+++ /dev/null
- subroutine interv ( xt, lxt, x, left, mflag )
-c from * a practical guide to splines * by C. de Boor
-computes left = max( i : xt(i) .lt. xt(lxt) .and. xt(i) .le. x ) .
-c
-c****** i n p u t ******
-c xt.....a real sequence, of length lxt , assumed to be nondecreasing
-c lxt.....number of terms in the sequence xt .
-c x.....the point whose location with respect to the sequence xt is
-c to be determined.
-c
-c****** o u t p u t ******
-c left, mflag.....both integers, whose value is
-c
-c 1 -1 if x .lt. xt(1)
-c i 0 if xt(i) .le. x .lt. xt(i+1)
-c i 0 if xt(i) .lt. x .eq. xt(i+1) .eq. xt(lxt)
-c i 1 if xt(i) .lt. xt(i+1) .eq. xt(lxt) .lt. x
-c
-c In particular, mflag = 0 is the 'usual' case. mflag .ne. 0
-c indicates that x lies outside the CLOSED interval
-c xt(1) .le. y .le. xt(lxt) . The asymmetric treatment of the
-c intervals is due to the decision to make all pp functions cont-
-c inuous from the right, but, by returning mflag = 0 even if
-C x = xt(lxt), there is the option of having the computed pp function
-c continuous from the left at xt(lxt) .
-c
-c****** m e t h o d ******
-c The program is designed to be efficient in the common situation that
-c it is called repeatedly, with x taken from an increasing or decrea-
-c sing sequence. This will happen, e.g., when a pp function is to be
-c graphed. The first guess for left is therefore taken to be the val-
-c ue returned at the previous call and stored in the l o c a l varia-
-c ble ilo . A first check ascertains that ilo .lt. lxt (this is nec-
-c essary since the present call may have nothing to do with the previ-
-c ous call). Then, if xt(ilo) .le. x .lt. xt(ilo+1), we set left =
-c ilo and are done after just three comparisons.
-c Otherwise, we repeatedly double the difference istep = ihi - ilo
-c while also moving ilo and ihi in the direction of x , until
-c xt(ilo) .le. x .lt. xt(ihi) ,
-c after which we use bisection to get, in addition, ilo+1 = ihi .
-c left = ilo is then returned.
-c
- integer left,lxt,mflag, ihi,ilo,istep,middle
- double precision x,xt(lxt)
- data ilo /1/
- save ilo
- ihi = ilo + 1
- if (ihi .lt. lxt) go to 20
- if (x .ge. xt(lxt)) go to 110
- if (lxt .le. 1) go to 90
- ilo = lxt - 1
- ihi = lxt
-c
- 20 if (x .ge. xt(ihi)) go to 40
- if (x .ge. xt(ilo)) go to 100
-c
-c **** now x .lt. xt(ilo) . decrease ilo to capture x .
- istep = 1
- 31 ihi = ilo
- ilo = ihi - istep
- if (ilo .le. 1) go to 35
- if (x .ge. xt(ilo)) go to 50
- istep = istep*2
- go to 31
- 35 ilo = 1
- if (x .lt. xt(1)) go to 90
- go to 50
-c **** now x .ge. xt(ihi) . increase ihi to capture x .
- 40 istep = 1
- 41 ilo = ihi
- ihi = ilo + istep
- if (ihi .ge. lxt) go to 45
- if (x .lt. xt(ihi)) go to 50
- istep = istep*2
- go to 41
- 45 if (x .ge. xt(lxt)) go to 110
- ihi = lxt
-c
-c **** now xt(ilo) .le. x .lt. xt(ihi) . narrow the interval.
- 50 middle = (ilo + ihi)/2
- if (middle .eq. ilo) go to 100
-c note. it is assumed that middle = ilo in case ihi = ilo+1 .
- if (x .lt. xt(middle)) go to 53
- ilo = middle
- go to 50
- 53 ihi = middle
- go to 50
-c**** set output and return.
- 90 mflag = -1
- left = 1
- return
- 100 mflag = 0
- left = ilo
- return
- 110 mflag = 1
- if (x .eq. xt(lxt)) mflag = 0
- left = lxt
- 111 if (left .eq. 1) return
- left = left - 1
- if (xt(left) .lt. xt(lxt)) return
- go to 111
- end
projects / mothur.git / blobdiff