def test_interpolate_rat_mp():
mp.dps = 100
X = mp_linspace(0, 1, 100)
##
def f(x):
return (x + 3) / ((x + 1) * (x + 2))
Z = mp_linspace(0, 1, 5)
r = baryrat.interpolate_rat(Z, f(Z))
assert np.linalg.norm(f(X) - r(X)) < 1e-90
assert r.order == 2
##
def f(x):
return (x * (x + 1) * (x + 2)) / (x + 3)
Z = mp_linspace(0, 1, 7)
r = baryrat.interpolate_rat(Z, f(Z))
assert np.linalg.norm(f(X) - r(X)) < 1e-90
assert r.order == 3
## test complex case
n = 9
Z = np.array([np.exp(2j * k / n * np.pi) for k in range(0, n)])
r = baryrat.interpolate_rat(Z, np.exp(Z), use_mp=True)
X = 1j * mp_linspace(-1, 1, 100)
assert abs(np.vectorize(mp.exp)(X) - r(X)).max() < 1e-7
## same thing with Z already in mpc form
Z = np.array([mp.exp(2j * k / n * np.pi) for k in range(0, n)])
r = baryrat.interpolate_rat(Z, np.vectorize(mp.exp)(Z))
X = 1j * mp_linspace(-1, 1, 100)
assert abs(np.vectorize(mp.exp)(X) - r(X)).max() < 1e-7
def test_jacobians():
Z = np.linspace(1, 5, 7)
r = baryrat.interpolate_rat(Z, np.sin(Z))
x = np.linspace(2, 4, 3)
Dz, Df, Dw = r.jacobians(x)
delta = 1e-6
# compare to finite differences
for k in range(len(r.nodes)):
z_delta = r.nodes.copy()
z_delta[k] += delta
r_delta = baryrat.BarycentricRational(z_delta, r.values, r.weights)
deriv = (r_delta(x) - r(x)) / delta
assert np.allclose(Dz[:, k], deriv)
f_delta = r.values.copy()
f_delta[k] += delta
r_delta = baryrat.BarycentricRational(r.nodes, f_delta, r.weights)
deriv = (r_delta(x) - r(x)) / delta
assert np.allclose(Df[:, k], deriv)
w_delta = r.weights.copy()
w_delta[k] += delta
r_delta = baryrat.BarycentricRational(r.nodes, r.values, w_delta)
deriv = (r_delta(x) - r(x)) / delta
assert np.allclose(Dw[:, k], deriv)
def test_reduce_order():
nodes = np.linspace(0, 1, 11)
r = baryrat.interpolate_rat(nodes, np.ones_like(nodes))
assert r.order == 5
r2 = r.reduce_order()
assert r2.order == 0
X = np.linspace(0, 1, 25)
assert np.allclose(r2(X), 1.0)
#
# another test with full order (no reduction)
r = baryrat.interpolate_rat(nodes, np.sin(nodes))
assert r.order == 5
r2 = r.reduce_order()
assert r2.order == 5
X = np.linspace(0, 1, 25)
assert np.allclose(r2(X), r(X))
def test_interpolate_rat():
Z = np.linspace(1, 5, 7)
F = np.sin(Z)
p = baryrat.interpolate_rat(Z, F)
assert np.allclose(p(Z), F)
X = np.linspace(1, 5, 100)
err = np.linalg.norm(p(X) - np.sin(X), np.inf)
assert err < 2e-3
def test_interpolate_rat_complex():
Z = np.linspace(0.0, 1.0, 9)
def f(z):
return np.exp(2j * np.pi * z)
F = f(Z)
r = baryrat.interpolate_rat(Z, F)
assert np.allclose(r(Z), F) # check interpolation property
X = np.linspace(0.0, 1.0, 100)
err = np.linalg.norm(r(X) - f(X), np.inf)
assert err < 1e-4 # check interpolation error
def test_interpolate_rat():
Z = np.linspace(1, 5, 7)
F = np.sin(Z)
r = baryrat.interpolate_rat(Z, F)
assert np.allclose(r(Z), F)
X = np.linspace(1, 5, 100)
err = np.linalg.norm(r(X) - np.sin(X), np.inf)
assert err < 2e-3
#
p, q = r.numerator(), r.denominator()
assert np.allclose(p(X) / q(X), r(X))
assert r.degree() == (3, 3)