Re: [eigen] Permuted Matrix

[Manoj Rajagopalan <rmanoj@xxxxxxxxx>]

If implementing in Eigen is not possible for any reason, can you, for your 
application, use the existing Eigen machinery as follows ...

The class Transpositions represents row/column interchanges. You can create 
one for row-interchanges and one for column and then apply them using the * 
operator like normal matrix multiplication.

eg: Transpositions rowTransp, colTransp; // initialize them
       MatrixXd A(N,N), B(N,N);
       B = rowTransp * A * colTransp; // () if/as necessary

If you want to store the product expression as a temporary then you will need 
to use typedefs to "cache" the fairly-involved type expressions (using 
ei_transposition_matrix_product_retval<> etc.). See Transpositions.h

Also, I see a Transpose<Transpositions<...> > and 
Transpose<PermutationMatrix<...> > in the doxygen documentation. They might 
be useful to you in achieving your objective indirectly.

cheers!
Manoj



On Monday 19 July 2010 05:39:11 pm ESCANDE Adrien 222264 wrote:
> Hello,
>
> I'd like to implement a permuted matrix i.e. a matrix P base on another M,
> such as P(i,j) = M(r[i], c[j]) for some permutation vectors r and c. It is
> very similar to the subject of another thread (how to create a "virtual"
> array or matrix) whose conclusion was to look at the way Minor class is
> implemented.
>
> Based on this Minor example, it is indeed easy to implement a
> PermutedMatrix class for read-only purpose. It goes like this:
> template<typename MatrixType> class PermutedMatrix
>
>   : public MatrixBase<PermutedMatrix<MatrixType> >
>
> {
>   ctor
>   overload of coeff and coeffRef
> }
>
> One can then access to coefficients of the matrix, use block expression,
> triangular view,...
>
> Writing in such a matrix is however a problem: PermutedMatrix can't have
> the DirectAccessBit bit because the "layout of the array of coefficients"
> is not "exactly the natural one suggested by rows(), cols(), outerStride(),
> innerStride(), and the RowMajorBit" DirectAccessBit documentation). Thus
> PermutedMatrix  only derives from DenseCoeffsBase<Derived, false> and not
> DenseCoeffsBase<Derived, true>. In particular, it does not inherit the good
> operator() (Index, Index), and the copyCoeffByOuterInner(Index, Index,
> const DenseBase<OtherDerived>&) methods, the latter being needed in the
> assignation.
>
> Adding these missing methods directly in PermutedMatrix solves part of the
> problem: one can do P(i,j) = some_value or P = some_matrix, but they are
> still missing in expression based on PermutedMatrix , thus one can not do
> P.block(i,j,r,c) = another_matrix, because the copyCoeffByOuterInner of
> DenseCoeffsBase<Expr<PermutedMatrix<MatrixType> > > (in my example, Expr is
> Block) is not correctly defined.
>
> Do I miss something on this problem ? Any direction I could take, or flag I
> don't know of ? I'm not very familiar with Eigen internals yet, so any
> pointers would be welcome.
>
> Thank you,
>
> Adrien Escande