def test_reproduction():
p = [-1.0, -2.0, -3.0]
def f(z):
return (z**3 - 2 * z**2 + 4 * z - 7) / ((z - p[0]) * (z - p[1]) *
(z - p[2]))
nodes = np.arange(1, 8, dtype=float)
r = baryrat.aaa(nodes, f(nodes))
assert np.allclose(f(nodes), r(nodes))
z = np.linspace(0, 1, 100)
assert np.allclose(f(z), r(z))
pol, res = r.polres()
assert np.allclose(sorted(p), sorted(pol))
ratfun = sum(res[j] / (z - pol[j]) for j in range(len(pol)))
bias = ratfun - f(z)
assert np.allclose(bias, bias[0]) # should be constant
mp.dps = 100
pol, res = r.polres(use_mp=True)
pol = np.real_if_close(np.array(pol, complex))
assert np.allclose(sorted(p), sorted(pol))
ratfun = sum(res[j] / (z - pol[j]) for j in range(len(pol)))
bias = np.array(ratfun - f(z), complex)
assert np.allclose(bias, bias[0]) # should be constant
def test_approx():
Z = np.linspace(0.0, 1.0, 101)
def f(z): return np.exp(z)*np.sin(2*np.pi*z)
F = f(Z)
r = baryrat.aaa(Z, F, mmax=10)
assert np.linalg.norm(r(Z) - F, np.inf) < 1e-10, 'insufficient approximation'
# check invoking with functions
r2 = baryrat.aaa(Z, f, mmax=10)
assert np.linalg.norm(r(Z) - r2(Z), np.inf) < 1e-15
# check that calling r works for scalars, vectors, matrices
assert np.isscalar(r(0.45))
assert r(np.ones(7)).shape == (7,)
assert r(np.ones((3,2))).shape == (3,2)
def test_aaa_complex():
Z = np.linspace(0.0, 1.0, 101)
def f(z):
return np.exp(2j * np.pi * z)
F = f(Z)
r = baryrat.aaa(Z, F, mmax=8)
assert np.linalg.norm(r(Z) - F,
np.inf) < 1e-10, 'insufficient approximation'
def test_reproduction():
p = [-1.0, -2.0, -3.0]
def f(z):
return (z**3 - 2*z**2 + 4*z - 7) / ((z - p[0])*(z - p[1])*(z - p[2]))
nodes = np.arange(1, 8, dtype=float)
r = baryrat.aaa(nodes, f(nodes))
assert np.allclose(f(nodes), r(nodes))
z = np.linspace(0, 1, 100)
assert np.allclose(f(z), r(z))
pol, res = r.polres()
assert np.allclose(sorted(p), sorted(pol))
def test_zeros():
Z = np.linspace(0.0, 1.0, 101)
F = np.exp(Z) * np.sin(2 * np.pi * Z)
r = baryrat.aaa(Z, F, mmax=6)
zer = r.zeros()
assert np.allclose(zer,
np.array([-0.38621461, 1.43052691, 0.49999907, 1., 0.]))
assert np.allclose(r(zer), 0.0)
zer2 = r.zeros(use_mp=True)
assert np.allclose(sorted(zer), sorted(zer2))
def test_polres():
Z = np.linspace(0.0, 1.0, 101)
F = np.exp(Z) * np.sin(2*np.pi*Z)
r = baryrat.aaa(Z, F, mmax=6)
pol, res = r.polres()
assert np.allclose(pol,
np.array([2.26333482+0.j, 0.2338428+0.90087977j,
0.2338428-0.90087977j, 0.96472415+0.85470621j,
0.96472415-0.85470621j]))
assert np.allclose(res,
np.array([69.08984183+0.j, 20.50747913-9.24908921j,
20.50747913+9.24908921j, 23.24692682+23.94602455j,
23.24692682-23.94602455j]))
polvals = r(pol)
assert np.min(np.abs(polvals)) > 1e13
