subroutine putit ( t, kpm, left, scrtch, dbiatx, q, nrow, b )
c from * a practical guide to splines * by c. de Boor (7 may 92)
calls bsplvd(bsplvb),difequ(*)
c to be called by e q b l o k .
c
c puts together one block of the collocation equation system
c
c****** i n p u t ******
c t knot sequence, of size left+kpm (at least)
c kpm order of spline
c left integer indicating interval of interest, viz the interval
c (t(left), t(left+1))
c nrow number of rows in block to be put together
c
c****** w o r k a r e a ******
c scrtch used in bsplvd, of size (kpm,kpm)
c dbiatx used to contain derivatives of b-splines, of size (kpm,m+1)
c with dbiatx(j,i+1) containing the i-th derivative of the
c j-th b-spline of interest
c
c****** o u t p u t ******
c q the block, of size (nrow,kpm)
c b the corresponding piece of the right side, of size (nrow)
c
c****** m e t h o d ******
c the k collocation equations for the interval (t(left),t(left+1))
c are constructed with the aid of the subroutine d i f e q u ( 2, .,
c . ) and interspersed (in order) with the side conditions (if any) in
c this interval, using d i f e q u ( 3, ., . ) for the information.
c the block q has kpm columns, corresponding to the kpm b-
c splines of order kpm which have the interval (t(left),t(left+1))
c in their support. the block's diagonal is part of the diagonal of the
c total system. the first equation in this block not overlapped by the
c preceding block is therefore equation l o w r o w , with lowrow = 1+
c number of side conditions in preceding intervals (or blocks).
c
integer kpm,left,nrow, i,irow,iside,itermx,j,k,ll,lowrow,m,mode
* ,mp1
real b(1),dbiatx(kpm,1),q(nrow,kpm),scrtch(1),t(1), dx,rho,sum
* ,v(20),xm,xside,xx
common /side/ m, iside, xside(10)
common /other/ itermx,k,rho(19)
mp1 = m+1
do 10 j=1,kpm
do 10 i=1,nrow
10 q(i,j) = 0.
xm = (t(left+1)+t(left))/2.
dx = (t(left+1)-t(left))/2.
c
ll = 1
lowrow = iside
do 30 irow=lowrow,nrow
if (ll .gt. k) go to 22
mode = 2
c next collocation point is ...
xx = xm + dx*rho(ll)
ll = ll + 1
c the corresp.collocation equation is next unless the next side
c condition occurs at a point at, or to the left of, the next
c collocation point.
if (iside .gt. m) go to 24
if (xside(iside) .gt. xx) go to 24
ll = ll - 1
22 mode = 3
xx = xside(iside)
24 call difequ ( mode, xx, v )
c the next equation, a collocation equation (mode = 2) or a side
c condition (mode = 3), reads
c (*) (v(m+1)*d**m + v(m)*d**(m-1) +...+ v(1)*d**0)f(xx) = v(m+2)
c in terms of the info supplied by difequ . the corresponding
c equation for the b-coeffs of f therefore has the left side of
c (*), evaluated at each of the kpm b-splines having xx in
c their support, as its kpm possibly nonzero coefficients.
call bsplvd ( t, kpm, xx, left, scrtch, dbiatx, mp1 )
do 26 j=1,kpm
sum = 0.
do 25 i=1,mp1
25 sum = v(i)*dbiatx(j,i) + sum
26 q(irow,j) = sum
30 b(irow) = v(m+2)
return
end