def test_api_and_all_types_and_1d_with_deriv():
# 1d example, deriv test
x = np.linspace(0, 10, 50)
z = np.sin(x)
xx = np.linspace(0, 10, 100)
for name in rbf.rbf_dct.keys():
print(name)
cases = [
(True, dict(rbf=name)),
(True, dict(p='mean')),
(False, dict(p='scipy')), # not accurate enough, only API test
(True, dict(rbf=name, r=1e-11)),
(True, dict(rbf=name, p=rbf.estimate_p(x[:, None]))),
(True, dict(rbf=name, p=rbf.estimate_p(x[:, None]), r=1e-11)),
]
for go, kwds in cases:
rbfi = rbf.Rbf(x[:, None], z, **kwds)
if go:
assert np.allclose(rbfi(xx[:, None]),
np.sin(xx),
rtol=0,
atol=1e-4)
assert np.allclose(rbfi(xx[:, None], der=1)[:, 0],
np.cos(xx),
rtol=0,
atol=1e-3)
def go(nn, ax):
x = np.linspace(0, 10, nn)
xi = np.linspace(x[0], x[-1], 300)
y = np.sin(x) + np.random.rand(len(x))
ax.plot(x, y, 'o', alpha=0.3)
for name in ['gauss', 'multi']:
f = rbf.Rbf(x[:, None], y, rbf=name)
ax.plot(xi, f(xi[:, None]), label=name)
def test_interpol_high_dim():
# 100 points in 40-dim space
#
# Test only API. Interpolating random points makes no sense, of course.
# However, on the center points (= data points = training points),
# interpolation must be "perfect".
X = rand(10, 40)
z = rand(10)
rbfi = rbf.Rbf(X, z)
assert np.abs(z - rbfi(X)).max() < 1e-13
def test_2d():
# 2d example, y = f(x1,x2) = sin(x1) + cos(x2)
x1 = np.linspace(-1, 1, 20)
X1, X2 = np.meshgrid(x1, x1)
X1 = X1.T
X2 = X2.T
z = (np.sin(X1) + np.cos(X2)).flatten()
X = np.array([X1.flatten(), X2.flatten()]).T
print(X.shape, z.shape)
rbfi = rbf.Rbf(X, z, p=1.5)
# test fit at 300 random points within [-1,1]^2
Xr = -1.0 + 2 * np.random.rand(300, 2)
zr = np.sin(Xr[:, 0]) + np.cos(Xr[:, 1])
err = np.abs(rbfi(Xr) - zr).max()
print(err)
assert err < 1e-6
# Big errors occur only at the domain boundary: -1, 1, errs at the points
# should be smaller
err = np.abs(z - rbfi(X)).max()
print(err)
assert err < 1e-6
y = XY[:, 1]
return (x**2 + y**2)
if __name__ == '__main__':
# Some nice 2D examples
fu = MexicanHat([-10, 20], [-10, 15], 20, 20, 'rand')
## fu = UpDown([-2,2], [-2,2], 20, 20, 'grid')
## fu = SinExp([-1,2.5], [-2,2], 40, 30, 'rand')
## fu = Square([-1,1], [-1,1], 20, 20, 'grid')
Z = fu(fu.XY)
rbfi = rbf.Rbf(fu.XY, Z, rbf='inv_multi', verbose=True)
dati = SurfaceData(fu.xlim, fu.ylim, fu.nx * 2, fu.ny * 2, 'grid')
ZI_func = fu(dati.XY)
ZI_rbf = rbfi(dati.XY)
ZG_func = ZI_func.reshape((dati.nx, dati.ny))
ZG_rbf = ZI_rbf.reshape((dati.nx, dati.ny))
zlim = [ZI_func.min(), ZI_func.max()]
fig, ax = mpl.fig_ax3d(clean=True)
ax.scatter(fu.XY[:, 0], fu.XY[:, 1], Z, color='b', label='f(x,y) samples')
dif = np.abs(ZI_func - ZI_rbf).reshape((dati.nx, dati.ny))
if not shiny:
ax.plot_wireframe(dati.XG,
rbf_kwds = dict(rbf='inv_multi', r=None)
fig, axs = plt.subplots(2, 1)
x = np.linspace(0, 10, 100)
rnd = np.random.RandomState(seed=123)
y = np.sin(x) + rnd.rand(len(x))
points = x[:,None]
values = y
xi = np.linspace(x[0], x[-1], len(x)*4)[:,None]
fe = rbf.FitError(points, values, rbf_kwds=rbf_kwds)
ax = axs[0]
ax.plot(x, y, 'o', alpha=0.3)
rbfi = rbf.Rbf(points, values, **rbf_kwds)
p_default = rbfi.get_params()[0]
ax.plot(xi, rbfi(xi), 'r', label='$p$ default')
rbfi = rbf.fit_opt(points, values, method='de', what='p',
opt_kwds=dict(bounds=[(0.1, 10)], maxiter=10),
rbf_kwds=rbf_kwds,
cv_kwds=None)
p_opt = rbfi.get_params()[0]
ax.plot(xi, rbfi(xi), 'g', label='$p$ opt')
rbfi = rbf.Rbf(points, values, p=10, **rbf_kwds)
p_cv = rbfi.get_params()[0]
ax.plot(xi, rbfi(xi), 'y', label='$p$ big')
rbfi = rbf.Rbf(points, values, p=rbf.estimate_p(points, 'scipy'),
def test_func_api():
X = rand(10, 3)
z = rand(10)
r1 = rbf.Rbf(X, z, rbf='multi')
r2 = rbf.Rbf(X, z, rbf=rbf.rbf_dct['multi'])
assert (r1(X) == r2(X)).all()
def test_p_api():
X = rand(10, 3)
z = rand(10)
for name in ['scipy', 'mean']:
f = rbf.Rbf(X, z, p=name)
assert f.p == rbf.estimate_p(X, method=name)