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From: dodson@convex.COM (Dave Dodson)
Newsgroups: comp.lang.fortran
Subject: Re: rounding a real to a whole number
Message-ID: <108130@convex.convex.com>
Date: 2 Nov 90 17:01:21 GMT
References: <U714092.90Nov1101629@eagle.larc.nasa.gov>
Sender: usenet@convex.com
Reply-To: dodson@convex.COM (Dave Dodson)
Organization: Convex Computer Corporation; Richardson, TX
Lines: 80

In article <U714092.90Nov1101629@eagle.larc.nasa.gov> u714092@eagle.larc.nasa.gov (prichard devon ) writes:
>what I want to do is to have a subroutine which, given a range of real
>numbers, for example  -123.445 -> 1033.02 , and choose whole numbers 
>outside that range. obviously the first application is axis values for
>x-y plots.  optionally, picking a 10-multiple of whole numbers ought to
>be included; for  -1.45567 -> 3.34112 , it should return -1.4 and 3.4 ...

If you are going to plot data, you may want the axis divisions to be "round"
numbers.  I wrote a subroutine many years ago that determined such an axis.
The following is how I remember it working.  Caution: not checked out...

	subroutine axis (n,x,ndiv,xmin,delx,xmax)
c  input:
	integer n	! length of x
	integer ndiv	! number of axis divisions
	real x(n)	! data array
c  output:
	real xmin	! axis minimum, multiple of delx
	real delx	! axis increment per division
	real xmax	! axis maximum, multiple of delx
c  local:
	real table(4)
	data table / 1.0, 2.0, 4.0, 5.0 /
	
	xmini = x(1)
	xmaxi = x(1)
	do 10 i = 2, n
	    xmini = min ( xmini, x(i)
	    xmaxi = max ( xmaxi, x(i)
   10	continue
	if ( xmini .eq. xmaxi ) then
	    < I don't remember what I did when all x(i) are equal >
	end if

	delta = ( xmaxi - xmini ) / ndiv
	ratio = 0.0
	do 40 i = 1, 4
	    trial = table(i)
   20	    if ( trial .lt. delta ) then
		trial = 10.0 * trial
		go to 20
	    end if
   30	    if ( trial / 10.0 .gt. delta ) then
		trial = trial / 10.0
		go to 30
	    end if
	    xmint = trial * aint ( xmini / trial )
	    if ( xmint .gt. xmini ) xmint = xmint - trial
	    xmaxt = trial * aint ( xmaxi / trial )
	    if ( xmaxt .lt. xmaxi ) xmaxt = xmaxt + trial
	    if ( xmint + ndiv * trial * 1.0001 .ge. xmaxt ) then
		if ( ( xmaxi - xmini ) / ( xmaxt - xmint ) .gt. ratio ) then
		    ratio = ( xmaxi - xmini ) / ( xmaxt - xmint )
		    xmin = xmint
		    delx = trial
		    xmax = xmaxt
		end if
	    end if
   40	continue
	return
	end

This begins by finding the max and min of the data.  Delta is set to
the minimum allowed increment per axis division.  Ratio is the fraction
of the axis that would be occupied by the graph; it is initialized to
zero.  Then each increment of the form 1 * 10^j, 2 * 10^j, and 4 * 10^j
is examined.  First the j in 10^j is adjusted up or down so that 
table(i) * 10^(j-1) <= delta <= table(i) * 10^j (actually, we don't care
about j, only trial := table(i) * 10^j).  Using trial as an increment
per axis division, we find xmint = the largest multiple of trial that
is .le. xmini and xmaxt = the smallest multiple of trial that is .ge. xmaxt.
If ndiv * trial spans the interval from xmint to xmaxt then we check to see
how much of the axis would be occupied by the graph.  We accept trial if
it uses more axis that the previous.  When we have inspected all 4 forms
for trial, we return with the best one.

----------------------------------------------------------------------

Dave Dodson		                             dodson@convex.COM
Convex Computer Corporation      Richardson, Texas      (214) 497-4234