Re: [eigen] solve API

[Gael Guennebaud <gael.guennebaud@xxxxxxxxx>]

On Mon, Jun 28, 2010 at 9:23 PM, Hauke Heibel
<hauke.heibel@xxxxxxxxxxxxxx> wrote:
> On Mon, Jun 28, 2010 at 3:19 PM, Gael Guennebaud
> <gael.guennebaud@xxxxxxxxx> wrote:
>> I really prefer inverse() because ...
>
> I agree with Gael, I also prefer inverse(). Not only because it is
> generic but also because
>
> x = A.lu().solver() * b
>
> looks a bit strange and would require template arguments for
> transposition and adjoint flags.
>
>> For rectangular matrices, inverse still make sense as the pseudo
>> inverse. The weird thing is that the returned Inverse expression would
>> become the left pseudo inverse or right pseudo inverse at the moment
>> it is applied to a matrix:
>>
>> Matrix m(r,c);
>>
>> x = m.svd().inverse() * m; // left pseudo inverse, x = identity(c,c);
>> x = m * m.svd().inverse(); // right pseudo inverse, x = identity(r,r);
>
> This is too bad because I just wanted to propose
>
> x = A.svd().pinv() * b
>
> or
>
> x = A.svd().pseudoinverse() * b
>
> By the way, thinking once again about your argument regarding generic
> algorithms, I am not sure anymore whether I would totally agree. QR
> and SVD for instance might be offering a unified ::pseudoinverse()
> function (well, in that direction) because in fact, whenever the
> matrix is not invertible, this is what the method return. Well, I hope
> I am right with that. :) On the other hand side, we could simply agree
> on the common understanding that inverse() might potentially be
> returning/computing the pseudo inverse.

yeah ! someone on my side :)

>
>> meaning that:
>>
>> mat = svd.inverse();
>>
>> would be undefined (illegal), but I think that's fine.
>
> So, you mean
>
> mat = A.svd().inverse()
>
> but what you say should only be true if A is not square. When A is
> square, that should be possible and as I mentioned before it were
> holding for QR too.

ah yes that's true.

gael

>
> - Hauke
>
>
>