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

[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. 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.
>
>
>