def make_interp_knots(
x: np.ndarray, k: int = 3, bc_type: BCType | None = None, check_finite: bool = True
) -> np.ndarray:
"""Compute the knots of the B-spline.
.. note::
This is a temporary implementation that should be moved to the main
scipy library - see `<https://github.com/scipy/scipy/issues/8810>`_.
Parameters
----------
x : array_like, shape (n,)
Abscissas.
k : int, optional
B-spline degree. Default is cubic, k=3.
bc_type : 2-tuple or None
Boundary conditions.
Default is None, which means choosing the boundary conditions
automatically. Otherwise, it must be a length-two tuple where the first
element sets the boundary conditions at ``x[0]`` and the second
element sets the boundary conditions at ``x[-1]``. Each of these must
be an iterable of pairs ``(order, value)`` which gives the values of
derivatives of specified orders at the given edge of the interpolation
interval.
check_finite : bool, optional
Whether to check that the input arrays contain only finite numbers.
Disabling may give a performance gain, but may result in problems
(crashes, non-termination) if the inputs do contain infinities or NaNs.
Default is True.
Returns
-------
numpy array with size = x.size + k + 1, representing the B-spline knots.
"""
if k < 2 and bc_type is not None:
raise ValueError("Too much info for k<2: bc_type can only be None.")
x = np.array(x)
if x.ndim != 1 or np.any(x[1:] <= x[:-1]):
raise ValueError("Expect x to be a 1-D sorted array-like.")
if k == 0:
t = np.r_[x, x[-1]]
elif k == 1:
t = np.r_[x[0], x, x[-1]]
elif bc_type is None:
if k == 2:
# OK, it's a bit ad hoc: Greville sites + omit
# 2nd and 2nd-to-last points, a la not-a-knot
t = (x[1:] + x[:-1]) / 2.0
t = np.r_[(x[0],) * (k + 1), t[1:-1], (x[-1],) * (k + 1)]
else:
t = _not_a_knot(x, k)
else:
t = _augknt(x, k)
return _as_float_array(t, check_finite)
def test_full_matrix(self):
np.random.seed(1234)
k, n = 3, 7
x = np.sort(np.random.random(size=n))
y = np.random.random(size=n)
t = _not_a_knot(x, k)
b = make_interp_spline(x, y, k, t)
cf = make_interp_full_matr(x, y, t, k)
assert_allclose(b.c, cf, atol=1e-14, rtol=1e-14)
def test_full_matrix(self):
np.random.seed(1234)
k, n = 3, 7
x = np.sort(np.random.random(size=n))
y = np.random.random(size=n)
t = _not_a_knot(x, k)
b = make_interp_spline(x, y, k, t)
cf = make_interp_full_matr(x, y, t, k)
assert_allclose(b.c, cf, atol=1e-14, rtol=1e-14)
