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Re: tiny negative numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg92867] Re: tiny negative numbers
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 16 Oct 2008 05:04:37 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <gd4dsk$bkv$1@smc.vnet.net>

a wrote:

> I am trying to solve a set of differential equations using NDSolve.
> But I'm seeing some really tiny negative numbers like this one:
> -1.28E-12. I'm guessing this is a machine-precision related problem.
> So I was wondering if I can somehow ensure that the variable values
> never go below 0, or alternatively, ensure that these tiny numbers
> equate to 0?

Use the command *Chop*. See

http://reference.wolfram.com/mathematica/ref/Chop.html

 From the online help:

   . Chop[expr] replaces approximate real numbers in expr
     that are close to zero by the exact integer 0.

   . Chop[expr,delta] replaces numbers smaller in absolute
     magnitude than delta by 0.

   . Chop uses a default tolerance of 10^-10.

   . Chop works on both Real and Complex numbers.

   In[1]:= Exp[N[Range[4] Pi I]]

   Out[1]= {-1. + 1.22461*10^-16 I,
     1.- 2.44921*10^-16 I, -1. + 3.67382*10^-16 I, 1.- 4.89843*10^-16 I}

   In[2]:= Chop[%]

   Out[2]= {-1., 1., -1., 1.}

Regards,
-- Jean-Marc