bvalue.f
164 lines
| 5.6 KiB
| text/x-fortran
|
FortranFixedLexer
| r1601 | c parameter(nn=20,kk=4) | |||
| c real ta(nn+kk),bcoef(nn) | ||||
| c k=kk | ||||
| c n=nn | ||||
| c do i=1,n+k | ||||
| c ta(i)=float(i) | ||||
| c end do | ||||
| c do i=1,n | ||||
| c bcoef(i)=float(i) | ||||
| c end do | ||||
| c do i=3,n+1 | ||||
| c write(*,*) ta(i)+0.5, bvalue (ta, bcoef, n, k, ta(i)+0.5, 0 ) | ||||
| c end do | ||||
| c stop | ||||
| c end | ||||
| 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 | ||||
| parameter (kmax = 20) | ||||
| integer jderiv,k,n,i,ilo,imk,j,jc,jcmin,jcmax,jj, | ||||
| c * kmax, | ||||
| * kmj,km1 | ||||
| * ,mflag,nmi,jdrvp1 | ||||
| C real bcoef(n),t(1),x, aj(20),dl(20),dr(20),fkmj | ||||
| real bcoef(n),x, aj(kmax),dl(kmax),dr(kmax),fkmj | ||||
| dimension t(n+k) | ||||
| c former fortran standard made it impossible to specify the length of t | ||||
| c precisely without the introduction of otherwise superfluous addition- | ||||
| c al arguments. | ||||
| 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 | ||||
