Re: problem with numerical values in Solve/NSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg63759] Re: problem with numerical values in Solve/NSolve
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Fri, 13 Jan 2006 04:49:00 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <dq53td$abp$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Jacob Grose wrote:
> Hello,
>
> I writing a physics simulation and I need to solve a system of 41 equations. However, I am having problems even with a more simple 5x5 matrix. The problem is as follows: If I symbolically solve the matrix m1:
>
> \!\(\*
> TagBox[
> RowBox[{"(", "\[NoBreak]", GridBox[{
> {\(\(-a\) - b - c\), "0", "f", "h", "l"},
> {"0", \(\(-c\) - d - e\), "g", "k", "m"},
> {"a", "c", \(\(-f\) - g\), "0", "0"},
> {"b", "d", "0", \(\(-h\) - k\), "0"},
> {"c", "e", "0", "0", \(\(-l\) - m\)}
> }], "\[NoBreak]", ")"}],
> Function[ BoxForm`e$,
> MatrixForm[ BoxForm`e$]]]\)
>
> Using the code:
>
> variables = Array[p, 5];
> evec = Simplify[Solve[m1.variables \[Equal] Table[0, {i, 1, 5}], Array[p, 4]]]
>
> I get a result. However, if I try to solve for a matrix (m) of the same form but with values substituted for the variables:
>
> \!\(\*
> TagBox[
> RowBox[{"(", "\[NoBreak]", GridBox[{
> {\(-1.870413280501348`*^10\),
> "0", "1.7479373054791087`*^8", "
> 7.607967609656633`*^9", "2.5605854781972427`*^7"},
> {"0
> ", \(-1.2870235495030115`*^10\), "206293.3885126606`", \
> "8.754725514677356`*^7", "1.3554510956434595`*^10"},
> {"1.747937063721231`*^10", "2.062933885126606`*^7
> ", \(-1.7500002393642354`*^8\), "0", "0"},
> {"1.2247621677975328`*^9", "8.754722967399057`*^9", "0", \
> \(-7.695514864803407`*^9\), "0"},
> {"0.0036402209477187386`", "4.094883188779791`*^9", "0", "0", \
> \(-1.3580116811216568`*^10\)}
> }], "\[NoBreak]", ")"}],
> Function[ BoxForm`e$,
> MatrixForm[ BoxForm`e$]]]\)
>
> Using the same code:
>
> variables = Array[p, 5];
> evec = Simplify[Solve[m.variables \[Equal] Table[0, {i, 1, 5}], Array[p, 4]]]
>
> mathematica returns: {}.
>
> I tried using Nsolve instead of solve, as well as setting $MaxExtraPrecision = 5000, but it didn't help. Any ideas?
>
> Thanks,
> Jacob
>
Hi Jacob,
According to Mathematica online documentation, "Solve gives {} if there
are no possible solutions to the equations."
Since some elements of m1 depend on the values of the others, have you
checked that the matrix m satisfies these requirements?
For example,
In[1]:=
m1 = {{-a - b - c, 0, f, h, l}, {0, -c - d - e, g, k, m},
{a, c, -f - g, 0, 0}, {b, d, 0, -h - k, 0}, {c, e, 0, 0, -l - m}};
In[2]:=
m2 = m1 /. {a -> 1, b -> 2, c -> 3, d -> 4, e -> 5, f -> 6, g -> 7, h -> 8,
i -> 9, j -> 10, k -> 11, l -> 12, m -> 13}
Out[2]=
{{-6, 0, 6, 8, 12}, {0, -12, 7, 11, 13}, {1, 3, -13, 0, 0},
{2, 4, 0, -19, 0}, {3, 5, 0, 0, -25}}
In[3]:=
variables = Array[p, 5];
evec = Simplify[Solve[m2 . variables == Table[0, {i, 1, 5}], Array[p, 4]]]
Out[4]=
{{p[1] -> (1535*p[5])/367, p[2] -> (914*p[5])/367, p[3] -> (329*p[5])/367,
p[4] -> (354*p[5])/367}}
In[5]:=
m3 = m2 /. -25 -> 25
Out[5]=
{{-6, 0, 6, 8, 12}, {0, -12, 7, 11, 13}, {1, 3, -13, 0, 0},
{2, 4, 0, -19, 0}, {3, 5, 0, 0, 25}}
In[6]:=
variables = Array[p, 5];
evec = Simplify[Solve[m3 . variables == Table[0, {i, 1, 5}], Array[p, 4]]]
Out[7]=
{}
Best regards,
/J.M.