`scipy.interpolate._dierckx:_coloc`

Summary

Build the B-spline colocation matrix.

Extended Summary

The colocation matrix is defined as $B_{j, l} = B_{l} (x_{j})$ , so that row j contains all the B-splines which are non-zero at x_j.

The matrix is constructed in the LAPACK banded storage. Basically, for an N-by-N matrix A with ku upper diagonals and kl lower diagonals, the shape of the array Ab is (2*kl + ku +1, N), where the last kl+ku+1 rows of Ab contain the diagonals of A, and the first kl rows of Ab are not referenced. For more info see, e.g. the docs for the *gbsv routine.

This routine is not supposed to be called directly, and does no error checking.

Parameters

x : ndarray, shape (n,): sorted 1D array of x values
t : ndarray, shape (nt + k + 1,): sorted 1D array of knots
k : int: spline order
ab : ndarray, shape (2*kl + ku + 1, nt), F-order: This parameter is modified in-place. On exit: B-spline colocation matrix in the band storage with ku upper diagonals and kl lower diagonals. Here kl = ku = k.
offset : int, optional: skip this many rows

Aliases

scipy.interpolate._dierckx._coloc