Re: [eigen] Why not Matrix<T, const int rows, const int cols> ?? |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Why not Matrix<T, const int rows, const int cols> ??*From*: Benoît Jacob <jacob@xxxxxxxxxxxxxxx>*Date*: Fri, 5 Jan 2007 15:18:14 +0100

Le vendredi 05 janvier 2007 13:59, Andre Krause a écrit : > Why is EIGEN restricted to square matrices? Ah, very good question! At the beginning, Eigen had rectangular matrices, with template arguments Width and Height as you suggest. Then it created complications with the multiplication operators. Eigen does not only provide fixed-size matrices, it also provides dynamic-size matrices (class MatrixX) and both inherit the same MatrixBase using a 'curiously recurring template pattern'. The problem is that multiplication of rectangular matrices works differently for fixed-size matrices than it does for dynamic-size matrices. Indeed, for fixed-size matrices this operator takes an additional template parameter, int other_width. The type of the 'other' matrix is not the same as the type of *this. On the other hand, with dynamic-size matrices, there is no need for an additional template parameter and all matrices are of the same type, MatrixX<T>. The only solution is to take the matrix-matrix product out of MatrixBase and implement it separately in Matrix and in MatrixX. Good, that's what I did. But there are other operator* and multiply() methods in MatrixBase, for matrix-vector product. They were now hidden by the operator* and multiply() implemented in the child class. So I had to remove them also from MatrixBase and implement them also in Matrix and MatrixX separately. At this point I started wondering whether all that was really useful. It was really starting to make Eigen less elegant, fatter, and partly defeated the point of having this curiously recurring template pattern. The goal of Eigen being to cover the needs of applications, I started to ask people around me what matrix width and height they planned to actually use in their apps. All answers mentionned only square matrices. Same for me. Only one person mentionned rectangular matrices, that was for linear regression, but since then I have implemented linear regression in Eigen using only square matrices (by unfolding the rectangular matrix product one needs to compute at some point. By the way that allowed for a +50% speed optimization). So I removed all the rectangular stuff, and was amazed at how much it simplified the source code, the API, the documentation, and the tests (the test app already weighs 2 MB, think how much it'd be with all the width/height combinations). Do you have a real need for rectangular matrices? > by the way - is there any code that shows how to implement > pseudo-inverse calculation using eigen? Hmm, the best way to do that is by singular values decomposition, which Eigen doesn't do. However, Eigen does LU decomposition with complete pivoting. I don't know, maybe that could is sounds precisely like something that could require rectangular matrices. Or better, Singular Values Decomposition, which Eigen doesn't have either help here. It decomposes you matrix as a product PLUQ where P and Q are permutation matrices, hence unitary, hence it is enough to compute the pseudoinverse of LU. As L and U are triangular, I guess their pseudoinverses are easily computed, and it remains to deduce from that the pseudoinverse of LU. I don't know if that's feasible. Hope that helps, Benoit

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**References**:**[eigen] Why not Matrix<T, const int rows, const int cols> ??***From:*Andre Krause

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