def test_exp_sparse(self):
a = rand_herm(100, sparse=True, density=0.1)
k = rand_ket(100)
out = mfn_multiply_slepc(a, k)
al, av = eigh(a.A)
expected = av @ np.diag(np.exp(al)) @ av.conj().T @ k
assert_allclose(out, expected)
def test_sqrt_sparse(self):
import scipy.sparse as sp
a = rand_pos(32, sparse=True, density=0.1)
a = a + 0.001 * sp.eye(32)
k = rand_ket(32)
out = mfn_multiply_slepc(a, k, fntype='sqrt', isherm=True)
al, av = eigh(a.A)
al[al < 0] = 0.0 # very small neg values spoil sqrt
expected = av @ np.diag(np.sqrt(al)) @ av.conj().T @ k
assert_allclose(out, expected, rtol=1e-6)