Matrix Polynomial

class fastmat.Polynomial

Bases: Matrix

For given coefficients \(a_k,\dots,a_0 \in \mathbb{C}\) and a linear mapping \(A \in \mathbb{C}^{n \times n}\), we define

\[M = a_n A^n + a_{n-1} A^{n-1} + a_1 A + a_0 I.\]

The transform \(M \cdot x\) can be calculated efficiently with Horner’s method.

>>> # import the package
>>> import fastmat as fm
>>>
>>> # define the transforms
>>> H = fm.Hadamard(n)
>>>
>>> # define the coefficient array
>>> arr_a = [1, 2 + 1j, -3.0, 0.0]
>>>
>>> # define the polynomial
>>> M = fm.Polynomial(H, arr_a)

Let \(H_n\) be the Hadamard matrix of order \(n\). And let \(a = (1, 2 + i, -3, 0) \in \mathbb{C}^{4}\) be a coefficient vector, then the polynomial is defined as

\[M = H_n^3 + (2+i) H_n^2 - 3 H_n.\]

__init__()

Initialize a Polynomial matrix instance.

Parameters

matfastmat.Matrix

A fastmat matrix instance subject to constructing the polynomial.

coeffnumpy.ndarray

A 1d vector defining the polynomial coefficients.

**optionsoptional

Additional keyworded arguments. Supports all optional arguments supported by fastmat.Matrix.

coeff

Return the polynomial coefficient vector.

(read only)