIFT -- Center the array after doing the FFT.
procedure rg_fshift (fft1, fft2, nx, ny)
real fft1[nx,ARB] #I input fft array
real fft2[nx,ARB] #O output fft array
int nx, ny #I fft array dimensions
int i, j
real fac
begin
fac = 1.0
do j = 1, ny {
do i = 1, nx, 2 {
fft2[i,j] = fac * fft1[i,j]
fft2[i+1,j] = fac * fft1[i+1,j]
fac = -fac
}
fac = -fac
}
end
# RG_MOVEXR -- Extract the portion of the FFT for which the computed lags
# are valid. The dimensions of the the FFT are a power of two
# and the 0 frequency is in the position nxfft / 2 + 1, nyfft / 2 + 1.
procedure rg_movexr (fft, nxfft, nyfft, xcor, xwindow, ywindow)
real fft[ARB] #I the input fft
int nxfft, nyfft #I the dimensions of the input fft
real xcor[ARB] #O the output cross-correlation function
int xwindow, ywindow #I the cross-correlation function window
int j, ix, iy, findex, xindex
begin
# Compute the starting index of the extraction array.
ix = 1 + nxfft - 2 * (xwindow / 2)
iy = 1 + nyfft / 2 - ywindow / 2
# Copy the real part of the Fourier transform into the
# cross-correlation array.
findex = ix + 2 * nxfft * (iy - 1)
xindex = 1
do j = 1, ywindow {
call rg_extract (fft[findex], xcor[xindex], xwindow)
findex = findex + 2 * nxfft
xindex = xindex + xwindow
}
end
# RG_EXTRACT -- Extract the real part of a complex array.
procedure rg_extract (a, b, npts)
real a[ARB] #I the input array
real b[ARB] #O the output array
int npts #I the number of data points
int i
begin
do i = 1, npts
b[i] = a[2*i-1]
end
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