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# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
include "im2interpdef.h"
include <math/iminterp.h>
# MSIDER -- Calculate the derivatives of the interpolant. The derivative
# der[i,j] = d f(x,y) / dx (i-1) dy (j-1). Therefore der[1,1] contains
# the value of the interpolant, der[2,1] the 1st derivative in x and
# der[1,2] the first derivative in y.
procedure msider (msi, x, y, der, nxder, nyder, len_der)
pointer msi # pointer to interpolant descriptor structure
real x[ARB] # x value
real y[ARB] # y value
real der[len_der,ARB] # derivative array
int nxder # number of x derivatives
int nyder # number of y derivatives
int len_der # row length of der, len_der >= nxder
int first_point, len_coeff
int nxterms, nyterms, nx, ny, nyd, nxd
int i, j, ii, jj
real sx, sy, tx, ty, xmin, xmax, ymin, ymax
real pcoeff[MAX_NTERMS,MAX_NTERMS], pctemp[MAX_NTERMS,MAX_NTERMS]
real sum[MAX_NTERMS], accum, deltax, deltay, tmpx[4], tmpy[4]
pointer index, ptr
begin
if (nxder < 1 || nyder < 1)
return
# set up coefficient array parameters
len_coeff = MSI_NXCOEFF(msi)
index = MSI_COEFF(msi) + MSI_FSTPNT(msi) - 1
# zero the derivatives
do j = 1, nyder {
do i = 1, nxder
der[i,j] = 0.
}
# calculate the appropriate number of terms of the polynomials in
# x and y
switch (MSI_TYPE(msi)) {
case II_BINEAREST:
nx = x[1] + 0.5
ny = y[1] + 0.5
ptr = index + (ny - 1) * len_coeff + nx
der[1,1] = COEFF(ptr)
return
case II_BISINC, II_BILSINC:
call ii_bisincder (x[1], y[1], der, nxder, nyder, len_der,
COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi), MSI_NXCOEFF(msi),
MSI_NYCOEFF(msi), MSI_NSINC(msi), DX, DY)
return
case II_BILINEAR:
nx = x[1]
ny = y[1]
sx = x[1] - nx
sy = y[1] - ny
tx = 1. - sx
ty = 1. - sy
ptr = index + (ny - 1) * len_coeff + nx
der[1,1] = tx * ty * COEFF(ptr) + sx * ty * COEFF(ptr+1) +
sy * tx * COEFF(ptr+len_coeff) +
sx * sy * COEFF(ptr+len_coeff+1)
if (nxder > 1)
der[2,1] = -ty * COEFF(ptr) + ty * COEFF(ptr+1) -
sy * COEFF(ptr+len_coeff) +
sy * COEFF(ptr+len_coeff+1)
if (nyder > 1)
der[1,2] = -tx * COEFF(ptr) - sx * COEFF(ptr+1) +
tx * COEFF(ptr+len_coeff) +
sx * COEFF(ptr+len_coeff+1)
if (nyder > 1 && nxder > 1)
der[2,2] = COEFF(ptr) - COEFF(ptr+1) - COEFF(ptr+len_coeff) +
COEFF(ptr+len_coeff+1)
return
case II_BIDRIZZLE:
if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), x, y, der[1,1], 1, MSI_BADVAL(msi))
#else if (MSI_XPIXFRAC(msi) <= 0.0 && MSI_YPIXFRAC(msi) <= 0.0)
#call ii_bidriz0 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
#MSI_NXCOEFF(msi), x, y, der[1,1], 1, MSI_BADVAL(msi))
else
call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), x, y, der[1,1], 1, MSI_XPIXFRAC(msi),
MSI_YPIXFRAC(msi), MSI_BADVAL(msi))
if (nxder > 1) {
xmax = max (x[1], x[2], x[3], x[4])
xmin = min (x[1], x[2], x[3], x[4])
ymax = max (y[1], y[2], y[3], y[4])
ymin = min (y[1], y[2], y[3], y[4])
deltax = xmax - xmin
if (deltax == 0.0)
der[2,1] = 0.0
else {
tmpx[1] = xmin; tmpy[1] = ymin
tmpx[2] = (xmax - xmin) / 2.0; tmpy[2] = ymin
tmpx[3] = (xmax - xmin) / 2.0; tmpy[3] = ymax
tmpx[4] = xmin; tmpy[4] = ymax
if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), tmpx, tmpy, accum, 1,
MSI_BADVAL(msi))
#else if (MSI_XPIXFRAC(msi) <= 0.0 &&
#MSI_YPIXFRAC(msi) <= 0.0)
#call ii_bidriz0 (COEFF(MSI_COEFF(msi)),
#MSI_FSTPNT(msi), MSI_NXCOEFF(msi), tmpx, tmpy,
#accum, 1, MSI_BADVAL(msi))
else
call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), tmpx, tmpy, accum, 1,
MSI_XPIXFRAC(msi), MSI_YPIXFRAC(msi),
MSI_BADVAL(msi))
tmpx[1] = (xmax - xmin) / 2.0; tmpy[1] = ymin
tmpx[2] = xmax; tmpy[2] = ymin
tmpx[3] = xmax; tmpy[3] = ymax
tmpx[4] = (xmax - xmin) / 2.0; tmpy[4] = ymax
if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), tmpx, tmpy, der[2,1], 1,
MSI_BADVAL(msi))
#else if (MSI_XPIXFRAC(msi) <= 0.0 &&
#MSI_YPIXFRAC(msi) <= 0.0)
#call ii_bidriz0 (COEFF(MSI_COEFF(msi)),
#MSI_FSTPNT(msi), MSI_NXCOEFF(msi), tmpx, tmpy,
#der[2,1], 1, MSI_BADVAL(msi))
else
call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), tmpx, tmpy, der[2,1], 1,
MSI_XPIXFRAC(msi), MSI_YPIXFRAC(msi),
MSI_BADVAL(msi))
der[2,1] = 2.0 * (der[2,1] - accum) / deltax
}
}
if (nyder > 1) {
deltay = ymax - ymin
if (deltay == 0.0)
der[1,2] = 0.0
else {
tmpx[1] = xmin; tmpy[1] = ymin
tmpx[2] = xmax; tmpy[2] = ymin
tmpx[3] = xmax; tmpy[3] = (ymax - ymin) / 2.0
tmpx[4] = xmin; tmpy[4] = (ymax - ymin) / 2.0
if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), tmpx, tmpy, accum, 1,
MSI_BADVAL(msi))
#else if (MSI_XPIXFRAC(msi) <= 0.0 &&
#MSI_YPIXFRAC(msi) <= 0.0)
#call ii_bidriz0 (COEFF(MSI_COEFF(msi)),
#MSI_FSTPNT(msi), MSI_NXCOEFF(msi), tmpx, tmpy,
#accum, 1, MSI_BADVAL(msi))
else
call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), tmpx, tmpy, accum, 1,
MSI_XPIXFRAC(msi), MSI_YPIXFRAC(msi),
MSI_BADVAL(msi))
tmpx[1] = xmin; tmpy[1] = (ymax - ymin) / 2.0
tmpx[2] = xmax; tmpy[2] = (ymax - ymin) / 2.0
tmpx[3] = xmax; tmpy[3] = ymax
tmpx[4] = xmin; tmpy[4] = ymax
if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), tmpx, tmpy, der[1,2], 1,
MSI_BADVAL(msi))
#else if (MSI_XPIXFRAC(msi) <= 0.0 &&
#MSI_YPIXFRAC(msi) <= 0.0)
#call ii_bidriz0 (COEFF(MSI_COEFF(msi)),
#MSI_FSTPNT(msi), MSI_NXCOEFF(msi), tmpx, tmpy,
#der[1,2], 1, MSI_BADVAL(msi))
else
call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
MSI_NXCOEFF(msi), tmpx, tmpy, der[1,2], 1,
MSI_XPIXFRAC(msi), MSI_YPIXFRAC(msi),
MSI_BADVAL(msi))
der[1,2] = 2.0 * (der[1,2] - accum) / deltay
}
}
return
case II_BIPOLY3:
nxterms = 4
nyterms = 4
nxd = min (nxder, 4)
nyd = min (nyder, 4)
nx = x[1]
sx = x[1] - nx
ny = y[1]
sy = y[1] - ny
first_point = MSI_FSTPNT(msi) + (ny - 2) * len_coeff + nx
call ii_pcpoly3 (COEFF(MSI_COEFF(msi)), first_point, len_coeff,
pcoeff, 6)
case II_BIPOLY5:
nxterms = 6
nyterms = 6
nxd = min (nxder, 6)
nyd = min (nyder, 6)
nx = x[1]
sx = x[1] - nx
ny = y[1]
sy = y[1] - ny
first_point = MSI_FSTPNT(msi) + (ny - 3) * len_coeff + nx
call ii_pcpoly5 (COEFF(MSI_COEFF(msi)), first_point, len_coeff,
pcoeff, 6)
case II_BISPLINE3:
nxterms = 4
nyterms = 4
nxd = min (nxder, 4)
nyd = min (nyder, 4)
nx = x[1]
sx = x[1] - nx
ny = y[1]
sy = y[1] - ny
first_point = MSI_FSTPNT(msi) + (ny - 2) * len_coeff + nx
call ii_pcspline3 (COEFF(MSI_COEFF(msi)), first_point, len_coeff,
pcoeff, 6)
}
# evaluate the derivatives by nested multiplication
do j = 1, nyd {
# set pctemp
do jj = nyterms, j, -1 {
do ii = 1, nxterms
pctemp[ii,jj] = pcoeff[ii,jj]
}
do i = 1, nxd {
# accumulate the partial sums in x
do jj = nyterms, j, -1 {
sum[jj] = pctemp[nxterms,jj]
do ii = nxterms - 1, i, -1
sum[jj] = pctemp[ii,jj] + sum[jj] * sx
}
# accumulate the sum in y
accum = sum[nyterms]
do jj = nyterms - 1, j, -1
accum = sum[jj] + accum * sy
# evaluate derivative
der[i,j] = accum
# differentiate in x
do jj = nyterms, j, -1 {
do ii = nxterms, i + 1, -1
pctemp[ii,jj] = (ii - i) * pctemp[ii,jj]
}
}
# differentiate in y
do jj = 1, nxterms {
do ii = nyterms, j + 1, -1
pcoeff[jj,ii] = (ii - j) * pcoeff[jj,ii]
}
}
end
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