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Discrete calculus

Divided differencing, discrete differentiation, and discrete integration.

divided_diff()
Divided differencing
discrete_deriv()
Discrete differentiation
discrete_integ()
Discrete integration

Matrix multiplication

Multiplication by discrete derivative and falling factorial basis matrices.

d_mat_mult()
Multiply by D matrix
b_mat_mult()
Multiply by B matrix
h_mat_mult()
Multiply by H matrix

Matrix construction

Construction of discrete derivative and discrete spline basis matrices.

d_mat()
Construct D matrix
b_mat()
Construct B matrix
h_mat()
Construct H matrix
n_mat()
Construct N matrix

Basis evaluation

Evaluation of falling factorial and discrete B-spline basis functions.

h_eval()
Evaluate H basis
n_eval()
Evaluate N basis

Interpolation

Interpolation within the “canonical” space of discrete splines.

dspline_interp()
Discrete spline interpolation

Projection

Least squares projection onto “custom” spaces of discrete splines.

dspline_solve()
Discrete spline projection

In-place computations

Divided differencing and matrix multiplication using in-place operations.