Structure and Evaluation of Univariate Polynomials [code201.0]

Demonstrates how to create and evaluate a univariate polynomial using Poly in vector exponent notation \(\alpha^\mathsf{T} x^q\).

Four evaluation cases are shown:

1. Print the polynomial's coefficient and exponent vectors.
2. Evaluate at a scalar \(x = 3\).
3. Evaluate over a 1-D array of \(x\) values.
4. Evaluate over a 3-D array and confirm the output shape.

Note: No graphical output.

Console Output

-- (1) --
(array([-0.3  ,  0.08 , -0.004]),), (array([0, 2, 4]),)
-- (2) --
0.09599999999999997
-- (3) --
[-0.3   -0.224 -0.044  0.096 -0.044]
-- (4) --
(2, 4, 6)

Code

r"""
Structure and Evaluation of Univariate Polynomials [code201.0]
============================================================

Demonstrates how to create and evaluate a univariate polynomial using
[`Poly`][lmlib.polynomial.poly.Poly] in vector exponent notation
$\alpha^\mathsf{T} x^q$.

Four evaluation cases are shown:

1. Print the polynomial's coefficient and exponent vectors.
2. Evaluate at a scalar $x = 3$.
3. Evaluate over a 1-D array of $x$ values.
4. Evaluate over a 3-D array and confirm the output shape.

"""
import numpy as np
import lmlib as lm

expo = [0, 2, 4]
coef = [-0.3, 0.08, -0.004]
poly = lm.Poly(coef, expo)

print("-- (1) --")
print(poly)

print("-- (2) --")
print(poly.eval(3))

print("-- (3) --")
print(poly.eval(np.arange(5)))

print("-- (4) --")
var = np.arange(2*4*6).reshape([2, 4, 6])
print(poly.eval(var).shape)