Hello.
I have developed the following method as an Eigen plugin to perform a multiple dot product between corresponding column vectors in two matrices:

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/**
 * @brief Performs the dot product between each corresponding column vector in this and
 *        that matrices. If either matrix is a column vector, the operation is performed
 *        between the vector against each row in the other matrix.
 * @param v the second matrix (or column vector)
 * @return a row vector containing the dot product results
 */
template <typename OtherDerived>
Matrix<RealScalar, 1, Dynamic> colwiseDot(const MatrixBase<OtherDerived> & that) const {
    assert(this->rows() == that.rows());
    if (that.cols() == 1) {
        return that.transpose() * *this;
    }
    if (this->cols() == 1) {
        return this->transpose() * that;
    }
    assert(this->cols() == that.cols());
    return (this->array() * that.array()).colwise().sum();
}


This works well according to my tests BUT id like this method to return an expression type instead of a calculated vector, so that I can take advantage of lazy evaluation. I've tried a number of approaches but I must confess I'm getting lost in the template forest.

Any help will be appreciated.
JLE

I don't get it, what your function is doing is just computing the diagonal of a matrix-matrix product:

(A.transpose() * B).diagonal()

This is already optimized to compute only the diagonal coefficient in a lazy way.

Ok, I should clarify this.

I understand that returning a Matrix<RealScalar, 1, Dynamic> forces the expression to be evaluated as a vector.
As long as I'm using this method within other expressions, I'd prefer to return an expression type instead of a regular vector.
I'd like to know if this is possible.

Thanks,
JLE

What I'm saying is that there is no need for writing a custom member for that. If you still want it, then you must remove the branches and always returns the same expression, for instance: (derived().transpose() * other.derived()).diagonal() which type should be :

Diagonal<const CoeffBasedProduct<const Transpose<const Derived>, const OtherDerived, 0>, 0>

The following works for a multiple dot product between two (mxn) matrices:

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template <typename OtherDerived>
const Diagonal<const CoeffBasedProduct<const Transpose<const Derived>, const OtherDerived, 0>, 0> colwiseDot(const MatrixBase<OtherDerived> & other) const {
    return (derived().transpose() * other.derived()).diagonal();
}


However, that method doesn't address the cases when one of the operands is a column vector. I understand I should write specific methods for those cases.

The reason why I want a method like the first colwiseDot I wrote is to maintain some readability of code like this:

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aMatrix.colwiseDot( bMatrix.colwise() - bVector ).array() /
aMatrix.colwiseDot( aVector ).array();


Thank you for illuminating my way from Matlab to Eigen.
JLE