scipy.interpolate.

NdBSpline#

class scipy.interpolate.NdBSpline(t, c, k, *, extrapolate=None)[source]#

Tensor product spline object.

The value at point xp = (x1, x2, ..., xN) is evaluated as a linear combination of products of one-dimensional b-splines in each of the N dimensions:

c[i1, i2, ..., iN] * B(x1; i1, t1) * B(x2; i2, t2) * ... * B(xN; iN, tN)

Here B(x; i, t) is the i-th b-spline defined by the knot vector t evaluated at x.

Parameters:

ttuple of 1D ndarrays: knot vectors in directions 1, 2, … N, len(t[i]) == n[i] + k + 1
cndarray, shape (n1, n2, …, nN, …): b-spline coefficients
kint or length-d tuple of integers: spline degrees. A single integer is interpreted as having this degree for all dimensions.
extrapolatebool, optional: Whether to extrapolate out-of-bounds inputs, or return nan. Default is to extrapolate.

Attributes:

ttuple of ndarrays: Knots vectors.
cndarray: Coefficients of the tensor-product spline.
ktuple of integers: Degrees for each dimension.
extrapolatebool, optional: Whether to extrapolate or return nans for out-of-bounds inputs. Defaults to true.

Methods

`__call__`(xi, *[, nu, extrapolate])	Evaluate the tensor product b-spline at `xi`.
`derivative`(nu)	Construct a new NdBSpline representing the partial derivative.
`design_matrix`(xvals, t, k[, extrapolate])	Construct the design matrix as a CSR format sparse array.

See also

BSpline: a one-dimensional B-spline object
NdPPoly: an N-dimensional piecewise tensor product polynomial

Notes

Array API Standard Support

NdBSpline has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	✅	⛔
JAX	⚠️ no JIT	⛔
Dask	⛔	n/a

See Support for the array API standard for more information.