ModelingToolkit + matrix variables: defaults & 1×1 scalars

[ChrisRackauckas]

@rasmuskovacs

Is it expected that defaults on the scalar components (x1, x2) do not propagate to the array variable (x) when using an equation like x ~ [x1 x2]'? Is there a recommended way to have defaults “flow” into x(t)[…] without manually building the vector for ODEProblem?

Yes, though we should probably throw a better error here @cryptic.ax

@rasmuskovacs

• When expressions like v*k naturally produce a 1×1 matrix, what’s the idiomatic way to feed a scalar variable on the LHS? Is (v*k)[1,1] the intended approach?

Yes it’s intended. See “Taking Vector Transposes Seriously” for details about this whole topic.

Taking Vector Transposes Seriously | Jiahao Chen | JuliaCon 2017

@rasmuskovacs

Is there a best practice for declaring vectors vs 2D “column vectors” in @variables/@parameters? For example, should “state vectors” generally be x(t)[1:2] (1D) rather than x(t)[1:2,1:1] (2D)? Any pitfalls to be aware of when mixing 1D and 2D shapes in equations?

It’s the same as in Julia. If you want a 1D object you should prefer using the 1D object. From my understanding our symbolic rules match Julia here, and Jiahao’s talk describes a lot of the reasoning behind it.