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From: Matt J on 21 Jul 2010 15:56
Here's a bit more embellished version of my last example that uses the
oneWithTol() function down at the bottom of the post to create the object in a single line. The object returned by oneWithTol allows you to do a series of tolerance-qualified comparisons with arbitrary numbers, all without function call syntax.

l=oneWithTol(.01); %Represents the number 1 with a tolerance of .01

%%Comparison operations

>> sum([.4 .3 .2 .1001])==l %Equal to one within tolerance of .01

ans =

1

>> sum([.4 .3 .2 .1001 9])==l %Not equal to one within tolerance of .01

ans =

0

>> sum([.4 .3 .2 .1001 9])==10*l %But it is equal to 10 within the tolerance

ans =

1

>> sum([.4 .3 .2 .15 9])==10*l %Not equal to 10 within the tolerance

ans =

0





function FuzzyOne=oneWithTol(tol,val)
%FuzzyOne=oneWithTol(tol) - Returns an object FuzzyOne representing the
%scalar 1, but with the property that operations expression==FuzzyOne will
%be evaluated with the input tolerance, tol
%
%Also, FuzzyOne can be scaled arbitrarily c*FuzzyOne to permit comparisons
%with numbers other than one.

if nargin<2, val=1; end %for now extra argout only used internally

FuzzyOne=MatrixObj;
FuzzyOne.Params.tol=tol;
FuzzyOne.Params.val=val;
FuzzyOne.Ops.eq=@(x,A) abs(A.Params.val-x)<=A.Params.tol;
FuzzyOne.Ops.mtimes=@(c,A) oneWithTol(A.Params.tol,c*A.Params.val);
From: Brandon Moore on 21 Jul 2010 16:30
Walter Roberson <roberson(a)hushmail.com> wrote in message
> histc() reserves the final output bin to count values that are exact equal to
> the last provided edge. If comparisons suddenly became slightly fuzzy in the
> manner described ("erring on the side of logical true"), then
>
> x < x
>
> and
>
> x == x
>
> would both be true and it would then be ambiguous as to whether the values
> exactly matching the last edge should be counted towards the second-last bin
> or toward the final bin or both.

Good point. Probably better to leave this alone and deal with approximation problems explicitly. At least until someone invents a computer that works with real numbers.
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