A.T.conj(): caching vs inline

atc.py

import perfplot
import numpy as np
from scipy.sparse import spdiags


def setup_dense(n):
    A = np.random.rand(n, n) + 1j * np.random.rand(n, n)
    AH = A.T.conj()
    x = np.random.rand(n) + 1j * np.random.rand(n)
    return A, AH, x


def setup_tridiag(n):
    A = spdiags(np.random.rand(3, n), [-1, 0, 1], n, n)
    AH = A.T.conj()
    x = np.random.rand(n) + 1j * np.random.rand(n)
    return A, AH, x


def AHx(Ax):
    A, _, x = Ax
    return A.T.conj() @ x


def ATx(Ax):
    A, _, x = Ax
    return (A.T @ x.conj()).conj()


def cached(Ax):
    _, AH, x = Ax
    return AH @ x


b = perfplot.bench(
    setup=setup_tridiag, kernels=[AHx, ATx, cached], n_range=[2 ** k for k in range(24)]
)
b.save("tridiag.png")
b.show()

For tridiagonal:

For dense: