scipy.interpolate.bisplrep(x, y, z, w=None, xb=None, xe=None, yb=None, ye=None, kx=3, ky=3, task=0, s=None, eps=9.9999999999999998e-17, tx=None, ty=None, full_output=0, nxest=None, nyest=None, quiet=1)

Find a bivariate B-spline representation of a surface.


Given a set of data points (x[i], y[i], z[i]) representing a surface z=f(x,y), compute a B-spline representation of the surface. Based on the routine SURFIT from FITPACK.


x, y, z – Rank-1 arrays of data points. w – Rank-1 array of weights. By default w=ones(len(x)). xb, xe – End points of approximation interval in x. yb, ye – End points of approximation interval in y.

By default xb, xe, yb, ye = x.min(), x.max(), y.min(), y.max()
kx, ky – The degrees of the spline (1 <= kx, ky <= 5). Third order
(kx=ky=3) is recommended.
task – If task=0, find knots in x and y and coefficients for a given
smoothing factor, s.
If task=1, find knots and coefficients for another value of the
smoothing factor, s. bisplrep must have been previously called with task=0 or task=1.

If task=-1, find coefficients for a given set of knots tx, ty.

s – A non-negative smoothing factor. If weights correspond
to the inverse of the standard-deviation of the errors in z, then a good s-value should be found in the range (m-sqrt(2*m),m+sqrt(2*m)) where m=len(x)
eps – A threshold for determining the effective rank of an
over-determined linear system of equations (0 < eps < 1) — not likely to need changing.

tx, ty – Rank-1 arrays of the knots of the spline for task=-1 full_output – Non-zero to return optional outputs. nxest, nyest – Over-estimates of the total number of knots.

If None then nxest = max(kx+sqrt(m/2),2*kx+3),
nyest = max(ky+sqrt(m/2),2*ky+3)

quiet – Non-zero to suppress printing of messages.

Outputs: (tck, {fp, ier, msg})

tck – A list [tx, ty, c, kx, ky] containing the knots (tx, ty) and
coefficients (c) of the bivariate B-spline representation of the surface along with the degree of the spline.

fp – The weighted sum of squared residuals of the spline approximation. ier – An integer flag about splrep success. Success is indicated if

ier<=0. If ier in [1,2,3] an error occurred but was not raised. Otherwise an error is raised.

msg – A message corresponding to the integer flag, ier.


SEE bisplev to evaluate the value of the B-spline given its tck representation.
See also:

splprep, splrep, splint, sproot, splev - evaluation, roots, integral UnivariateSpline, BivariateSpline - an alternative wrapping

of the FITPACK functions

Notes: Based on algorithms from:

Dierckx P. : An algorithm for surface fitting with spline functions
Ima J. Numer. Anal. 1 (1981) 267-283.
Dierckx P. : An algorithm for surface fitting with spline functions
report tw50, Dept. Computer Science,K.U.Leuven, 1980.
Dierckx P. : Curve and surface fitting with splines, Monographs on
Numerical Analysis, Oxford University Press, 1993.

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