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# RG_PG10F -- Fetch the 0 component of the fft.
real procedure rg_pg10f (fft, nxfft, nyfft)
real fft[nxfft,nyfft] #I array containing 2 real ffts
int nxfft #I x dimension of complex array
int nyfft #I y dimension of complex array
int xcen, ycen
begin
xcen = nxfft / 2 + 1
ycen = nyfft / 2 + 1
return (fft[xcen,ycen])
end
# RG_PG1NORM -- Estimate the normalization factor by computing the amplitude
# of the best fitting Gaussian. This routine may eventually be replaced by
# on which does a complete Gaussian fit. The Gaussian is assumed to be
# of the form g = a * exp (b * r * r). The input array is a 2D real array
# storing 1 fft of dimension nxfft by nyfft in complex order with the
# zero frequency in the center.
real procedure rg_pg1norm (fft, nxfft, nyfft)
real fft[nxfft,nyfft] #I array containing 2 real ffts
int nxfft #I x dimension of complex array
int nyfft #I y dimension of complex array
int xcen, ycen
real ln1, ln2, cx, cy
begin
xcen = nxfft / 2 + 1
ycen = nyfft / 2 + 1
if (nxfft >= 8) {
ln1 = log (sqrt (fft[xcen-2,ycen] ** 2 + fft[xcen-1,ycen] ** 2))
ln2 = log (sqrt (fft[xcen-4,ycen] ** 2 + fft[xcen-3,ycen] ** 2))
cx = exp ((4.0 * ln1 - ln2) / 3.0)
} else
cx = 0.0
if (nyfft >= 4) {
ln1 = log (sqrt (fft[xcen,ycen-1] ** 2 + fft[xcen+1,ycen-1] ** 2))
ln2 = log (sqrt (fft[xcen,ycen-2] ** 2 + fft[xcen+1,ycen-2] ** 2))
cy = exp ((4.0 * ln1 - ln2) / 3.0)
} else
cy = 0.0
if (cx <= 0.0)
return (cy)
else if (cy <= 0.0)
return (cx)
else
return (0.5 * (cx + cy))
end
# RG_PG20F -- Fetch the 0 component of the fft.
real procedure rg_pg20f (fft, nxfft, nyfft)
real fft[nxfft,nyfft] #I array containing 2 real ffts
int nxfft #I x dimension of complex array
int nyfft #I y dimension of complex array
int xcen, ycen
begin
xcen = nxfft / 2 + 1
ycen = nyfft / 2 + 1
return (fft[xcen,ycen] / fft[xcen+1,ycen])
end
# RG_PG2NORM -- Estimate the normalization factor by computing the amplitude
# of the best fitting Gaussian. This routine may eventually be replaced by
# on which does a complete Gaussian fit. The Gaussian is assumed to be
# of the form g = a * exp (b * r * r). The input array is a 2D real array
# storing 2 2D ffts of dimension nxfft by nyfft in complex order with the
# zero frequency in the center.
real procedure rg_pg2norm (fft, nxfft, nyfft)
real fft[nxfft,nyfft] #I array containing 2 real ffts
int nxfft #I x dimension of complex array
int nyfft #I y dimension of complex array
int xcen, ycen
real fftr, ffti, ln1r, ln2r, ln1i, ln2i, cxr, cyr, cxi, cyi, ampr, ampi
begin
xcen = nxfft / 2 + 1
ycen = nyfft / 2 + 1
# Compute the x amplitude for the first fft.
if (nxfft >= 8) {
fftr = 0.5 * (fft[xcen+2,ycen] + fft[xcen-2,ycen])
ffti = 0.5 * (fft[xcen+3,ycen] - fft[xcen-1,ycen])
ln1r = log (sqrt (fftr ** 2 + ffti ** 2))
fftr = 0.5 * (fft[xcen+4,ycen] + fft[xcen-4,ycen])
ffti = 0.5 * (fft[xcen+5,ycen] - fft[xcen-3,ycen])
ln2r = log (sqrt (fftr ** 2 + ffti ** 2))
fftr = 0.5 * (fft[xcen+3,ycen] + fft[xcen-1,ycen])
ffti = -0.5 * (fft[xcen+2,ycen] - fft[xcen-2,ycen])
ln1i = log (sqrt (fftr ** 2 + ffti ** 2))
fftr = 0.5 * (fft[xcen+5,ycen] + fft[xcen-3,ycen])
ffti = -0.5 * (fft[xcen+4,ycen] - fft[xcen-4,ycen])
ln2i = log (sqrt (fftr ** 2 + ffti ** 2))
cxr = exp ((4.0 * ln1r - ln2r) / 3.0)
cxi = exp ((4.0 * ln1i - ln2i) / 3.0)
} else {
cxr = 0.0
cxi = 0.0
}
# Compute the y ratio.
if (nyfft >= 4) {
fftr = 0.5 * (fft[xcen,ycen+1] + fft[xcen,ycen-1])
ffti = 0.5 * (fft[xcen+1,ycen+1] - fft[xcen+1,ycen-1])
ln1r = log (sqrt (fftr ** 2 + ffti ** 2))
fftr = 0.5 * (fft[xcen,ycen+2] + fft[xcen,ycen-2])
ffti = 0.5 * (fft[xcen+1,ycen+2] - fft[xcen+1,ycen-2])
ln2r = log (sqrt (fftr ** 2 + ffti ** 2))
fftr = 0.5 * (fft[xcen+1,ycen+1] + fft[xcen+1,ycen-1])
ffti = -0.5 * (fft[xcen,ycen+1] - fft[xcen,ycen-1])
ln1i = log (sqrt (fftr ** 2 + ffti ** 2))
fftr = 0.5 * (fft[xcen+1,ycen+2] + fft[xcen+1,ycen-2])
ffti = -0.5 * (fft[xcen,ycen+2] - fft[xcen,ycen-2])
ln2i = log (sqrt (fftr ** 2 + ffti ** 2))
cyr = exp ((4.0 * ln1r - ln2r) / 3.0)
cyi = exp ((4.0 * ln1i - ln2i) / 3.0)
} else {
cyr = 0.0
cyi = 0.0
}
if (cxr <= 0.0)
ampr = cyr
else if (cyr <= 0.0)
ampr = cxr
else
ampr = 0.5 * (cxr + cyr)
if (cxi <= 0.0)
ampi = cyi
else if (cyi <= 0.0)
ampi = cxi
else
ampi = 0.5 * (cxi + cyi)
if (ampi <= 0.0)
return (INDEFR)
else
return (ampr /ampi)
end
# RG_PDIVFFT -- Unpack the two fft's, save the first fft, and compute the
# quotient of the two ffts.
procedure rg_pdivfft (fft1, fftnum, fftdenom, fft2, nxfft, nyfft)
real fft1[nxfft,nyfft] # array containing 2 ffts of 2 real functions
real fftnum[nxfft,nyfft] # the numerator fft
real fftdenom[nxfft,nyfft] # the denominator fft
real fft2[nxfft,nyfft] # fft of psf matching function
int nxfft, nyfft # dimensions of fft
int i, j, xcen, ycen, nxp2, nxp3, nyp2
real c1, c2, h1r, h1i, h2r, h2i, denom
begin
c1 = 0.5
c2 = -0.5
xcen = nxfft / 2 + 1
ycen = nyfft / 2 + 1
nxp2 = nxfft + 2
nxp3 = nxfft + 3
nyp2 = nyfft + 2
# Compute the 0 frequency point.
h1r = fft1[xcen,ycen]
h1i = 0.0
h2r = fft1[xcen+1,ycen]
h2i = 0.0
fftnum[xcen,ycen] = h1r
fftnum[xcen+1,ycen] = 0.0
fftdenom[xcen,ycen] = h2r
fftdenom[xcen+1,ycen] = 0.0
fft2[xcen,ycen] = h1r / h2r
fft2[xcen+1,ycen] = 0.0
#call eprintf ("fft11=%g fft21=%g\n")
#call pargr (fft1[1,1])
#call pargr (fft1[2,1])
# Compute the first point.
h1r = c1 * (fft1[1,1] + fft1[1,1])
h1i = 0.0
h2r = -c2 * (fft1[2,1] + fft1[2,1])
h2i = 0.0
fftnum[1,1] = h1r
fftnum[2,1] = h1i
fftdenom[1,1] = h2r
fftdenom[2,1] = h2i
denom = h2r * h2r + h2i * h2i
if (denom == 0.0) {
fft2[1,1] = 1.0
fft2[2,1] = 0.0
} else {
fft2[1,1] = (h1r * h2r + h1i * h2i) / denom
fft2[2,1] = (h1i * h2r - h2i * h1r) / denom
}
# Compute the x symmetry axis points.
do i = 3, xcen - 1, 2 {
h1r = c1 * (fft1[i,ycen] + fft1[nxp2-i,ycen])
h1i = c1 * (fft1[i+1,ycen] - fft1[nxp3-i,ycen])
h2r = -c2 * (fft1[i+1,ycen] + fft1[nxp3-i,ycen])
h2i = c2 * (fft1[i,ycen] - fft1[nxp2-i,ycen])
fftnum[i,ycen] = h1r
fftnum[i+1,ycen] = h1i
fftnum[nxp2-i,ycen] = h1r
fftnum[nxp3-i,ycen] = -h1i
fftdenom[i,ycen] = h2r
fftdenom[i+1,ycen] = h2i
fftdenom[nxp2-i,ycen] = h2r
fftdenom[nxp3-i,ycen] = -h2i
denom = h2r * h2r + h2i * h2i
if (denom == 0.0) {
fft2[i,ycen] = 1.0
fft2[i+1,ycen] = 0.0
} else {
fft2[i,ycen] = (h1r * h2r + h1i * h2i) / denom
fft2[i+1,ycen] = (h1i * h2r - h2i * h1r) / denom
}
fft2[nxp2-i,ycen] = fft2[i,ycen]
fft2[nxp3-i,ycen] = -fft2[i+1,ycen]
}
# Quit if the transform is 1D.
if (nyfft < 2)
return
# Compute the x axis points.
do i = 3, xcen + 1, 2 {
h1r = c1 * (fft1[i,1] + fft1[nxp2-i,1])
h1i = c1 * (fft1[i+1,1] - fft1[nxp3-i,1])
h2r = -c2 * (fft1[i+1,1] + fft1[nxp3-i,1])
h2i = c2 * (fft1[i,1] - fft1[nxp2-i,1])
fftnum[i,1] = h1r
fftnum[i+1,1] = h1i
fftnum[nxp2-i,1] = h1r
fftnum[nxp3-i,1] = -h1i
fftdenom[i,1] = h2r
fftdenom[i+1,1] = h2i
fftdenom[nxp2-i,1] = h2r
fftdenom[nxp3-i,1] = -h2i
denom = h2r * h2r + h2i * h2i
if (denom == 0) {
fft2[i,1] = 1.0
fft2[i+1,1] = 0.0
} else {
fft2[i,1] = (h1r * h2r + h1i * h2i) / denom
fft2[i+1,1] = (h1i * h2r - h2i * h1r) / denom
}
fft2[nxp2-i,1] = fft2[i,1]
fft2[nxp3-i,1] = -fft2[i+1,1]
}
# Compute the y symmetry axis points.
do i = 2, ycen - 1 {
h1r = c1 * (fft1[xcen,i] + fft1[xcen, nyp2-i])
h1i = c1 * (fft1[xcen+1,i] - fft1[xcen+1,nyp2-i])
h2r = -c2 * (fft1[xcen+1,i] + fft1[xcen+1,nyp2-i])
h2i = c2 * (fft1[xcen,i] - fft1[xcen,nyp2-i])
fftnum[xcen,i] = h1r
fftnum[xcen+1,i] = h1i
fftnum[xcen,nyp2-i] = h1r
fftnum[xcen+1,nyp2-i] = -h1i
fftdenom[xcen,i] = h2r
fftdenom[xcen+1,i] = h2i
fftdenom[xcen,nyp2-i] = h2r
fftdenom[xcen+1,nyp2-i] = -h2i
denom = h2r * h2r + h2i * h2i
if (denom == 0.0) {
fft2[xcen,i] = 1.0
fft2[xcen+1,i] = 0.0
} else {
fft2[xcen,i] = (h1r * h2r + h1i * h2i) / denom
fft2[xcen+1,i] = (h1i * h2r - h2i * h1r) / denom
}
fft2[xcen,nyp2-i] = fft2[xcen,i]
fft2[xcen+1,nyp2-i] = -fft2[xcen+1,i]
}
# Compute the y axis points.
do i = 2, ycen {
h1r = c1 * (fft1[1,i] + fft1[1,nyp2-i])
h1i = c1 * (fft1[2,i] - fft1[2,nyp2-i])
h2r = -c2 * (fft1[2,i] + fft1[2,nyp2-i])
h2i = c2 * (fft1[1,i] - fft1[1,nyp2-i])
fftnum[1,i] = h1r
fftnum[2,i] = h1i
fftnum[1,nyp2-i] = h1r
fftnum[2,nyp2-i] = -h1i
fftdenom[1,i] = h2r
fftdenom[2,i] = h2i
fftdenom[1,nyp2-i] = h2r
fftdenom[2,nyp2-i] = -h2i
denom = h2r * h2r + h2i * h2i
if (denom == 0.0) {
fft2[1,i] = 1.0
fft2[2,i] = 0.0
} else {
fft2[1,i] = (h1r * h2r + h1i * h2i) / denom
fft2[2,i] = (h1i * h2r - h2i * h1r) / denom
}
fft2[1,nyp2-i] = fft2[1,i]
fft2[2,nyp2-i] = -fft2[2,i]
}
# Compute the remainder of the transform.
do j = 2, ycen - 1 {
do i = 3, xcen - 1, 2 {
h1r = c1 * (fft1[i,j] + fft1[nxp2-i, nyp2-j])
h1i = c1 * (fft1[i+1,j] - fft1[nxp3-i,nyp2-j])
h2r = -c2 * (fft1[i+1,j] + fft1[nxp3-i,nyp2-j])
h2i = c2 * (fft1[i,j] - fft1[nxp2-i,nyp2-j])
fftnum[i,j] = h1r
fftnum[i+1,j] = h1i
fftnum[nxp2-i,nyp2-j] = h1r
fftnum[nxp3-i,nyp2-j] = -h1i
fftdenom[i,j] = h2r
fftdenom[i+1,j] = h2i
fftdenom[nxp2-i,nyp2-j] = h2r
fftdenom[nxp3-i,nyp2-j] = -h2i
denom = h2r * h2r + h2i * h2i
if (denom == 0.0) {
fft2[i,j] = 1.0
fft2[i+1,j] = 0.0
} else {
fft2[i,j] = (h1r * h2r + h1i * h2i) / denom
fft2[i+1,j] = (h1i * h2r - h2i * h1r) / denom
}
fft2[nxp2-i,nyp2-j] = fft2[i,j]
fft2[nxp3-i,nyp2-j] = - fft2[i+1,j]
}
do i = xcen + 2, nxfft, 2 {
h1r = c1 * (fft1[i,j] + fft1[nxp2-i, nyp2-j])
h1i = c1 * (fft1[i+1,j] - fft1[nxp3-i,nyp2-j])
h2r = -c2 * (fft1[i+1,j] + fft1[nxp3-i,nyp2-j])
h2i = c2 * (fft1[i,j] - fft1[nxp2-i,nyp2-j])
fftnum[i,j] = h1r
fftnum[i+1,j] = h1i
fftnum[nxp2-i,nyp2-j] = h1r
fftnum[nxp3-i,nyp2-j] = -h1i
fftdenom[i,j] = h2r
fftdenom[i+1,j] = h2i
fftdenom[nxp2-i,nyp2-j] = h2r
fftdenom[nxp3-i,nyp2-j] = -h2i
denom = h2r * h2r + h2i * h2i
if (denom == 0.0) {
fft2[i,j] = 1.0
fft2[i+1,j] = 0.0
} else {
fft2[i,j] = (h1r * h2r + h1i * h2i) / denom
fft2[i+1,j] = (h1i * h2r - h2i * h1r) / denom
}
fft2[nxp2-i,nyp2-j] = fft2[i,j]
fft2[nxp3-i,nyp2-j] = - fft2[i+1,j]
}
}
end
# RG_PNORM -- Insert the normalization value into the 0 frequency of the
# fft. The fft is a 2D fft stored in a real array in complex order.
# The fft is assumed to be centered.
procedure rg_pnorm (fft, nxfft, nyfft, norm)
real fft[ARB] #I the input fft
int nxfft #I the x dimension of fft (complex storage)
int nyfft #I the y dimension of the fft
real norm #I the flux ratio
int index
begin
index = nxfft + 1 + 2 * (nyfft / 2) * nxfft
fft[index] = norm
fft[index+1] = 0.0
end
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