reflect

Laurent polynomial or Laurent matrix reflection

Since R2021b

Syntax

Q = reflect(P)

Description

Q = reflect(P) returns the reflection of the Laurent polynomial or the Laurent matrix specified by P. If P is a Laurent matrix, the function reflects the matrix elements.

Note

The laurentPolynomial and laurentMatrix objects have their own versions of reflect. The input data type determines which version is executed.

Examples

Laurent Polynomial Reflection

Create a Laurent polynomial $$a(z)=5z^6+4z^5+3z^4+2z^3$$.

a = laurentPolynomial(Coefficients=[5 4 3 2],MaxOrder=6)

a = 
  laurentPolynomial with properties:

    Coefficients: [5 4 3 2]
        MaxOrder: 6

Obtain the reflection of $$a(z)$$. Confirm the maximum order of the reflection is –3.

b = reflect(a)

b = 
  laurentPolynomial with properties:

    Coefficients: [2 3 4 5]
        MaxOrder: -3

Laurent Matrix Reflection

Create two Laurent polynomials:

• $$a(z)=-z^3+2z^2-3z+4$$

• $$b(z)=5z^2-z-z^{-1}+z^{-2}$$

lpA = laurentPolynomial(Coefficients=[-1 2 -3 4],MaxOrder=3);
lpB = laurentPolynomial(Coefficients=[5 -1 0 -1 1],MaxOrder=1);

Create the Laurent matrix $\left[\begin{array}{cc}\mathit{a}\left(\mathit{z}\right)& 0\\ 1& \mathit{b}\left(\mathit{z}\right)\end{array}\right]$.

lmat = laurentMatrix(Elements={lpA,0;1,lpB});

Obtain the reflection of the matrix. Inspect the diagonal elements of the reflection.

lmatref = reflect(lmat);
lmatref.Elements{1,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: [4 -3 2 -1]
        MaxOrder: 0

lmatref.Elements{2,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: [1 -1 0 -1 5]
        MaxOrder: 3

Input Arguments

P — Laurent polynomial or Laurent matrix

laurentPolynomial object | laurentMatrix object

Laurent polynomial or Laurent matrix, specified as a laurentPolynomial object or a laurentMatrix object, respectively.

Output Arguments

Q — Reflection

laurentPolynomial object | laurentMatrix object

Reflection of a Laurent polynomial or a Laurent matrix, returned as a laurentPolynomial object or a laurentMatrix object. The reflection of a Laurent polynomial P(z) is the Laurent polynomial Q(z) = P(1/z).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2021b