SciPy

scipy.interpolate.bisplrep

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=1e-16, tx=None, ty=None, full_output=0, nxest=None, nyest=None, quiet=1)[source]

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.

Parameters :

x, y, z : ndarray

Rank-1 arrays of data points.

w : ndarray, optional

Rank-1 array of weights. By default w=np.ones(len(x)).

xb, xe : float, optional

End points of approximation interval in x. By default xb = x.min(), xe=x.max().

yb, ye : float, optional

End points of approximation interval in y. By default yb=y.min(), ye = y.max().

kx, ky : int, optional

The degrees of the spline (1 <= kx, ky <= 5). Third order (kx=ky=3) is recommended.

task : int, optional

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 : float, optional

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 : float, optional

A threshold for determining the effective rank of an over-determined linear system of equations (0 < eps < 1). eps is not likely to need changing.

tx, ty : ndarray, optional

Rank-1 arrays of the knots of the spline for task=-1

full_output : int, optional

Non-zero to return optional outputs.

nxest, nyest : int, optional

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 : int, optional

Non-zero to suppress printing of messages.

Returns :

tck : array_like

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 : ndarray

The weighted sum of squared residuals of the spline approximation.

ier : int

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 : str

A message corresponding to the integer flag, ier.

Notes

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

References

[R44]Dierckx P.:An algorithm for surface fitting with spline functions Ima J. Numer. Anal. 1 (1981) 267-283.
[R45]Dierckx P.:An algorithm for surface fitting with spline functions report tw50, Dept. Computer Science,K.U.Leuven, 1980.
[R46]Dierckx P.:Curve and surface fitting with splines, Monographs on Numerical Analysis, Oxford University Press, 1993.