# cpn2Lin

Computes the Jacobian of a CPN1 MTI object around an operating point

## Contents

- Syntax
- Description
- Input Arguments
- Output Arguments
- Example:
- References
- See also

## 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.

## See also

jacobian, cpn2LinSparse, linearize