Re: [eigen] Inverse of an array through .matrix()

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

2010/6/27 Carlos Becker <carlosbecker@xxxxxxxxx>:
> Ok great, so I should point out that .matrix() and .array() can be lvalues
> and rvalues,

yes,
> and also point out that conversion between matrix and array is
> not always automatic

Be more precise: mixing matrix and array in an expression is
forbidden; while assigning a matrix to an array (or conversely) is
allowed.

Benoit

 (or at least remove it, since i was saying this was
> true).
> Any comments on this?
>
> On Sun, Jun 27, 2010 at 2:41 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx>
> wrote:
>>
>> 2010/6/27 Gael Guennebaud <gael.guennebaud@xxxxxxxxx>:
>> > On Sun, Jun 27, 2010 at 2:21 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx>
>> > wrote:
>> >> 2010/6/27 Carlos Becker <carlosbecker@xxxxxxxxx>:
>> >>> Hi everyone again. I am still writing some examples for the tutorials
>> >>> and
>> >>> came out with the following piece of code:
>> >>> #include <Eigen/Dense>
>> >>> #include <iostream>
>> >>> using namespace Eigen;
>> >>> using namespace std;
>> >>> int main()
>> >>> {
>> >>>   ArrayXXf m(2,2);
>> >>>   m << 1,2,3,4;
>> >>>   // this compiles OK
>> >>>   MatrixXf ww = m.matrix().inverse();
>> >>>   // ERROR: no matching function for call to
>> >>> ‘Eigen::TriangularView<Eigen::Matrix<float, 33331, 33331, 0, 33331,
>> >>> 33331>,
>> >>> 2u>::solveInPlace(....
>> >>>   ArrayXXf xx = m.matrix().inverse();
>> >>
>> >> That can't work: m.matrix().inverse() wants to return a matrix
>> >> expression, so you can't assign that to an array expression. This
>> >> works:
>> >>
>> >>  ArrayXXf xx = m.matrix().inverse().array();
>> >
>> >
>> > on the other hand:
>> >
>> > MatrixXf m1, m2;
>> >  ArrayXXf a = m1 + m2;
>> >
>> > is legal and works fine.
>>
>> Thanks for the heads up, i had forgotten that this was legal. Makes sense!
>>
>> Benoit
>>
>> > What is not allowed is to mix matrix and
>> > array in the right and side (e.g., array+matrix is forbidden). What
>> > happens here is that .inverse() returns a proxy object which is
>> > compiled as:
>> >
>> > m.matrix().lu().compute_the_inverse_into(xx);
>> >
>> > (the function compute_the_inverse_into does not exist, it is just to
>> > get the idea)
>> >
>> > => we are mixing matrix and arrays.
>> >
>> > However, I think it is fine that this example does not compile,
>> > because it does not make sense to do pure linear algebra on arrays.
>> >
>> > gael
>> >
>> >
>> >>
>> >> Notice that eigen3's .matrix() and .array() are very different from
>> >> eigen2's .cwise(): while .cwise() was just a prefix for the next
>> >> method call, .matrix() and .array() are permanently switching your
>> >> expression between the Matrix and Array worlds.
>> >>
>> >> Please don't mention .inverse() in the Array page, as
>> >>  - it is nontrivial linear algebra so should not be mentioned before
>> >> the linear algebra page
>> >>  - implementation-wise it is very nontrivial and special, whence the
>> >> weird error messages that you got.
>> >>
>> >> Benoit
>> >>
>> >>
>> >>> }
>> >>> I just wanted to ask if this is the way it should work or not, since I
>> >>> supposed that the last line should be fine.
>> >>> Thanks.
>> >>
>> >>
>> >>
>> >
>> >
>> >
>>
>>
>
>