The observation equations are A @ c = y , and the normal equations are A.T @ A @ c = A.T @ y . This routine fills in the rhs and lhs for the latter.

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

The normal eq matrix has at most :None:None:`2k+1` bands and is constructed in the LAPACK symmetrix banded storage: A[i, j] == ab[i-j, j] with :None:None:`i >= j`. See the doctsring for scipy.linalg.cholesky_banded for more info.

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

y : ndarray, shape (n, s)

a 2D array of y values. The second dimension contains all trailing dimensions of the original array of ordinates.

w : ndarray, shape(n,)

Weights.

ab : ndarray, shape (k+1, n), in Fortran order.

This parameter is modified in-place. On entry: should be zeroed out. On exit: LHS of the normal equations.

rhs : ndarray, shape (n, s), in Fortran order.

This parameter is modified in-place. On entry: should be zeroed out. On exit: RHS of the normal equations.

Construct the normal equations for the B-spline LSQ problem.

Examples

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

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