Problem of evaluate Numerically Eigensystem in Nminimize

• To: mathgroup at smc.vnet.net
• Subject: [mg97083] Problem of evaluate Numerically Eigensystem in Nminimize
• From: Anh Ngoc LAI <laianhngoc at yahoo.com>
• Date: Thu, 5 Mar 2009 04:52:15 -0500 (EST)

```Dear all,

I have to compute NUMERICALLY (not analytically) the Eigensystem a 3x3
Matrix, put the result into a function and use Nminimize to optimize. I pos=
e:

M[t6_,
t7_, t8_, t9_, t10_] :=Eigensystem[N[{{t6, 0, 0}, {t7, t8, t9},{0, 0, t10=
}}]];

M221[t6_?NumericQ,
t7_?NumericQ, t8_?NumericQ, t9_?NumericQ, t10_?NumericQ]:= M[t6, t7, t8, =
t9, t10][[2,
3, 1]];

M222[t6_?NumericQ,
t7_?NumericQ, t8_?NumericQ, t9_?NumericQ, t10_?NumericQ] := M[t6, t7, t8,=
t9, t10][[2,
3, 2]];

M232[t6_?NumericQ,
t7_?NumericQ, t8_?NumericQ, t9_?NumericQ, t10_?NumericQ] := M[t6, t7, t8,=
t9,
t10][[2, 1, 2]];

M233[t6_?NumericQ,
t7_?NumericQ, t8_?NumericQ, t9_?NumericQ, t10_?NumericQ] := M[t6, t7, t8,=
t9,
t10][[2, 1, 3]];

M2 = Transpose[{{0,
1, 0}, {M221[t6, t7, t8, t9, t10],M222[t6, t7, t8, t9, t10], 0}, {0, M232[t=
6,
t7, t8, t9, t10],M233[t6, t7, t8, t9, t10]}}];

I have to Inverse
M2 in my function (type Maximum Likelihood), and then use Nminimize to opti=
mize.
But Mathematica give an error message:

Power::infy: Infinite expression 1/0
encountered.

That comes from the
fact, I have (1/M221) and (1/M233) in the objective function and I
searched and don=E2=80=99t know how to solve this problem. I think that in =
the others software,
they don=E2=80=99t have this problem because the Eigensystem is computed di=
rectly numerically.

Any ideas will be much appreciated?

LAI.

```

• Prev by Date: Re: GraphComplement doesn't work in 7.0
• Next by Date: Re: Re: "Do What I Mean" - a suggestion for improving
• Previous by thread: Announcing Mathematica 7.0.1
• Next by thread: Bug in Pattern Matching with Condition?