ndsplines.NDSpline

class ndsplines.NDSpline(knots, coefficients, degrees, periodic=False, extrapolate=True)

Multivariate tensor-product spline in the B-spline basis. A general N dimensional tensor product B-spline is given by

\[S(x_1, ..., x_N) = \sum_{i_1=0}^{n_1-1} \cdots \sum_{i_N=0}^{n_N-1} c_{i_1, ..., i_N} \prod_{j = i}^{N} B_{i_j;k_j,t_j}(x_j)\]

where \(B_{i_j;k_j,t_j}\) is the \(i_j\)-th B-spline basis function of degree \(k_j\) over the knots \({t_j}\) with coefficients \(c_{i_1, ..., i_N}\)

Parameters:

• knots (list of ndarrays, shapes=[n_0+degrees[i]+1, ..., n_ndim+degrees[-1]+1], dtype=np.float_) – List of knots in each dimension, \([t_1, t_2, \ldots, t_N]\).

• coefficients (ndarray, shape=(n_1, n_2, ..., n_xdim) + yshape, dtype=np.float_) – N-D array of coefficients, \(c_{i_1, ..., i_N}\).

• degrees (ndarray, shape=(xdim,), dtype=np.int_) – Array of the degree of each dimension, \([k_1, k_2, \ldots, k_N]\).

• periodic (ndarray, shape=(xdim,), dtype=bool) – Array of periodicity flags for each dimension.

• extrapolate (ndarray, shape=(xdim,2), dtype=bool) – Array of extrapolation flags for each side in each dimension.

knots

List of knots in each dimension, \([t_1, t_2, \ldots, t_N]\).

Type:

list of ndarrays, shapes=[n_0+degrees[i]+1, …, n_ndim+degrees[-1]+1], dtype=np.float_

xdim

Dimension of spline input space.

Type:

int

coefficients

N-D array of coefficients, \(c_{i_1, ..., i_N}\).

Type:

ndarray, shape=(n_1, n_2, …, n_xdim, ydim), dtype=np.float_

ydim

Dimension of spline output space.

Type:

int

yshape

Shape of spline output.

Type:

tuple of ints

__init__(knots, coefficients, degrees, periodic=False, extrapolate=True)

Methods

__init__(knots, coefficients, degrees[, ...])
allocate_workspace_arrays(num_points)	Allocate workspace arrays for the N-dimensional B-spline evaluation.
antiderivative(dim[, nu])	Return NDSpline representing the nu-th antiderivative in the dim-th dimension.
compute_basis_coefficient_selector(x[, nus])	Evaluate the N-dimensional B-spline basis functions and coefficient selectors.
copy()	Return a deep copy of this NDSpline object.
derivative(dim[, nu])	Return NDSpline representing the nu-th derivative in the dim-th dimension.
to_file(file[, compress])	Save attributes of NDSpline object to binary file in NumPy .npz format so that the object can be re-created.

Attributes

extrapolate
periodic