--- /dev/null
+ real function bvalue ( t, bcoef, n, k, x, jderiv )
+c from * a practical guide to splines * by c. de boor
+calls interv
+c
+calculates value at x of jderiv-th derivative of spline from b-repr.
+c the spline is taken to be continuous from the right, EXCEPT at the
+c rightmost knot, where it is taken to be continuous from the left.
+c
+c****** i n p u t ******
+c t, bcoef, n, k......forms the b-representation of the spline f to
+c be evaluated. specifically,
+c t.....knot sequence, of length n+k, assumed nondecreasing.
+c bcoef.....b-coefficient sequence, of length n .
+c n.....length of bcoef and dimension of spline(k,t),
+c a s s u m e d positive .
+c k.....order of the spline .
+c
+c w a r n i n g . . . the restriction k .le. kmax (=20) is imposed
+c arbitrarily by the dimension statement for aj, dl, dr below,
+c but is n o w h e r e c h e c k e d for.
+c
+c x.....the point at which to evaluate .
+c jderiv.....integer giving the order of the derivative to be evaluated
+c a s s u m e d to be zero or positive.
+c
+c****** o u t p u t ******
+c bvalue.....the value of the (jderiv)-th derivative of f at x .
+c
+c****** m e t h o d ******
+c The nontrivial knot interval (t(i),t(i+1)) containing x is lo-
+c cated with the aid of interv . The k b-coeffs of f relevant for
+c this interval are then obtained from bcoef (or taken to be zero if
+c not explicitly available) and are then differenced jderiv times to
+c obtain the b-coeffs of (d**jderiv)f relevant for that interval.
+c Precisely, with j = jderiv, we have from x.(12) of the text that
+c
+c (d**j)f = sum ( bcoef(.,j)*b(.,k-j,t) )
+c
+c where
+c / bcoef(.), , j .eq. 0
+c /
+c bcoef(.,j) = / bcoef(.,j-1) - bcoef(.-1,j-1)
+c / ----------------------------- , j .gt. 0
+c / (t(.+k-j) - t(.))/(k-j)
+c
+c Then, we use repeatedly the fact that
+c
+c sum ( a(.)*b(.,m,t)(x) ) = sum ( a(.,x)*b(.,m-1,t)(x) )
+c with
+c (x - t(.))*a(.) + (t(.+m-1) - x)*a(.-1)
+c a(.,x) = ---------------------------------------
+c (x - t(.)) + (t(.+m-1) - x)
+c
+c to write (d**j)f(x) eventually as a linear combination of b-splines
+c of order 1 , and the coefficient for b(i,1,t)(x) must then be the
+c desired number (d**j)f(x). (see x.(17)-(19) of text).
+c
+ integer jderiv,k,n, i,ilo,imk,j,jc,jcmin,jcmax,jj,kmax,kmj,km1
+ * ,mflag,nmi,jdrvp1
+ parameter (kmax = 20)
+ real bcoef(n),t(n+k),x, aj(kmax),dl(kmax),dr(kmax),fkmj
+ bvalue = 0.
+ if (jderiv .ge. k) go to 99
+c
+c *** Find i s.t. 1 .le. i .lt. n+k and t(i) .lt. t(i+1) and
+c t(i) .le. x .lt. t(i+1) . If no such i can be found, x lies
+c outside the support of the spline f , hence bvalue = 0.
+c (The asymmetry in this choice of i makes f rightcontinuous, except
+c at t(n+k) where it is leftcontinuous.)
+ call interv ( t, n+k, x, i, mflag )
+ if (mflag .ne. 0) go to 99
+c *** if k = 1 (and jderiv = 0), bvalue = bcoef(i).
+ km1 = k - 1
+ if (km1 .gt. 0) go to 1
+ bvalue = bcoef(i)
+ go to 99
+c
+c *** store the k b-spline coefficients relevant for the knot interval
+c (t(i),t(i+1)) in aj(1),...,aj(k) and compute dl(j) = x - t(i+1-j),
+c dr(j) = t(i+j) - x, j=1,...,k-1 . set any of the aj not obtainable
+c from input to zero. set any t.s not obtainable equal to t(1) or
+c to t(n+k) appropriately.
+ 1 jcmin = 1
+ imk = i - k
+ if (imk .ge. 0) go to 8
+ jcmin = 1 - imk
+ do 5 j=1,i
+ 5 dl(j) = x - t(i+1-j)
+ do 6 j=i,km1
+ aj(k-j) = 0.
+ 6 dl(j) = dl(i)
+ go to 10
+ 8 do 9 j=1,km1
+ 9 dl(j) = x - t(i+1-j)
+c
+ 10 jcmax = k
+ nmi = n - i
+ if (nmi .ge. 0) go to 18
+ jcmax = k + nmi
+ do 15 j=1,jcmax
+ 15 dr(j) = t(i+j) - x
+ do 16 j=jcmax,km1
+ aj(j+1) = 0.
+ 16 dr(j) = dr(jcmax)
+ go to 20
+ 18 do 19 j=1,km1
+ 19 dr(j) = t(i+j) - x
+c
+ 20 do 21 jc=jcmin,jcmax
+ 21 aj(jc) = bcoef(imk + jc)
+c
+c *** difference the coefficients jderiv times.
+ if (jderiv .eq. 0) go to 30
+ do 23 j=1,jderiv
+ kmj = k-j
+ fkmj = float(kmj)
+ ilo = kmj
+ do 23 jj=1,kmj
+ aj(jj) = ((aj(jj+1) - aj(jj))/(dl(ilo) + dr(jj)))*fkmj
+ 23 ilo = ilo - 1
+c
+c *** compute value at x in (t(i),t(i+1)) of jderiv-th derivative,
+c given its relevant b-spline coeffs in aj(1),...,aj(k-jderiv).
+ 30 if (jderiv .eq. km1) go to 39
+ jdrvp1 = jderiv + 1
+ do 33 j=jdrvp1,km1
+ kmj = k-j
+ ilo = kmj
+ do 33 jj=1,kmj
+ aj(jj) = (aj(jj+1)*dl(ilo) + aj(jj)*dr(jj))/(dl(ilo)+dr(jj))
+ 33 ilo = ilo - 1
+ 39 bvalue = aj(1)
+c
+ 99 return
+ end
projects / mothur.git / blobdiff