--- /dev/null
+ subroutine bsplvb ( t, lent,jhigh, index, x, left, biatx )
+c implicit none
+c -------------
+
+calculates the value of all possibly nonzero b-splines at x of order
+c
+c jout = dmax( jhigh , (j+1)*(index-1) )
+c
+c with knot sequence t .
+c
+c****** i n p u t ******
+c t.....knot sequence, of length left + jout , assumed to be nonde-
+c creasing.
+c a s s u m p t i o n : t(left) < t(left + 1)
+c d i v i s i o n b y z e r o will result if t(left) = t(left+1)
+c
+c jhigh,
+c index.....integers which determine the order jout = max(jhigh,
+c (j+1)*(index-1)) of the b-splines whose values at x are to
+c be returned. index is used to avoid recalculations when seve-
+c ral columns of the triangular array of b-spline values are nee-
+c ded (e.g., in bvalue or in bsplvd ). precisely,
+c if index = 1 ,
+c the calculation starts from scratch and the entire triangular
+c array of b-spline values of orders 1,2,...,jhigh is generated
+c order by order , i.e., column by column .
+c if index = 2 ,
+c only the b-spline values of order j+1, j+2, ..., jout are ge-
+c nerated, the assumption being that biatx , j , deltal , deltar
+c are, on entry, as they were on exit at the previous call.
+c in particular, if jhigh = 0, then jout = j+1, i.e., just
+c the next column of b-spline values is generated.
+c
+c w a r n i n g . . . the restriction jout <= jmax (= 20) is
+c imposed arbitrarily by the dimension statement for deltal and
+c deltar below, but is n o w h e r e c h e c k e d for .
+c
+c x.....the point at which the b-splines are to be evaluated.
+c left.....an integer chosen (usually) so that
+c t(left) <= x <= t(left+1) .
+c
+c****** o u t p u t ******
+c biatx.....array of length jout , with biatx(i) containing the val-
+c ue at x of the polynomial of order jout which agrees with
+c the b-spline b(left-jout+i,jout,t) on the interval (t(left),
+c t(left+1)) .
+c
+c****** m e t h o d ******
+c the recurrence relation
+c
+c x - t(i) t(i+j+1) - x
+c b(i,j+1)(x) = ----------- b(i,j)(x) + --------------- b(i+1,j)(x)
+c t(i+j)-t(i) t(i+j+1)-t(i+1)
+c
+c is used (repeatedly) to generate the
+c (j+1)-vector b(left-j,j+1)(x),...,b(left,j+1)(x)
+c from the j-vector b(left-j+1,j)(x),...,b(left,j)(x),
+c storing the new values in biatx over the old. the facts that
+c b(i,1) = 1 if t(i) <= x < t(i+1)
+c and that
+c b(i,j)(x) = 0 unless t(i) <= x < t(i+j)
+c are used. the particular organization of the calculations follows
+c algorithm (8) in chapter x of the text.
+c
+
+C Arguments
+ integer lent, jhigh, index, left
+ double precision t(lent),x, biatx(jhigh)
+c dimension t(left+jout), biatx(jout)
+c -----------------------------------
+c current fortran standard makes it impossible to specify the length of
+c t and of biatx precisely without the introduction of otherwise
+c superfluous additional arguments.
+
+C Local Variables
+ integer jmax
+ parameter(jmax = 20)
+ integer i,j,jp1
+ double precision deltal(jmax), deltar(jmax),saved,term
+
+ save j,deltal,deltar
+ data j/1/
+c
+ go to (10,20), index
+ 10 j = 1
+ biatx(1) = 1d0
+ if (j .ge. jhigh) go to 99
+c
+ 20 jp1 = j + 1
+ deltar(j) = t(left+j) - x
+ deltal(j) = x - t(left+1-j)
+ saved = 0d0
+ do 26 i=1,j
+ term = biatx(i)/(deltar(i) + deltal(jp1-i))
+ biatx(i) = saved + deltar(i)*term
+ 26 saved = deltal(jp1-i)*term
+ biatx(jp1) = saved
+ j = jp1
+ if (j .lt. jhigh) go to 20
+c
+ 99 return
+ end
projects / mothur.git / blobdiff