putit.f

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      subroutine putit ( t, kpm, left, scrtch, dbiatx, q, nrow, b )

c*********************************************************************72
c
cc PUTIT puts together one block of the collocation equation system.
c
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
      implicit none

      integer kpm,left,nrow,   i,irow,iside,itermx,j,k,ll,lowrow,m,mode
     &                        ,mp1
      double precision 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) = 0.0d+00
      xm = (t(left+1)+t(left))/2.0d+00
      dx = (t(left+1)-t(left))/2.0d+00
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 = 0.0d+00
            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