RE: strange problem

[Thomas Shores]

If one is only cleaning a final product, clean() is a good idea. If,
however, one is at an intermediate stage, there might be problems.
Consider, for example,


octave:10> function
xout=clean(xin,prec);xout=xin*(abs(xin>prec));endfunction
octave:11> A=1e-16*eye(2);inv(A)
ans =

   1.0000e+16  -0.0000e+00
   0.0000e+00   1.0000e+16

octave:12> B=clean(A,eps);inv(B)
warning: inverse: matrix singular to machine precision, rcond = 0
ans =

  0  0
  0  0


The point is that error is a relative matter. So I suggest a slight
modification:

octave:13> function
xout=clean(xin,prec);relprec=prec*norm(xin,inf);xout=xin*(abs(xin>relprec));endfunction
octave:14> B=clean(A,eps);inv(B)
ans =

   1.0000e+16  -0.0000e+00
   0.0000e+00   1.0000e+16


Tom Shores



On Fri, 2003-11-28 at 05:39, THOMAS Paul Richard wrote:
> Gerald,
> 
> I am glad that the function did it for you.  As several of the respondents
> said, this is a result of limitations in floating point arithmetic.
> 
> Not only is the response time of this list good but you should check out the
> times of the replies and the locations of some of our friends on this list.
> I sort of wonder if they have homes to go to?
> 
> Paul
> 
> -----Message d'origine-----
> De : Gerald Ebberink [mailto:address@hidden
> Envoyé : vendredi 28 novembre 2003 11:39
> À : address@hidden
> Objet : Re: strange problem
> 
> 
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
> 
> Problem solved,
> thnx all
> 
> since I don't work under windows the function gives me a nice way of
> cleaning th results after each multiplication.
> 
> by the way, this list has a very low response time. Other programs have
> far worse lists.
> 
> THOMAS Paul Richard wrote:
> | Dear All,
> |
> | The matrix multiplication gives zero for ans(1,1) in octave 2.1.49 (under
> | Cygwin)!  However, Matlab5 gives the same result as Gerald's.
> |
> | Compiling the expression 1-(100*-1)/100 in g++ or intel C++ give 0.  I
> would
> | conclude that this is some peculiarity of BLAS that seems to have been
> | eliminated in later versions of Octave/BLAS.
> |
> | It seems to me that Gerald's work-around might be to use
> |
> | function xout=clean(xin,prec);xout=xin.*(abs(xin)>prec);endfunction;
> |
> | so that
> |
> | a=clean([1,100;0,1]*[1,0;(-1/100),1],1E-16);
> |
> | a(1,1) yields 0
> |
> | Paul
> |
> | ---
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> - --
> Ing. Gerald Ebberink
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-- 
Thomas Shores <address@hidden>
Department of Mathematics, UNL



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