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# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
include "im2interpdef.h"
include <math/iminterp.h>
# MRIDER -- Procedure to evaluate the derivatives of the interpolant
# without the storage overhead required by the sequential version.
# The derivatives are stored such that der[1,1] = the value of the
# interpolant at x and y, der[2,1] = the first derivative in x and
# der[2,1] = the first derivative in y.
procedure mrider (x, y, datain, nxpix, nypix, len_datain, der, nxder, nyder,
len_der, interp_type)
real x[ARB] # x value
real y[ARB] # y value
real datain[len_datain,ARB] # data array
int nxpix # number of x data points
int nypix # number of y data points
int len_datain # row length of datain
real der[len_der, ARB] # array of derivatives
int nxder # number of derivatives in x
int nyder # number of derivatives in y
int len_der # row length of der, len_der >= nxder
int interp_type # interpolant type
int nx, ny, nxterms, nyterms, row_length
int index, xindex, yindex, first_row, last_row
int i, j, ii, jj, kx, ky
pointer tmp
real coeff[SPLPTS+3,SPLPTS+3], pcoeff[MAX_NTERMS,MAX_NTERMS]
real pctemp[MAX_NTERMS,MAX_NTERMS], sum[MAX_NTERMS]
real hold21, hold12, hold22, accum, deltax, deltay, tmpx[4], tmpy[4]
real xmin, xmax, ymin, ymax, sx, sy, tx, ty
errchk malloc, calloc, mfree
begin
if (nxder < 1 || nyder < 1)
return
# zero the derivatives
do j = 1, nyder {
do i = 1, nxder
der[i,j] = 0.
}
switch (interp_type) {
case II_BINEAREST:
der[1,1] = datain[int (x[1]+.5), int (y[1]+.5)]
return
case II_BISINC, II_BILSINC:
call ii_bisincder (x[1], y[1], der, nxder, nyder, len_der, datain,
0, len_datain, nypix, NSINC, DX, DY)
return
case II_BILINEAR:
nx = x[1]
sx = x[1] - nx
tx = 1. - sx
ny = y[1]
sy = y[1] - ny
ty = 1. - sy
# protect against the case where x = nxpix and/or y = nypix
if (nx >= nxpix)
hold21 = 2. * datain[nx,ny] - datain[nx-1,ny]
else
hold21 = datain[nx+1,ny]
if (ny >= nypix)
hold12 = 2. * datain[nx,ny] - datain[nx,ny-1]
else
hold12 = datain[nx,ny+1]
if (nx >= nxpix && ny >= nypix)
hold22 = 2. * hold21 - (2. * datain[nx,ny-1] -
datain[nx-1,ny-1])
else if (nx >= nxpix)
hold22 = 2. * hold12 - datain[nx-1,ny+1]
else if (ny >= nypix)
hold 22 = 2. * hold21 - datain[nx+1,ny-1]
else
hold22 = datain[nx+1,ny+1]
# evaluate the derivatives
der[1,1] = tx * ty * datain[nx,ny] + sx * ty * hold21 +
sy * tx * hold12 + sx * sy * hold22
if (nxder > 1)
der[2,1] = - ty * datain[nx,ny] + ty * hold21 -
sy * hold12 + sy * hold22
if (nyder > 1)
der[1,2] = - tx * datain[nx,ny] - sx * hold21 +
tx * hold12 + sx * hold22
if (nxder > 1 && nyder > 1)
der[2,2] = datain[nx,ny] - hold21 - hold12 + hold22
return
case II_BIDRIZZLE:
call ii_bidriz1 (datain, 0, len_datain, x, y, der[1,1], 1, BADVAL)
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
call ii_bidriz1 (datain, 0, len_datain, tmpx, tmpy,
accum, 1, BADVAL)
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
call ii_bidriz1 (datain, 0, len_datain, tmpx, tmpy,
der[2,1], 1, BADVAL)
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
call ii_bidriz1 (datain, 0, len_datain, tmpx, tmpy,
accum, 1, BADVAL)
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
call ii_bidriz1 (datain, 0, len_datain, tmpx, tmpy,
der[1,2], 1, BADVAL)
der[1,2] = 2.0 * (der[1,2] - accum) / deltay
}
}
return
case II_BIPOLY3:
row_length = SPLPTS + 3
nxterms = 4
nyterms = 4
nx = x[1]
ny = y[1]
sx = x[1] - nx
sy = y[1] - ny
# use boundary projection to extend the data rows
yindex = 1
for (j = ny - 1; j <= ny + 2; j = j + 1) {
# check that the data row is defined
if (j >= 1 && j <= nypix) {
# extend the rows
xindex = 1
for (i = nx - 1; i <= nx + 2; i = i + 1) {
if (i < 1)
coeff[xindex,yindex] = 2. * datain[1,j] -
datain[2-i,j]
else if (i > nxpix)
coeff[xindex,yindex] = 2. * datain[nxpix,j] -
datain[2*nxpix-i,j]
else
coeff[xindex,yindex] = datain[i,j]
xindex = xindex + 1
}
} else if (j == (nypix + 2)) {
# allow for the final row
xindex = 1
for (i = nx - 1; i <= nx + 2; i = i + 1) {
if (i < 1)
coeff[xindex,nyterms] = 2. * datain[1,nypix-2] -
datain[2-i,nypix-2]
else if (i > nxpix)
coeff[xindex,nyterms] = 2. * datain[nxpix,nypix-2] -
datain[2*nxpix-i,nypix-2]
else
coeff[xindex,nyterms] = datain[i,nypix-2]
xindex = xindex + 1
}
}
yindex = yindex + 1
}
# project columns
first_row = max (1, 3 - ny)
if (first_row > 1) {
for (j = 1; j < first_row; j = j + 1)
call awsur (coeff[1, first_row], coeff[1, 2*first_row-j],
coeff[1,j], nxterms, 2., -1.)
}
last_row = min (nxterms, nypix - ny + 2)
if (last_row < nxterms) {
for (j = last_row + 1; j <= nxterms - 1; j = j + 1)
call awsur (coeff[1,last_row], coeff[1,2*last_row-j],
coeff[1,j], nxterms, 2., -1.)
if (last_row == 2)
call awsur (coeff[1,last_row], coeff[1,4], coeff[1,4],
nxterms, 2., -1.)
else
call awsur (coeff[1,last_row], coeff[1,2*last_row-4],
coeff[1,4], nxterms, 2., -1.)
}
# calculate the coefficients of the bicubic polynomial
call ii_pcpoly3 (coeff, 2, row_length, pcoeff, MAX_NTERMS)
case II_BIPOLY5:
row_length = SPLPTS + 3
nxterms = 6
nyterms = 6
nx = x[1]
ny = y[1]
sx = x[1] - nx
sy = y[1] - ny
# extend rows of data
yindex = 1
for (j = ny - 2; j <= ny + 3; j = j + 1) {
# select the rows containing data
if (j >= 1 && j <= nypix) {
# extend the rows
xindex = 1
for (i = nx - 2; i <= nx + 3; i = i + 1) {
if (i < 1)
coeff[xindex,yindex] = 2. * datain[1,j] -
datain[2-i,j]
else if (i > nxpix)
coeff[xindex,yindex] = 2. * datain[nxpix,j] -
datain[2*nxpix-i,j]
else
coeff[xindex,yindex] = datain[i,j]
xindex = xindex + 1
}
} else if (j == (ny + 3)) {
# extend the rows
xindex = 1
for (i = nx - 2; i <= nx + 3; i = i + 1) {
if (i < 1)
coeff[xindex,yindex] = 2. * datain[1,nypix-3] -
datain[2-i,nypix-3]
else if (i > nxpix)
coeff[xindex,yindex] = 2. * datain[nxpix,nypix-3] -
datain[2*nxpix-i,nypix-3]
else
coeff[xindex,yindex] = datain[i,nypix-3]
xindex = xindex + 1
}
}
yindex = yindex + 1
}
# project columns
first_row = max (1, 4 - ny)
if (first_row > 1) {
for (j = 1; j < first_row; j = j + 1)
call awsur (coeff[1,first_row], coeff[1,2*first_row-j],
coeff[1,j], nxterms, 2., -1.)
}
last_row = min (nxterms, nypix - ny + 3)
if (last_row < nxterms) {
for (j = last_row + 1; j <= nxterms - 1; j = j + 1)
call awsur (coeff[1,last_row], coeff[1,2*last_row-j],
coeff[1,j], nxterms, 2., -1.)
if (last_row == 3)
call awsur (coeff[1,last_row], coeff[1,6], coeff[1,6],
nxterms, 2., -1.)
else
call awsur (coeff[1,last_row], coeff[1,2*last_row-6],
coeff[1,6], nxterms, 2., -1.)
}
# caculate the polynomial coeffcients
call ii_pcpoly5 (coeff, 3, row_length, pcoeff, MAX_NTERMS)
case II_BISPLINE3:
row_length = SPLPTS + 3
nxterms = 4
nyterms = 4
nx = x[1]
ny = y[1]
sx = x[1] - nx
sy = y[1] - ny
# allocate space for temporary array and 0 file
call calloc (tmp, row_length * row_length, TY_REAL)
ky = 0
# maximum number of points used in each direction is SPLPTS
for (j = ny - SPLPTS/2 + 1; j <= ny + SPLPTS/2; j = j + 1) {
if (j < 1 || j > nypix)
;
else {
ky = ky + 1
if (ky == 1)
yindex = ny - j + 1
kx = 0
for (i = nx - SPLPTS/2 + 1; i <= nx + SPLPTS/2; i = i + 1) {
if (i < 1 || i > nxpix)
;
else {
kx = kx + 1
if (kx == 1)
xindex = nx - i + 1
coeff[kx+1,ky+1] = datain[i,j]
}
}
coeff[1,ky+1] = 0.
coeff[kx+2,ky+1] = 0.
coeff[kx+3,ky+1] = 0.
}
}
# zero out 1st and last 2 rows
call amovkr (0., coeff[1,1], kx+3)
call amovkr (0., coeff[1,ky+2], kx+3)
call amovkr (0., coeff[1,ky+3],kx+3)
# calculate the spline coefficients
call ii_spline2d (coeff, Memr[tmp], kx, ky+2, row_length,
row_length)
call ii_spline2d (Memr[tmp], coeff, ky, kx+2, row_length,
row_length)
# calculate the polynomial coefficients
index = (yindex - 1) * row_length + xindex + 1
call ii_pcspline3 (coeff, index, row_length, pcoeff, MAX_NTERMS)
# free space
call mfree (tmp, TY_REAL)
}
# evaluate the derivatives of the higher order interpolants
do j = 1, nyder {
# set pctemp
do jj = nyterms, j, -1 {
do ii = 1, nxterms
pctemp[ii,jj] = pcoeff[ii,jj]
}
do i = 1, nxder {
# 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
# evaulate the 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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