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ParametersReturns

Parameters

t : ndarray, shape (nt + k + 1,)

sorted 1D array of knots

k : int

spline order

xval: float :

argument at which to evaluate the B-splines

m : int

index of the left edge of the evaluation interval, t[m] <= x < t[m+1]

nu : int, optional

Evaluate derivatives order nu. Default is zero.

Returns

ndarray, shape (k+1,)

The values of B-splines [B_{m-k}(xval), ..., B_{m}(xval)] if nu is zero, otherwise the derivatives of order nu.

Examples

k = 3
t = [0., 1., 2., 3., 4.]   # internal knots
a, b = t[0], t[-1]    # base interval is [a, b)
t = np.array([a]*k + t + [b]*k)  # add boundary knots

import matplotlib.pyplot as plt
xx = np.linspace(a, b, 100)
plt.plot(xx, BSpline.basis_element(t[k:-k])(xx),
         lw=3, alpha=0.5, label='basis_element')

for i in range(k+1):
   x1, x2 = t[2*k - i], t[2*k - i + 1]
   xx = np.linspace(x1 - 0.5, x2 + 0.5)
   yy = [evaluate_all_bspl(t, k, x, 2*k - i)[i] for x in xx]
   plt.plot(xx, yy, '--', label=str(i))

plt.grid(True)
plt.legend()
plt.show()

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them