lstsq_size()

lstsq_size(modelform, r, m=0, affines=None)

Calculate the number of columns in the operator matrix O in the Operator Inference least-squares problem. This is also the number of columns in the data matrix D.

Parameters

modelformstr containing ‘c’, ‘A’, ‘H’, ‘G’, and/or ‘B’

The structure of the desired reduced-order model. Each character indicates the presence of a different term in the model: ‘c’ : Constant term c ‘A’ : Linear state term Ax. ‘H’ : Quadratic state term H(x⊗x). ‘G’ : Cubic state term G(x⊗x⊗x). ‘B’ : Input term Bu. For example, modelform==”AB” means f(x,u) = Ax + Bu.

rint

The dimension of the reduced order model.

mint

The dimension of the inputs of the model. Must be zero unless ‘B’ is in modelform.

affinesdict(str -> list(callables))

Functions that define the structures of the affine operators. Keys must match the modelform: * ‘c’: Constant term c(µ). * ‘A’: Linear state matrix A(µ). * ‘H’: Quadratic state matrix H(µ). * ‘G’: Cubic state matrix G(µ). * ‘B’: linear Input matrix B(µ). For example, if the constant term has the affine structure c(µ) = θ1(µ)c1 + θ2(µ)c2 + θ3(µ)c3, then ‘c’ -> [θ1, θ2, θ3].

Returns

ncolsint

The number of columns in the Operator Inference least-squares problem.