--- /dev/null
+ subroutine bsplvd ( t, lent, k, x, left, a, dbiatx, nderiv )
+c -------- ------
+c implicit none
+
+C calculates value and deriv.s of all b-splines which do not vanish at x
+C calls bsplvb
+c
+c****** i n p u t ******
+c t the knot array, of length left+k (at least)
+c k the order of the b-splines to be evaluated
+c x the point at which these values are sought
+c left an integer indicating the left endpoint of the interval of
+c interest. the k b-splines whose support contains the interval
+c (t(left), t(left+1))
+c are to be considered.
+c a s s u m p t i o n - - - it is assumed that
+c t(left) < t(left+1)
+c division by zero will result otherwise (in b s p l v b ).
+c also, the output is as advertised only if
+c t(left) <= x <= t(left+1) .
+c nderiv an integer indicating that values of b-splines and their
+c derivatives up to but not including the nderiv-th are asked
+c for. ( nderiv is replaced internally by the integer in (1,k)
+c closest to it.)
+c
+c****** w o r k a r e a ******
+c a an array of order (k,k), to contain b-coeff.s of the derivat-
+c ives of a certain order of the k b-splines of interest.
+c
+c****** o u t p u t ******
+c dbiatx an array of order (k,nderiv). its entry (i,m) contains
+c value of (m-1)st derivative of (left-k+i)-th b-spline of
+c order k for knot sequence t , i=m,...,k; m=1,...,nderiv.
+c
+c****** m e t h o d ******
+c values at x of all the relevant b-splines of order k,k-1,...,
+c k+1-nderiv are generated via bsplvb and stored temporarily
+c in dbiatx . then, the b-coeffs of the required derivatives of the
+c b-splines of interest are generated by differencing, each from the
+c preceding one of lower order, and combined with the values of b-
+c splines of corresponding order in dbiatx to produce the desired
+c values.
+
+C Args
+ integer lent,k,left,nderiv
+ double precision t(lent),x, dbiatx(k,nderiv), a(k,k)
+C Locals
+ double precision factor,fkp1mm,sum
+ integer i,ideriv,il,j,jlow,jp1mid, kp1,kp1mm,ldummy,m,mhigh
+
+ mhigh = max0(min0(nderiv,k),1)
+c mhigh is usually equal to nderiv.
+ kp1 = k+1
+ call bsplvb(t,lent,kp1-mhigh,1,x,left,dbiatx)
+ if (mhigh .eq. 1) go to 99
+c the first column of dbiatx always contains the b-spline values
+c for the current order. these are stored in column k+1-current
+c order before bsplvb is called to put values for the next
+c higher order on top of it.
+ ideriv = mhigh
+ do 15 m=2,mhigh
+ jp1mid = 1
+ do 11 j=ideriv,k
+ dbiatx(j,ideriv) = dbiatx(jp1mid,1)
+ 11 jp1mid = jp1mid + 1
+ ideriv = ideriv - 1
+ call bsplvb(t,lent,kp1-ideriv,2,x,left,dbiatx)
+ 15 continue
+c
+c at this point, b(left-k+i, k+1-j)(x) is in dbiatx(i,j) for
+c i=j,...,k and j=1,...,mhigh ('=' nderiv). in particular, the
+c first column of dbiatx is already in final form. to obtain cor-
+c responding derivatives of b-splines in subsequent columns, gene-
+c rate their b-repr. by differencing, then evaluate at x.
+c
+ jlow = 1
+ do 20 i=1,k
+ do 19 j=jlow,k
+ 19 a(j,i) = 0d0
+ jlow = i
+ 20 a(i,i) = 1d0
+c at this point, a(.,j) contains the b-coeffs for the j-th of the
+c k b-splines of interest here.
+c
+ do 40 m=2,mhigh
+ kp1mm = kp1 - m
+ fkp1mm = dble(kp1mm)
+ il = left
+ i = k
+c
+c for j=1,...,k, construct b-coeffs of (m-1)st derivative of
+c b-splines from those for preceding derivative by differencing
+c and store again in a(.,j) . the fact that a(i,j) = 0 for
+c i < j is used.sed.
+ do 25 ldummy=1,kp1mm
+ factor = fkp1mm/(t(il+kp1mm) - t(il))
+c the assumption that t(left) < t(left+1) makes denominator
+c in factor nonzero.
+ do 24 j=1,i
+ 24 a(i,j) = (a(i,j) - a(i-1,j))*factor
+ il = il - 1
+ 25 i = i - 1
+c
+c for i=1,...,k, combine b-coeffs a(.,i) with b-spline values
+c stored in dbiatx(.,m) to get value of (m-1)st derivative of
+c i-th b-spline (of interest here) at x , and store in
+c dbiatx(i,m). storage of this value over the value of a b-spline
+c of order m there is safe since the remaining b-spline derivat-
+c ive of the same order do not use this value due to the fact
+c that a(j,i) = 0 for j < i .
+ do 40 i=1,k
+ sum = 0.d0
+ jlow = max0(i,m)
+ do 35 j=jlow,k
+ 35 sum = a(j,i)*dbiatx(j,m) + sum
+ 40 dbiatx(i,m) = sum
+ 99 return
+ end
projects / mothur.git / blobdiff