Matrix Polynomial¶

class fastmat.Polynomial

Bases: fastmat.Matrix.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
>>>
>>> # 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: mat : fastmat.Matrix A fastmat matrix instance subject to constructing the polynomial. coeff : numpy.ndarray A 1d vector defining the polynomial coefficients. **options : optional Additional keyworded arguments. Supports all optional arguments supported by fastmat.Matrix.
coeff

Return the polynomial coefficient vector.