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# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
.help
procedure asigrl
This procedure finds the integral of the interpolant from a to b
assuming both a and b land in the array.
.endhelp
real procedure asigrl(a,b,coeff) # returns value of integral
include "interpdef.h"
include "asidef.h"
real a,b # integral limits
real coeff[ARB]
int na,nb,i,j,n0,nt
real s,t,ac,xa,xb,pc[6]
begin
xa = a
xb = b
if ( a > b ) { # flip order and sign at end
xa = b
xb = a
}
na = xa
nb = xb
ac = 0. # zero accumulator
# set number of terms
switch (ITYPEI) { # switch on interpolator type
case IT_NEAREST :
nt = 0
case IT_LINEAR :
nt = 1
case IT_POLY3 :
nt = 4
case IT_POLY5 :
nt = 6
case IT_SPLINE3 :
nt = 4
}
# NEAREST_NEIGHBOR and LINEAR are handled differently because of
# storage. Also probably good for speed.
if (nt == 0) { # NEAREST_NEIGHBOR
# reset segment to center values
na = xa + 0.5
nb = xb + 0.5
# set up for first segment
s = xa - na
# for clarity one segment case is handled separately
if ( nb == na ) { # only one segment involved
t = xb - nb
n0 = COFF + na
ac = ac + (t - s) * coeff[n0]
} else { # more than one segment
# first segment
n0 = COFF + na
ac = ac + (0.5 - s) * coeff[n0]
# middle segments
do j = na+1, nb-1 {
n0 = COFF + j
ac = ac + coeff[n0]
}
# last segment
n0 = COFF + nb
t = xb - nb
ac = ac + (t + 0.5) * coeff[n0]
}
} else if (nt == 1) { # LINEAR
# set up for first segment
s = xa - na
# for clarity one segment case is handled separately
if ( nb == na ) { # only one segment involved
t = xb - nb
n0 = COFF + na
ac = ac + (t - s) * coeff[n0] +
0.5 * (coeff[n0+1] - coeff[n0]) * (t*t - s*s)
} else { # more than one segment
# first segment
n0 = COFF + na
ac = ac + (1. - s) * coeff[n0] +
0.5 * (coeff[n0+1] - coeff[n0]) * (1. - s*s)
# middle segments
do j = na+1, nb-1 {
n0 = COFF + j
ac = ac + 0.5 * (coeff[n0+1] + coeff[n0])
}
# last segment
n0 = COFF + nb
t = xb - nb
ac = ac + coeff[n0] * t + 0.5 *
(coeff[n0+1] - coeff[n0]) * t * t
}
} else { # A higher order interpolant
# set up for first segment
s = xa - na
# for clarity one segment case is handled separately
if ( nb == na ) { # only one segment involved
t = xb - nb
n0 = COFF + na
call iigetpc(n0,pc,coeff)
do i = 1,nt
ac = ac + (1./i) * pc[i] * (t ** i - s ** i)
} else { # more than one segment
# first segment
n0 = COFF + na
call iigetpc(n0,pc,coeff)
do i = 1,nt
ac = ac + (1./i) * pc[i] * (1. - s ** i)
# middle segments
do j = na+1, nb-1 {
n0 = COFF + j
call iigetpc(n0,pc,coeff)
do i = 1,nt
ac = ac + (1./i) * pc[i]
}
# last segment
n0 = COFF + nb
t = xb - nb
call iigetpc(n0,pc,coeff)
do i = 1,nt
ac = ac + (1./i) * pc[i] * t ** i
}
}
if ( a < b )
return(ac)
else
return(-ac)
end
procedure iigetpc(n0, pc, coeff) # generates polynomial coefficients
# if spline or poly3 or poly5
int n0 # coefficients wanted for n0 < x n0 + 1
real coeff[ARB]
real pc[ARB]
int i,k,nt
real d[6]
begin
# generate polynomial coefficients, first for spline.
if (ITYPEI == IT_SPLINE3) {
pc[1] = coeff[n0-1] + 4. * coeff[n0] + coeff[n0+1]
pc[2] = 3. * (coeff[n0+1] - coeff[n0-1])
pc[3] = 3. * (coeff[n0-1] - 2. * coeff[n0] + coeff[n0+1])
pc[4] = -coeff[n0-1] + 3. * coeff[n0] - 3. * coeff[n0+1] +
coeff[n0+2]
} else {
if (ITYPEI == IT_POLY5)
nt = 6
else # must be POLY3
nt = 4
# Newton's form written in line to get polynomial from data
# load data
do i = 1,nt
d[i] = coeff[n0 - nt/2 + i]
# generate difference table
do k = 1, nt-1
do i = 1,nt-k
d[i] = (d[i+1] - d[i]) / k
# shift to generate polynomial coefficients of (x - n0)
do k = nt,2,-1
do i = 2,k
d[i] = d[i] + d[i-1] * (k - i - 2)
do i = 1,nt
pc[i] = d[nt + 1 - i]
}
return
end
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