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)
- Reply-to: laianhngoc at yahoo.com
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?
Thanks in advance.
LAI.