cpn2Lin
Computes the Jacobian of a CPN1 MTI object around an operating point
Contents
Syntax
cpn2Lin(obj,x)
Description
cpn2Lin(obj,x) Computes the Jacobian of an explicit multilinear model stored in the CP-decomposed norm-1 format obj around an operating point x. For further information on the implementation of the algorithm see [1].
Input Arguments
obj: CPN1 object
x : operating point, scalar or vector
Output Arguments
J: Jacobian matrix
Example:
Assume we have the following thrird-order explicit MTI model . We write the explicit MTI model as a CPN1 object by defining the structural matrix S to form the monomial
S=[0.5 -0.5; 1 0; 0 1];
and the parameter matrix with corresponding coefficients of the summands:
phi=[2 0; 4 6; 0 8];
Then we can create explicit MTI model as a CPN1 object
obj=CPN1(S,phi);
and assume the operating point
x_op=[-1;1;3];
Then we can calcute the Jacobian
J = cpn2Lin(obj,x_op)
J = 1 0 0 -7 0 6 -12 0 8
References
[1] C. Kaufmann, D. Crespí, G. Lichtenberg, G. Pangalos, and C. Cateriano Yáñez, "Efficient Linearization of Explicit Multilinear Systems using Normalized Decomposed Tensors," IFAC-PapersOnLine, vol. 56, no. 2, pp. 7312–7317, Jan. 2023, doi: https://doi.org/10.1016/j.ifacol.2023.10.344.