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# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
include <math.h>
# II_PCPOLY3 -- Procedure to evaluate the polynomial coefficients
# of third order in x and y using Everetts formuala.
procedure ii_pcpoly3 (coeff, index, len_coeff, pcoeff, len_pcoeff)
real coeff[ARB] # 1D array of interpolant coeffcients
int index # pointer into coeff array
int len_coeff # row length of coeffcients
real pcoeff[len_pcoeff,ARB] # polynomial coefficients
int len_pcoeff # row length of pcoeff
int tptr
int i, j
real cd20, cd21, temp[4]
begin
# determine polynomial coefficients in x
tptr = index
do i = 1, 4 {
# calculate the central differences
cd20 = 1./6. * (coeff[tptr+1] - 2. * coeff[tptr] + coeff[tptr-1])
cd21 = 1./6. * (coeff[tptr+2] - 2. * coeff[tptr+1] + coeff[tptr])
# calculate the polynomial coefficients in x at each y
pcoeff[1,i] = coeff[tptr]
pcoeff[2,i] = coeff[tptr+1] - coeff[tptr] - 2. * cd20 - cd21
pcoeff[3,i] = 3. * cd20
pcoeff[4,i] = cd21 - cd20
tptr = tptr + len_coeff
}
# calculate polynomial coefficients in y
do j = 1, 4 {
# calculate the central differences
cd20 = 1./6. * (pcoeff[j,3] - 2. * pcoeff[j,2] + pcoeff[j,1])
cd21 = 1./6. * (pcoeff[j,4] - 2. * pcoeff[j,3] + pcoeff[j,2])
# calculate the final coefficients
temp[1] = pcoeff[j,2]
temp[2] = pcoeff[j,3] - pcoeff[j,2] - 2. * cd20 - cd21
temp[3] = 3. * cd20
temp[4] = cd21 - cd20
do i = 1, 4
pcoeff[j,i] = temp[i]
}
end
# II_PCPOLY5 -- Procedure to evaluate the polynomial coefficients
# of fifth order in x and y using Everetts formuala.
procedure ii_pcpoly5 (coeff, index, len_coeff, pcoeff, len_pcoeff)
real coeff[ARB] # 1D array of interpolant coeffcients
int index # pointer into coeff array
int len_coeff # row length of coeffcients
real pcoeff[len_pcoeff,ARB] # polynomial coefficients
int len_pcoeff # row length of pcoeff array
int tptr
int i, j
real cd20, cd21, cd40, cd41, temp[6]
begin
# determine polynomial coefficients in x
tptr = index
do i = 1, 6 {
# calculate the central differences
cd20 = 1./6. * (coeff[tptr+1] - 2. * coeff[tptr] + coeff[tptr-1])
cd21 = 1./6. * (coeff[tptr+2] - 2. * coeff[tptr+1] + coeff[tptr])
cd40 = 1./120. * (coeff[tptr-2] - 4. * coeff[tptr-1] +
6. * coeff[tptr] - 4. * coeff[tptr+1] +
coeff[tptr+2])
cd41 = 1./120. * (coeff[tptr-1] - 4. * coeff[tptr] +
6. * coeff[tptr+1] - 4. * coeff[tptr+2] +
coeff[tptr+3])
# calculate coefficients in x for each y
pcoeff[1,i] = coeff[tptr]
pcoeff[2,i] = coeff[tptr+1] - coeff[tptr] - 2. * cd20 - cd21 +
6. * cd40 + 4. * cd41
pcoeff[3,i] = 3. * cd20 - 5. * cd40
pcoeff[4,i] = cd21 - cd20 - 5. * (cd40 + cd41)
pcoeff[5,i] = 5. * cd40
pcoeff[6,i] = cd41 - cd40
tptr = tptr + len_coeff
}
# calculate polynomial coefficients in y
do j = 1, 6 {
# calculate the central differences
cd20 = 1./6. * (pcoeff[j,4] - 2. * pcoeff[j,3] + pcoeff[j,2])
cd21 = 1./6. * (pcoeff[j,5] - 2. * pcoeff[j,4] + pcoeff[j,3])
cd40 = 1./120. * (pcoeff[j,1] - 4. * pcoeff[j,2] +
6. * pcoeff[j,3] - 4. * pcoeff[j,4] + pcoeff[j,5])
cd41 = 1./120. * (pcoeff[j,2] - 4. * pcoeff[j,3] +
6. * pcoeff[j,4] - 4. * pcoeff[j,5] + pcoeff[j,6])
# calculate the final coefficients
temp[1] = pcoeff[j,3]
temp[2] = pcoeff[j,4] - pcoeff[j,3] - 2. * cd20 - cd21 +
6. * cd40 + 4. * cd41
temp[3] = 3. * cd20 - 5. * cd40
temp[4] = cd21 - cd20 - 5. * (cd40 + cd41)
temp[5] = 5. * cd40
temp[6] = cd41 - cd40
do i = 1, 6
pcoeff[j,i] = temp[i]
}
end
# II_PCSPLINE3 -- Procedure to evaluate the polynomial coefficients
# of bicubic spline.
procedure ii_pcspline3 (coeff, index, len_coeff, pcoeff, len_pcoeff)
real coeff[ARB] # 1D array of interpolant coeffcients
int index # pointer into coeff array
int len_coeff # row length of coeffcients
real pcoeff[len_pcoeff,ARB] # polynomial coefficients
int len_pcoeff # row length of pcoeff
int tptr
int i, j
real temp[4]
begin
# determine polynomial coefficients in x
tptr = index
do i = 1, 4 {
pcoeff[1,i] = coeff[tptr+1] + 4. * coeff[tptr] + coeff[tptr-1]
pcoeff[2,i] = 3. * (coeff[tptr+1] - coeff[tptr-1])
pcoeff[3,i] = 3. * (coeff[tptr-1] - 2. * coeff[tptr] +
coeff[tptr+1])
pcoeff[4,i] = -coeff[tptr-1] + 3. * coeff[tptr] -
3. * coeff[tptr+1] + coeff[tptr+2]
tptr = tptr + len_coeff
}
# calculate polynomial coefficients in y
do j = 1, 4 {
temp[1] = pcoeff[j,3] + 4. * pcoeff[j,2] + pcoeff[j,1]
temp[2] = 3. * (pcoeff[j,3] - pcoeff[j,1])
temp[3] = 3. * (pcoeff[j,1] - 2. * pcoeff[j,2] + pcoeff[j,3])
temp[4] = -pcoeff[j,1] + 3. * pcoeff[j,2] - 3. * pcoeff[j,3] +
pcoeff[j,4]
do i = 1, 4
pcoeff[j,i] = temp[i]
}
end
# II_BISINCDER -- Evaluate the derivatives of the 2D sinc interpolator. If the
# function value only is needed call ii_bisinc. This routine computes only
# the first 2 derivatives in x and y. The second derivative is computed
# even if only the first derivative is needed. The sinc truncation length
# is nsinc. The taper is a cosbell approximated by a quartic polynomial.
# The data value if returned if x is closer to x[i] than mindx and y is
# closer to y[i] than mindy.
procedure ii_bisincder (x, y, der, nxder, nyder, len_der, coeff, first_point,
nxpix, nypix, nsinc, mindx, mindy)
real x, y # the input x and y values
real der[len_der,ARB] # the output derivatives array
int nxder, nyder # the number of derivatives to compute
int len_der # the width of the derivatives array
real coeff[ARB] # the coefficient array
int first_point # offset of first data point into the array
int nxpix, nypix # size of the coefficient array
int nsinc # the sinc truncation length
real mindx, mindy # the precision of the sinc interpolant
double sumx, normx[3], normy[3], norm[3,3], sum[3,3]
int i, j, k, jj, kk, xc, yc, nconv, index
int minj, maxj, offj, mink, maxk, offk, last_point
pointer sp, ac, ar
real sconst, a2, a4, dx, dy, dxn, dyn, dx2, taper, sdx, ax, ay, ctanx, ctany
real zx, zy
real px[3], py[3]
begin
# Return if no derivatives ar to be computed.
if (nxder == 0 || nyder == 0)
return
# Initialize the derivatives to zero.
do jj = 1, nyder {
do kk = 1, nxder
der[kk,jj] = 0.0
}
# Return if the data is outside range.
xc = nint (x)
yc = nint (y)
if (xc < 1 || xc > nxpix || yc < 1 || yc > nypix)
return
# Call ii_bsinc if only the function value is requested.
if (nxder == 1 && nyder == 1) {
call ii_bisinc (coeff, first_point, nxpix, nypix, x, y, der[1,1],
1, nsinc, mindx, mindy)
return
}
# Compute the constants for the cosine bell taper approximation.
sconst = (HALFPI / nsinc) ** 2
a2 = -0.49670
a4 = 0.03705
# Allocate some working space.
nconv = 2 * nsinc + 1
call smark (sp)
call salloc (ac, 3 * nconv, TY_REAL)
call salloc (ar, 3 * nconv, TY_REAL)
call aclrr (Memr[ac], 3 * nconv)
call aclrr (Memr[ar], 3 * nconv)
# Initialize.
dx = x - xc
dy = y - yc
if (dx == 0.0)
ctanx = 0.0
else
ctanx = 1.0 / tan (PI * dx)
if (dy == 0.0)
ctany = 0.0
else
ctany = 1.0 / tan (PI * dy)
index = - 1 - nsinc
dxn = -1 - nsinc - dx
dyn = -1 - nsinc - dy
if (mod (nsinc, 2) == 0)
sdx = 1.0
else
sdx = -1.0
do jj = 1, 3 {
normy[jj] = 0.0d0
normx[jj] = 0.0d0
}
do i = 1, nconv {
dx2 = sconst * (i + index) ** 2
taper = sdx * (1.0 + a2 * dx2 + a4 * dx2 * dx2) ** 2
#ax = dxn + i
#ay = dyn + i
ax = -dxn - i
ay = -dyn - i
if (ax == 0.0) {
px[1] = 1.0
px[2] = 0.0
px[3] = - 1.0 / 3.0
} else if (dx == 0.0) {
px[1] = 0.0
px[2] = 0.0
px[3] = 0.0
} else {
zx = 1.0 / ax
px[1] = taper * zx
px[2] = px[1] * (ctanx - zx)
px[3] = -px[1] * (1.0 + 2.0 * zx * (ctanx - zx))
}
if (ay == 0.0) {
py[1] = 1.0
py[2] = 0.0
py[3] = - 1.0 / 3.0
} else if (dy == 0.0) {
py[1] = 0.0
py[2] = 0.0
py[3] = 0.0
} else {
zy = 1.0 / ay
py[1] = taper * zy
py[2] = py[1] * (ctany - zy)
py[3] = -py[1] * (1.0 + 2.0 * zy * (ctany - zy))
}
Memr[ac+i-1] = px[1]
Memr[ac+nconv+i-1] = px[2]
Memr[ac+2*nconv+i-1] = px[3]
Memr[ar+i-1] = py[1]
Memr[ar+nconv+i-1] = py[2]
Memr[ar+2*nconv+i-1] = py[3]
do jj = 1, 3 {
normx[jj] = normx[jj] + px[jj]
normy[jj] = normy[jj] + py[jj]
}
sdx = -sdx
}
# Normalize.
do jj = 1, 3 {
do kk = 1, 3
norm[kk,jj] = normx[kk] * normy[jj]
}
# Do the convolution.
minj = max (1, yc - nsinc)
maxj = min (nypix, yc + nsinc)
mink = max (1, xc - nsinc)
maxk = min (nxpix, xc + nsinc)
do jj = 1, nyder {
offj = ar + (jj - 1) * nconv - yc + nsinc
do kk = 1, nxder {
offk = ac + (kk - 1) * nconv - xc + nsinc
sum[kk,jj] = 0.0d0
# Do the convolutions.
do j = yc - nsinc, minj - 1 {
sumx = 0.0d0
do k = xc - nsinc, mink - 1
sumx = sumx + Memr[k+offk] * coeff[first_point+1]
do k = mink, maxk
sumx = sumx + Memr[k+offk] * coeff[first_point+k]
do k = maxk + 1, xc + nsinc
sumx = sumx + Memr[k+offk] * coeff[first_point+nxpix]
sum[kk,jj] = sum[kk,jj] + Memr[j+offj] * sumx
}
do j = minj, maxj {
index = first_point + (j - 1) * nxpix
sumx = 0.0d0
do k = xc - nsinc, mink - 1
sumx = sumx + Memr[k+offk] * coeff[index+1]
do k = mink, maxk
sumx = sumx + Memr[k+offk] * coeff[index+k]
do k = maxk + 1, xc + nsinc
sumx = sumx + Memr[k+offk] * coeff[index+nxpix]
sum[kk,jj] = sum[kk,jj] + Memr[j+offj] * sumx
}
do j = maxj + 1, yc + nsinc {
last_point = first_point + (nypix - 1) * nxpix
sumx = 0.0d0
do k = xc - nsinc, mink - 1
sumx = sumx + Memr[k+offk] * coeff[last_point+1]
do k = mink, maxk
sumx = sumx + Memr[k+offk] * coeff[last_point+k]
do k = maxk + 1, xc + nsinc
sumx = sumx + Memr[k+offk] * coeff[last_point+nxpix]
sum[kk,jj] = sum[kk,jj] + Memr[j+offj] * sumx
}
}
}
# Build the derivatives.
der[1,1] = sum[1,1] / norm[1,1]
if (nxder > 1)
der[2,1] = sum[2,1] / norm[1,1] - (sum[1,1] * norm[2,1]) /
norm[1,1] ** 2
if (nxder > 2)
der[3,1] = sum[3,1] / norm[1,1] - (norm[3,1] * sum[1,1] +
2.0d0 * sum[2,1] * norm[2,1]) / norm[1,1] ** 2 +
2.0d0 * sum[1,1] * norm[2,1] * norm[2,1] / norm[1,1] ** 3
if (nyder > 1) {
der[1,2] = sum[1,2] / norm[1,1] - (sum[1,1] * norm[1,2]) /
norm[1,1] ** 2
if (nxder > 1)
der[2,2] = sum[2,2] / norm[1,1] - (sum[2,1] * norm[1,2] +
sum[1,2] * norm[2,1] + norm[2,2] * sum[1,1]) /
norm[1,1] ** 2 + (2.0d0 * sum[1,1] * norm[2,1] *
norm[1,2]) / norm[1,1] ** 3
if (nxder > 2)
der[3,2] = sum[3,2] / norm[1,1] - (sum[3,1] * norm[1,2] +
2.0 * norm[2,2] * sum[2,1] + 2.0 * sum[2,2] *
norm[2,1] + norm[3,1] * sum[1,2] + norm[3,2] *
sum[1,1]) / norm[1,1] ** 2 + (4.0 * norm[2,1] *
sum[2,1] * norm[1,2] + 2.0 * norm[2,1] * sum[1,2] *
norm[2,1] + 4.0 * norm[2,1] * norm[2,2] * sum[1,1] +
2.0 * norm[3,1] * norm[1,2] * sum[1,1]) /
norm[1,1] ** 3 - 6.0 * norm[2,1] * norm[2,1] *
norm[1,2] * sum[1,1] / norm[1,1] ** 4
}
if (nyder > 2) {
der[1,3] = sum[1,3] / norm[1,1] - (norm[1,3] * sum[1,1] +
2.0d0 * sum[1,2] * norm[1,2]) / norm[1,1] ** 2 +
2.0d0 * sum[1,1] * norm[1,2] * norm[1,2] / norm[1,1] ** 3
if (nxder > 1)
der[2,3] = sum[2,3] / norm[1,1] - (sum[1,3] * norm[2,1] +
2.0 * norm[2,2] * sum[1,2] + 2.0 * sum[2,2] *
norm[1,2] + norm[1,3] * sum[2,1] + norm[2,3] *
sum[1,1]) / norm[1,1] ** 2 + (4.0 * norm[1,2] *
sum[1,2] * norm[2,1] + 2.0 * norm[1,2] * sum[2,1] *
norm[1,2] + 4.0 * norm[1,2] * norm[2,2] * sum[1,1] +
2.0 * norm[1,3] * norm[2,1] * sum[1,1]) /
norm[1,1] ** 3 - 6.0 * norm[1,2] * norm[1,2] *
norm[2,1] * sum[1,1] / norm[1,1] ** 4
if (nxder > 2)
der[3,3] = sum[3,3] / norm[1,1] - (2.0 * sum[2,3] * norm[2,1] +
norm[3,1] * sum[1,3] + 2.0 * norm[3,2] * sum[1,2] +
4.0 * sum[2,2] * norm[2,2] + 2.0 * sum[3,2] *
norm[1,2] + 2.0 * norm[2,3] * sum[2,1] + sum[3,1] *
norm[1,3] + norm[3,3] * sum[1,1]) / norm[1,1] ** 2 +
(2.0 * norm[2,1] * norm[2,1] * sum[1,3] + 8.0 *
norm[2,1] * sum[1,2] * norm[2,2] + 8.0 * norm[2,1] *
norm[1,2] * sum[2,2] + 4.0 * norm[2,1] * sum[2,1] *
norm[1,3] + 4.0 * norm[2,1] * norm[2,3] * sum[1,1] +
4.0 * norm[1,2] * sum[1,2] * norm[3,1] + 8.0 *
norm[2,2] * sum[2,1] * norm[1,2] + 2.0 * norm[1,2] *
norm[1,2] * sum[3,1] + 4.0 * norm[2,2] * norm[2,2] *
sum[1,1] + 4.0 * norm[1,2] * norm[3,2] * sum[1,1] +
2.0 * norm[1,3] * norm[3,1] * sum[1,1]) /
norm[1,1] ** 3 - (12.0 * norm[2,1] * norm[2,1] *
norm[1,2] * sum[1,2] + 12.0 * norm[2,1] * norm[1,2] *
norm[1,2] * sum[2,1] + 24.0 * norm[2,1] * norm[1,2] *
norm[2,2] * sum[1,1] + 6.0 * norm[2,1] * norm[2,1] *
norm[1,3] * sum[1,1] + 6.0 * norm[1,2] * norm[1,2] *
norm[3,1] * sum[1,1]) / norm[1,1] ** 4 + ( 24.0 *
norm[1,2] * norm[1,2] * norm[2,1] * norm[2,1] *
sum[1,1]) / norm[1,1] ** 5
}
call sfree (sp)
end
|
