ENH: Optimize as_series

[eendebakpt]

Optimize numpy.polynomial.polyutils.as_series for the common case (arrays which are not of object dtype).

Benchmark:

import timeit
import numpy as np
from numpy.polynomial.polyutils import as_series
x=np.array([1.])
y=np.array([1.], dtype=object)

number=1_000_000
for alist in [ [x,], [x, x], [x, y]]:
    dt = timeit.timeit('as_series(alist, trim=True)', globals=globals(), number=number)
    print(f'as_series({alist}): {1e6*dt/number:.3f} [us]')

On main:

as_series([array([1.])]): 2.394 [us]
as_series([array([1.]), array([1.])]): 3.820 [us]
as_series([array([1.]), array([1.0], dtype=object)]): 3.349 [us]

This PR:

as_series([array([1.])]): 1.537 [us]
as_series([array([1.]), array([1.])]): 2.736 [us]
as_series([array([1.]), array([1.0], dtype=object)]): 3.190 [us]

[mattip]

What happens for larger array?

[eendebakpt]

What happens for larger array?

The main computation time is in overhead and checking the dtypes and shapes, the actual computation with the data is small. Here is a benchmark for larger arrays:

Main:
as_series(['array(float64, shape (1000,))']): 2.241 [us]
as_series(['array(float64, shape (1000,))', 'array(float64, shape (1000,))']): 3.460 [us]
as_series(['array(float64, shape (1000,))', 'array(object, shape (300,))']): 13.872 [us]

PR:
as_series(['array(float64, shape (1000,))']): 1.525 [us]
as_series(['array(float64, shape (1000,))', 'array(float64, shape (1000,))']): 2.598 [us]
as_series(['array(float64, shape (1000,))', 'array(object, shape (300,))']): 14.192 [us]

The as_series is used for coefficients of polynomials. I suspect the arrays will not be much larger than 1000.

@mattip