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From |
"Randy Akee " <[email protected]> |

To |
<[email protected]> |

Subject |
RE: st: Mata and Optimize Command |

Date |
Mon, 24 Sep 2007 18:04:06 +0200 |

```
Thanks for this, this was extremely helpful.
R
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Jeff
Pitblado, StataCorp LP
Sent: Montag, 24. September 2007 16:49
To: [email protected]
Subject: Re: st: Mata and Optimize Command
Randy Akee <[email protected]> is getting a conformability error in the
-md0()-
Mata routine he wrote for use with -optimize()-:
> I am trying to use the MATA Optimize command to get a minimum distance
> estimator of some parameters of interest. I have six equations and
six
> unknown parameters - my actual problem is a bit more complex, but I
> can't seem to get the simple version to work below:
>
> I've typed in two matrices, c and f. I'm trying to find the
parameters,
> p, that minimize: (c-f(p))'(c-f(p)).
>
> The error that I get is that the function is not conformable, does
> anyone have a suggestion on how I could correct this in what I've
done?
> I believe the issue is that I need somehow to specify the dimensions
of
> the parameter vector, p. I'm just not sure if that is possible to do,
> any ideas would be appreciated.
Randy also reported the Mata code that reproduces the error. Here is
Randy's
evaluator function:
> void md0(todo, p, c, f, lnf, S, H)
> {
> lnf = (c-f*p)'*(c-f*p)
> }
Here is a brief description of the arguments to this function:
Input variables:
----------------
todo -- a scalar message variable from -optimize()- that
indicates
whether to compute 1st and 2nd order derivatives;
this
variable can safely be ignored if your routine is not
going
to compute derivatives
p -- the current value of the parameter vector (a
rowvector)
c -- Randy's first user-defined argument
> : c
> 1
> +-----+
> 1 | 1 |
> 2 | 2 |
> 3 | 3 |
> 4 | 4 |
> 5 | 5 |
> 6 | 6 |
> +-----+
f -- Randy's second user-defined argument
> : f
> 1 2 3 4 5 6
> +-------------------------+
> 1 | 1 1 0 0 0 0 |
> 2 | 0 1 1 0 0 0 |
> 3 | 0 0 1 1 0 0 |
> 4 | 0 0 0 1 1 0 |
> 5 | 0 0 0 0 1 1 |
> 6 | 1 0 0 0 0 1 |
> +-------------------------+
Output variables:
-----------------
lnf -- the value of the objective function that is being
optimized
g -- the gradient vector
H -- the Hessian matrix
The problem with Randy's evaluator it that with 'c' a 6x1 column vector
and 'f' a 6x6 matrix, 'p' would need to be a 6x1 column vector. There
are two
reasons why this is a problem:
1. -optimize()- requires that 'p' is a rowvector
2. Randy set the starting values using
> : optimize_init_params(S,(0,0))
which is a 1x2 rowvector.
In this case, 'p' needs to be a 1x6 rowvector, so there are missing
transpose
operators in Randy's -md0()- function. Here is how I would code Randy's
evaluator and starting values:
void md0(todo, p, c, f, lnf, S, H)
{
real colvector diff
diff = c - f*p'
lnf = cross(diff,diff)
}
optimize_init_params(S, J(1,6,0))
[-cross(z,z)- is faster that -z'*z-]
Note that 'lnf' will be a scalar, but Randy coded 'md0()' as a type -v0-
evaluator.
If Randy wants to return a column vector of the squared differences, he
can
use the following function evaluator
void mv0(todo, p, c, f, lnf, S, H)
{
lnf = (c - f*p') :* (c - f*p')
}
Here is the do-file I composed while looking into Randy's code.
***** BEGIN:
mata:
c = (1,2,3,4,5,6)'
f =
(1,1,0,0,0,0\0,1,1,0,0,0\0,0,1,1,0,0\0,0,0,1,1,0\0,0,0,0,1,1\1,0,0,0,0,1
)
void md0(todo, p, c, f, lnf, S, H)
{
real colvector diff
diff = c - f*p'
lnf = cross(diff,diff)
}
Sd = optimize_init()
optimize_init_evaluator(Sd, &md0())
optimize_init_evaluatortype(Sd, "d0")
optimize_init_params(Sd, J(1,6,0))
optimize_init_which(Sd, "min")
optimize_init_argument(Sd, 1, c)
optimize_init_argument(Sd, 2, f)
optimize(Sd)
void mv0(todo, p, c, f, lnf, S, H)
{
lnf = (c - f*p') :* (c - f*p')
}
Sv = optimize_init()
optimize_init_evaluator(Sv, &md0())
optimize_init_evaluatortype(Sv, "v0")
optimize_init_params(Sv, J(1,6,0))
optimize_init_which(Sv, "min")
optimize_init_argument(Sv, 1, c)
optimize_init_argument(Sv, 2, f)
optimize(Sv)
end
***** END:
--Jeff
[email protected]
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```

**References**:**Re: st: Mata and Optimize Command***From:*[email protected] (Jeff Pitblado, StataCorp LP)

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