Eigen::Array colwise/rowwise broadcasting is asymmetric?

Question

The following code multiplies the i-th column of A by the i-th element of V.

#include <Eigen/Core>
Eigen::Array<double, 8, 2>
f(const Eigen::Array<double, 8, 2>& A, const Eigen::Array<double, 1, 2>& V) {
    return A.rowwise() * V;
}

Apparently if one multiplies the other way, as in

Eigen::Array<double, 8, 2>
g(const Eigen::Array<double, 8, 2>& A, const Eigen::Array<double, 1, 2>& V) {
    return V * A.rowwise();
}

g++ (15.1) and clang (20.1) will reject the code (with error: no match for 'operator*' (operand types are 'const Eigen::Array<double, 1, 2>' and 'Eigen::DenseBase<Eigen::Array<double, 8, 2> >::ConstRowwiseReturnType' {aka 'const Eigen::VectorwiseOp<const Eigen::Array<double, 8, 2>, 1>'}) and error: no type named 'type' in 'struct Eigen::internal::promote_scalar_arg<double, Eigen::VectorwiseOp<const Eigen::Array<double, 8, 2>, 1>, false>')

I'm wondering why this is and what is special about the return type of rowwise/colwise.

What are the rules regarding what can be multiplied by what when broadcasting (in Eigen 3.4 - if it matters)?

something like find Eigen/. -name "*.h" -exec grep -H operator\\\* {} \; will answer your last question ... with 159 results — bruno
– bruno, Commented Jul 14 at 9:29
If V * A.rowwise() did work, I'd expect the result to be Eigen::Array<double, 1, 2>. Or a vector of those, one for each row. — Eljay
– Eljay, Commented Jul 14 at 12:38
@Eljay do you mean that the first operand "shall" determine the shape of the result? — YiFei
– YiFei, Commented Jul 14 at 14:59

chtz · Accepted Answer · 2025-07-14 13:59:49Z

2

Yes, rowwise and colwise generally expect the non-broadcasted object to be on the left side. I assume that is mostly to reduce the number of necessary operator overloads and avoid some ambiguities, especially if more than two objects are combined.

If you want to have V on the left side of the expression, you can usually write an equivalent expression using replicate (after optimization, this should generate the same code). Try the following (I did not test it):

// instead of V * A.rowwise()
V.rowwise().replicate(A.rows()) * A;
// or simpler, but possibly harder to optimize for the compiler:
V.replicate(A.rows(), 1) * A;

If you really want to write V * A.rowwise() you could provide an operator* which takes an ArrayBase object on the left and a VectorwiseOp on the right. For non-commutative operators the implementation gets complicated of course. And if you are not careful with the implementation that could lead to lots of ambiguous overloads quickly.

answered Jul 14 at 13:59

chtz

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1 Comment

YiFei Jul 14 at 14:56

Thanks! I looked into the eigen headers. It seems that the relevant operator* is defined in Eigen/src/plugins/ArrayCwiseBinaryOps.h (for expressions derived from ArrayBase). The return type of {row,col}wise are VectorwiseOp, which are not derived from ArrayBase, and the operators of which are separately overloaded in Eigen/src/Core/VectorwiseOp.h. I think ambiguous overload is a good point.

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