The collocation 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: zeroed out. On exit: B-spline collocation matrix in the band storage with ku upper diagonals and kl lower diagonals. Here kl = ku = k .

offset : int, optional

skip this many rows

Build the B-spline collocation matrix.

Examples

See :

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