cpn2LinSparse
Computes the Jacobian of a sparse CPN1 MTI object around an operating point
Contents
Syntax
cpn2LinSparse(obj,x)
Description
cpn2LinSparse(obj,x) Computes the Jacobian of an explicit multilinear model stored in the CP-decomposed norm-1 format obj around an operating point x. This implementation makes use of the sparsity of the model for an efficient computation of the Jacobian. For further information on the implementation of the algorithm see [1].
Input Arguments
obj: CPN1 object
x : operating point, scalar or vector
Output Arguments
Jsparse: sparse 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
Jsparse = cpn2LinSparse(obj,x_op)
Jsparse = 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.