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# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
.help
arider -- random interpolator returns derivatives
First looks at type of interpolator requested, then calls routine
to evaluate.
No error traps are included -- unreasonable values for the number of
data points or the x position will either produce hard errors or garbage.
.endhelp
procedure arider(x, datain, n, derivs, nderiv, interptype)
include "interpdef.h"
real x # need 1 <= x <= n
real datain[ARB] # data values
int n # number of data values
real derivs[ARB] # derivatives out -- beware derivs[1] is
# function value
int nderiv # total number of values returned in derivs
int interptype
int i, j, k, nt, nd, nx
real pc[6], ac, s
begin
if(nderiv <= 0)
return
# zero out derivs array
do i = 1, nderiv
derivs[i] = 0.
switch (interptype) {
case IT_NEAREST :
derivs[1] = datain[int(x + 0.5)]
return
case IT_LINEAR :
nx = x
if( nx >= n )
nx = nx - 1
derivs[1] = (x - nx) * datain[nx+1] + (nx + 1 - x) * datain[nx]
if(nderiv >= 2)
derivs[2] = datain[nx+1] - datain[nx]
return
# The other cases call subroutines to generate polynomial coeff.
case IT_POLY3 :
call iidr_poly3(x, datain, n, pc)
nt = 4
case IT_POLY5 :
call iidr_poly5(x, datain, n, pc)
nt = 6
case IT_SPLINE3 :
call iidr_spline3(x, datain, n, pc)
nt = 4
}
nx = x
s = x - nx
nd = nderiv
if (nderiv > nt)
nd = nt
do k = 1,nd {
ac = pc[nt - k + 1] # evluate using nested multiplication
do j = nt - k, 1, -1
ac = pc[j] + s * ac
derivs[k] = ac
do j = 1, nt - k # differentiate
pc[j] = j * pc[j + 1]
}
end
procedure iidr_poly3(x, datain, n, pc)
real x
real datain[ARB]
int n
real pc[ARB]
int i, k, nx, nt
real a[4]
begin
nx = x
# The major complication is that near the edge interior polynomial
# must somehow be defined.
k = 0
for(i = nx - 1; i <= nx + 2; i = i + 1){
k = k + 1
# project data points into temporary array
if ( i < 1 )
a[k] = 2. * datain[1] - datain[2 - i]
else if ( i > n )
a[k] = 2. * datain[n] - datain[2 * n - i]
else
a[k] = datain[i]
}
nt = 4
# generate diffrence table for Newton's form
do k = 1, nt-1
do i = 1, nt-k
a[i] = (a[i+1] - a[i]) / k
# shift to generate polynomial coefficients
do k = nt,2,-1
do i = 2,k
a[i] = a[i] + a[i-1] * (k - i - nt/2)
do i = 1,nt
pc[i] = a[nt+1-i]
return
end
procedure iidr_poly5(x, datain, n, pc)
real x
real datain[ARB]
int n
real pc[ARB]
int i, k, nx, nt
real a[6]
begin
nx = x
# The major complication is that near the edge interior polynomial
# must somehow be defined.
k = 0
for(i = nx - 2; i <= nx + 3; i = i + 1){
k = k + 1
# project data points into temporary array
if ( i < 1 )
a[k] = 2. * datain[1] - datain[2 - i]
else if ( i > n )
a[k] = 2. * datain[n] - datain[2 * n - i]
else
a[k] = datain[i]
}
nt = 6
# generate diffrence table for Newton's form
do k = 1, nt-1
do i = 1, nt-k
a[i] = (a[i+1] - a[i]) / k
# shift to generate polynomial coefficients
do k = nt,2,-1
do i = 2,k
a[i] = a[i] + a[i-1] * (k - i - nt/2)
do i = 1,nt
pc[i] = a[nt+1-i]
return
end
procedure iidr_spline3(x, datain, n, pc)
real x
real datain[ARB]
int n
real pc[ARB]
int i, k, nx, px
real temp[SPLPTS+2], bcoeff[SPLPTS+2], h
begin
nx = x
h = x - nx
k = 0
# maximum number of points used is SPLPTS
for(i = nx - SPLPTS/2 + 1; i <= nx + SPLPTS/2; i = i + 1){
if(i < 1 || i > n)
;
else {
k = k + 1
if(k == 1)
px = nx - i + 1
bcoeff[k+1] = datain[i]
}
}
bcoeff[1] = 0.
bcoeff[k+2] = 0.
# Use special routine for cardinal splines.
call iif_spline(bcoeff, temp, k)
px = px + 1
pc[1] = bcoeff[px-1] + 4. * bcoeff[px] + bcoeff[px+1]
pc[2] = 3. * (bcoeff[px+1] - bcoeff[px-1])
pc[3] = 3. * (bcoeff[px-1] - 2. * bcoeff[px] + bcoeff[px+1])
pc[4] = -bcoeff[px-1] + 3. * bcoeff[px] - 3. * bcoeff[px+1] +
bcoeff[px+2]
return
end
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