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From: NP on 9 Aug 2010 05:15
Hi,

Thank you all so much for the helpful solutions with explanations!

On a similar theme, I got the following to work for the case where
options are not constants

Clear[f1];
f1[A_?MatrixQ, epsilon_: Automatic] := Module[{cv = epsilon},
If[cv === Automatic,
cv = IdentityMatrix[Dimensions[A][[1]]] + (1/Det[A]) A,
IdentityMatrix[Dimensions[A][[1]]] + epsilon A]]
f1[{{1, 2}, {3, 4}}]

but not the following (only change is in the second argument)

Clear[f2];
f2[A_?MatrixQ, epsilon:(_?NumericQ):Automatic] :=
Module[{cv = epsilon},
If[cv === Automatic,
cv = IdentityMatrix[Dimensions[A][[1]]] + (1/Det[A]) A,
IdentityMatrix[Dimensions[A][[1]]] + epsilon A]]
f2[{{1, 2}, {3, 4}}]


Thanks in advance!

NP

From: Leonid Shifrin on 10 Aug 2010 03:58
Not that this is a complete answer, but I have a hunch that the value of
the constant part in the optional pattern must match the pattern. In the
previous case, we had say

x:(_Integer?Positive):3,

and 3 was matching the pattern (_Integer?Positive). Now, Automatic does not
match the pattern _?NumericQ, thus your result. The following hack
therefore
works:

Clear[f3];
f3[A_?MatrixQ, epsilon : (_?NumericQ | Automatic) : Automatic] :=
Module[{cv = epsilon},
If[cv === Automatic,
cv = IdentityMatrix[Dimensions[A][[1]]] + (1/Det[A]) A,
IdentityMatrix[Dimensions[A][[1]]] + epsilon A]]

In[9]:= f3[{{1, 2}, {3, 4}}]

Out[9]= {{1/2, -1}, {-(3/2), -1}}

Regards,
Leonid


On Mon, Aug 9, 2010 at 1:15 PM, NP <nomplume69(a)gmail.com> wrote:

> Hi,
>
> Thank you all so much for the helpful solutions with explanations!
>
> On a similar theme, I got the following to work for the case where
> options are not constants
>
> Clear[f1];
> f1[A_?MatrixQ, epsilon_: Automatic] := Module[{cv = epsilon},
> If[cv === Automatic,
> cv = IdentityMatrix[Dimensions[A][[1]]] + (1/Det[A]) A,
> IdentityMatrix[Dimensions[A][[1]]] + epsilon A]]
> f1[{{1, 2}, {3, 4}}]
>
> but not the following (only change is in the second argument)
>
> Clear[f2];
> f2[A_?MatrixQ, epsilon:(_?NumericQ):Automatic] :=
> Module[{cv = epsilon},
> If[cv === Automatic,
> cv = IdentityMatrix[Dimensions[A][[1]]] + (1/Det[A]) A,
> IdentityMatrix[Dimensions[A][[1]]] + epsilon A]]
> f2[{{1, 2}, {3, 4}}]
>
>
> Thanks in advance!
>
> NP
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