Re: numerics

• To: mathgroup at smc.vnet.net
• Subject: [mg27283] Re: [mg27276] numerics
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Sat, 17 Feb 2001 03:30:59 -0500 (EST)
• References: <200102160858.DAA13479@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```It seems the problem arises from precision. See, if you look at FullForm:

In[1]:=
FullForm[newmat]

Out[1]//FullForm=
List[List[-0.19999999999999996`, 0.1`, 0],
List[0.1`, -0.30000000000000004`, 0.1`],
List[0.1`, 0.2`, -0.09999999999999998`]]

and this messes up the whole situation. Of course, it all depends on the
actual numbers you're dealing with in your problem, but if you rationalize
the input in your example, you obtain

In[2]:=
mat2 = Rationalize[mat1]
Out[2]=
{{4/5, 1/10, 1/10}, {1/10, 7/10, 1/5}, {0, 1/10, 9/10}}

Now you take

In[3]:=
newmat2 = Transpose[mat2] - imat

so that

In[4]:=
newmat2 == mat
Out[4]=
True

and now

In[5]:=
Reduce[newmat2.{x1, x2, x3} == {0, 0, 0}, {x1, x2, x3}]
Out[5]=
x1 == x2/2 && x3 == (5*x2)/2

which is what you were expecting. No loss of precision with rationals.

Tomas Garza
Mexico City

----- Original Message -----
From: <Matt.Johnson at autolivasp.com>
To: mathgroup at smc.vnet.net
Subject: [mg27283] [mg27276] numerics

> mathematica gurus--
>
> Here's a frustrating problem, which seems to be simple.  I can calculate a
> matrix by hand and enter it into Solve or Reduce and get the correct
> relationships:
>
> In[108]:=
> mat = Partition[{-0.2, 0.1, 0, 0.1, -0.3, 0.1, 0.1, 0.2, -0.1}, 3];
> Reduce[mat.{x1, x2, x3} == {0, 0, 0}, {x1, x2, x3}]
> Out[109]=
> x1 == 0.5 x2 && x3 == 2.5 x2
>
> However, if I try to manipulate the matrix in Mathematica then solve, it
doesn't work:
>
> In[110]:=
> mat1 = Partition[{0.8, 0.1, 0.1, 0.1, 0.7, 0.2, 0, 0.1, 0.9}, 3];
> imat = IdentityMatrix[Length[mat1]];
> newmat = Transpose[mat1] - imat;
> In[113]:=
> newmat == mat
> Out[113]=
> True
> In[114]:=
> newmat === mat
> Out[114]=
> False
> In[115]:=
> Reduce[newmat.{x1, x2, x3} == {0, 0, 0}, {x1, x2, x3}]
> Out[115]=
> x1 == 0. && x2 == 0. && x3 == 0.
>
> any input?
>
> -matt
>
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```

• References:
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• From: Matt.Johnson@autolivasp.com
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