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subroutine fpbfou(t,n,par,ress,resc)
c subroutine fpbfou calculates the integrals
c /t(n-3)
c ress(j) = ! nj,4(x)*sin(par*x) dx and
c t(4)/
c /t(n-3)
c resc(j) = ! nj,4(x)*cos(par*x) dx , j=1,2,...n-4
c t(4)/
c where nj,4(x) denotes the cubic b-spline defined on the knots
c t(j),t(j+1),...,t(j+4).
c
c calling sequence:
c call fpbfou(t,n,par,ress,resc)
c
c input parameters:
c t : real array,length n, containing the knots.
c n : integer, containing the number of knots.
c par : real, containing the value of the parameter par.
c
c output parameters:
c ress : real array,length n, containing the integrals ress(j).
c resc : real array,length n, containing the integrals resc(j).
c
c restrictions:
c n >= 10, t(4) < t(5) < ... < t(n-4) < t(n-3).
c ..
c ..scalar arguments..
integer n
real*8 par
c ..array arguments..
real*8 t(n),ress(n),resc(n)
c ..local scalars..
integer i,ic,ipj,is,j,jj,jp1,jp4,k,li,lj,ll,nmj,nm3,nm7
real*8 ak,beta,con1,con2,c1,c2,delta,eps,fac,f1,f2,f3,one,quart,
* sign,six,s1,s2,term
c ..local arrays..
real*8 co(5),si(5),hs(5),hc(5),rs(3),rc(3)
c ..function references..
real*8 cos,sin,abs
c ..
c initialization.
one = 0.1e+01
six = 0.6e+01
eps = 0.1e-07
quart = 0.25e0
con1 = 0.5e-01
con2 = 0.12e+03
nm3 = n-3
nm7 = n-7
if(par.ne.0.) term = six/par
beta = par*t(4)
co(1) = cos(beta)
si(1) = sin(beta)
c calculate the integrals ress(j) and resc(j), j=1,2,3 by setting up
c a divided difference table.
do 30 j=1,3
jp1 = j+1
jp4 = j+4
beta = par*t(jp4)
co(jp1) = cos(beta)
si(jp1) = sin(beta)
call fpcsin(t(4),t(jp4),par,si(1),co(1),si(jp1),co(jp1),
* rs(j),rc(j))
i = 5-j
hs(i) = 0.
hc(i) = 0.
do 10 jj=1,j
ipj = i+jj
hs(ipj) = rs(jj)
hc(ipj) = rc(jj)
10 continue
do 20 jj=1,3
if(i.lt.jj) i = jj
k = 5
li = jp4
do 20 ll=i,4
lj = li-jj
fac = t(li)-t(lj)
hs(k) = (hs(k)-hs(k-1))/fac
hc(k) = (hc(k)-hc(k-1))/fac
k = k-1
li = li-1
20 continue
ress(j) = hs(5)-hs(4)
resc(j) = hc(5)-hc(4)
30 continue
if(nm7.lt.4) go to 160
c calculate the integrals ress(j) and resc(j),j=4,5,...,n-7.
do 150 j=4,nm7
jp4 = j+4
beta = par*t(jp4)
co(5) = cos(beta)
si(5) = sin(beta)
delta = t(jp4)-t(j)
c the way of computing ress(j) and resc(j) depends on the value of
c beta = par*(t(j+4)-t(j)).
beta = delta*par
if(abs(beta).le.one) go to 60
c if !beta! > 1 the integrals are calculated by setting up a divided
c difference table.
do 40 k=1,5
hs(k) = si(k)
hc(k) = co(k)
40 continue
do 50 jj=1,3
k = 5
li = jp4
do 50 ll=jj,4
lj = li-jj
fac = par*(t(li)-t(lj))
hs(k) = (hs(k)-hs(k-1))/fac
hc(k) = (hc(k)-hc(k-1))/fac
k = k-1
li = li-1
50 continue
s2 = (hs(5)-hs(4))*term
c2 = (hc(5)-hc(4))*term
go to 130
c if !beta! <= 1 the integrals are calculated by evaluating a series
c expansion.
60 f3 = 0.
do 70 i=1,4
ipj = i+j
hs(i) = par*(t(ipj)-t(j))
hc(i) = hs(i)
f3 = f3+hs(i)
70 continue
f3 = f3*con1
c1 = quart
s1 = f3
if(abs(f3).le.eps) go to 120
sign = one
fac = con2
k = 5
is = 0
do 110 ic=1,20
k = k+1
ak = k
fac = fac*ak
f1 = 0.
f3 = 0.
do 80 i=1,4
f1 = f1+hc(i)
f2 = f1*hs(i)
hc(i) = f2
f3 = f3+f2
80 continue
f3 = f3*six/fac
if(is.eq.0) go to 90
is = 0
s1 = s1+f3*sign
go to 100
90 sign = -sign
is = 1
c1 = c1+f3*sign
100 if(abs(f3).le.eps) go to 120
110 continue
120 s2 = delta*(co(1)*s1+si(1)*c1)
c2 = delta*(co(1)*c1-si(1)*s1)
130 ress(j) = s2
resc(j) = c2
do 140 i=1,4
co(i) = co(i+1)
si(i) = si(i+1)
140 continue
150 continue
c calculate the integrals ress(j) and resc(j),j=n-6,n-5,n-4 by setting
c up a divided difference table.
160 do 190 j=1,3
nmj = nm3-j
i = 5-j
call fpcsin(t(nm3),t(nmj),par,si(4),co(4),si(i-1),co(i-1),
* rs(j),rc(j))
hs(i) = 0.
hc(i) = 0.
do 170 jj=1,j
ipj = i+jj
hc(ipj) = rc(jj)
hs(ipj) = rs(jj)
170 continue
do 180 jj=1,3
if(i.lt.jj) i = jj
k = 5
li = nmj
do 180 ll=i,4
lj = li+jj
fac = t(lj)-t(li)
hs(k) = (hs(k-1)-hs(k))/fac
hc(k) = (hc(k-1)-hc(k))/fac
k = k-1
li = li+1
180 continue
ress(nmj) = hs(4)-hs(5)
resc(nmj) = hc(4)-hc(5)
190 continue
return
end
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