Average values over ranges of one variable Given X (size N*1) and Y (N*M), this function splits the range of X into up to K intervals (bins) containing approximately equal numbers of elements, and ...

Returns the piecewise polynomial form of the Catmull-Rom cubic spline interpolating F at the points X.

cubic spline interpolation

cubic spline interpolation with various end conditions. creates the pp-form of the cubic spline.

Cubic spline approximation (smoothing) approximate [X,Y], weighted by W (inverse variance of the Y values; if not given, equal weighting is assumed), at XI

Cubic spline approximation with smoothing parameter estimation Approximately interpolates [X,Y], weighted by W (inverse variance; if not given, equal weighting is assumed), at XI.

De-duplication and sorting to facilitate spline smoothing Points are sorted in ascending order of X, with each set of duplicates (values with the same X, within TOL) replaced by a weighted average.

differentiate the spline in pp-form

plots spline

r = fnval(pp,x) or r = fnval(x,pp) Compute the value of the piece-wise polynomial pp at points x.

Apply a Tikhonov regularization, the functional to be minimized is F = FD + LAMBDA1*F1 + LAMBDA2*F2 = sum_(i=1)^M (y_i-u(x_i))^2 + LAMBDA1*int_a^b (u'(x) - G1(x))^2 dx + LAMBDA2*int_a^b (u"(x) - G2...

Apply a Tikhonov regularization, the functional to be minimized is F = FD + LAMBDA1 * F1 + LAMBDA2 * F2 = sum_(i=1)^M (y_i-u(x_i))^2 + + LAMBDA1 * dintegral (du/dx)^2+(du/dy)^2 dA + + LAMBDA2 * din...

Thin plate smoothing of scattered values in multi-D approximately interpolate [X,Y] at XI

Evaluates a thin plate spline at given points XI

Evaluates the first derivative of a thin plate spline at given points XI