snippet

main.py

from typing import Any
import numpy as np
from nptyping import NDArray
def main(name):
    # Use a breakpoint in the code line below to debug your script.
    print(f'Hi, {name}')  # Press Ctrl+F8 to toggle the breakpoint.
    f: NDArray[(3, 3), Any] = lambda A, f: A ** f
    ak = 3
    n = 2

    A: NDArray[(n, n), Any]
    Fk: NDArray[(ak, n), Any]
    Pk: NDArray[(n, n), Any]
    phik: NDArray[(n, n), Any]
    Gk: NDArray[(n, n), Any]
    Wk: NDArray[(n, n), Any]
    Omegak: NDArray[(n, n * ak), Any]
    Xk: NDArray[(n, n)]
    lk: NDArray[(ak, ak)]

    phi_k: NDArray[(n, n), Any] = lambda A, tkp, tk: np.expm(A * (tkp - tk))
    Theta_k: NDArray[(ak, n), Any] = lambda lk, Fk, Pk, phik, Gk, Wk, Omegak: (
                lk @ Fk @ Pk @ phi_k.T + lk @ Gk @ Wk @ Omegak.T)
    Gamma1k: NDArray[(ak, ak), Any] = lambda lk, Fk, Pk: (lk @ Fk @ Pk @ Fk.T @ lk.T)
    Gamma2k: NDArray[(ak, ak), Any] = lambda Fk, Xk, lk: np.dot((Fk @ Xk @ Fk.T), (lk - lk ** 2))
    Gamma3k: NDArray[(ak, ak), Any] = lambda lk, Gk, Wk: lk @ Gk @ Wk @ f(Gk.T, lk) + np.dot(Gk @ Wk @ Gk.T,
                                                                                             lk - lk ** 2)
    Gamma4k: NDArray[(ak, ak), Any] = lambda lk, Dk, Vk: lk @ Dk @ Vk @ f(Dk.T, lk) + np.dot(Dk @ Vk @ Dk.T,
                                                                                             lk - lk ** 2)
    Omegak: NDArray[(n, ak * n), Any] = lambda ak, A, Delta: np.vstack(
        [np.expm(A @ Delta * (_ - 1)) for _ in range(1, ak + 1)])
    Xkplus1: NDArray[(n, n), Any] = lambda phik, Xk, Omegak, Wk: phik @ Xk @ phik.T + Omegak @ Wk @ Wk.T


# Press the green button in the gutter to run the script.
if __name__ == '__main__':
    main('PyCharm')

# See PyCharm help at https://www.jetbrains.com/help/pycharm/