如何将矩阵提高到数组中元素按升序递增的幂？

Question

Currently I have a C matrix generated by:

def c_matrix(n):
    exp = np.exp(1j*np.pi/n)
    exp_n = np.array([[exp, 0], [0, exp.conj()]], dtype=complex)
    c_matrix = np.array([exp_n**i for i in range(1, n, 1)], dtype=complex)
    return c_matrix

What this does is basically generate a list of number from 0 to n-1 using list comprehension, then returns a list of the matrix exp_n being raised to the elements of the ascendingly increasing list. ie

exp_n**[0, 1, ..., n-1] = [exp_n**0, exp_n**1, ..., exp_n**(n-1)]

So I was wondering if there's a more numpythonic way of doing it(in order to make use of Numpy's broadcasting ability) like:

exp_n**np.arange(1,n,1) = np.array(exp_n**0, exp_n**1, ..., exp_n**(n-1))

Answer 1

You're speaking of a Vandermonde matrix. Numpy has numpy.vander

---

def c_matrix_vander(n):
    exp = np.exp(1j*np.pi/n)
    exp_n = np.array([[exp, 0], [0, exp.conj()]], dtype=complex)
    return np.vander(exp_n.ravel(), n, increasing=True)[:, 1:].swapaxes(0, 1).reshape(n-1, 2, 2)

---

Performance

In [184]: %timeit c_matrix_vander(10_000)
849 µs ± 14.4 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

In [185]: %timeit c_matrix(10_000)
41.5 ms ± 549 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

Validation

>>> np.isclose(c_matrix(10_000), c_matrix_vander(10_000)).all()
True