Matrix Operations

ad_trait is designed to handle linear algebra efficiently. The AD trait includes requirements for matrix-scalar multiplication, which is the foundation for differentiating through linear systems.

Scalar-Matrix Multiplication

Types implementing AD must provide:

• mul_by_nalgebra_matrix: Multiplies an AD scalar by a nalgebra matrix.
• mul_by_ndarray_matrix_ref: Multiplies an AD scalar by an ndarray array.

Why this is necessary

By providing these specialized methods at the trait level, ad_trait can ensure that matrix operations are handled correctly for each AD mode. For example, in ForwardAD, the matrix multiplication also propagates the tangent through every element of the matrix.

Performance Considerations

When performing large matrix multiplications, it is often more efficient to use a differentiation mode that minimizes the number of passes (like ReverseAD or ForwardADMulti).