class scipy.interpolate.SmoothBivariateSpline(x, y, z, w=None, bbox=[None, None, None, None], kx=3, ky=3, s=None, eps=1e-16)[source]#

Smooth bivariate spline approximation.

x, y, zarray_like

1-D sequences of data points (order is not important).

warray_like, optional

Positive 1-D sequence of weights, of same length as x, y and z.

bboxarray_like, optional

Sequence of length 4 specifying the boundary of the rectangular approximation domain. By default, bbox=[min(x), max(x), min(y), max(y)].

kx, kyints, optional

Degrees of the bivariate spline. Default is 3.

sfloat, optional

Positive smoothing factor defined for estimation condition: sum((w[i]*(z[i]-s(x[i], y[i])))**2, axis=0) <= s Default s=len(w) which should be a good value if 1/w[i] is an estimate of the standard deviation of z[i].

epsfloat, optional

A threshold for determining the effective rank of an over-determined linear system of equations. eps should have a value within the open interval (0, 1), the default is 1e-16.

See also


a base class for bivariate splines.


a smooth univariate spline to fit a given set of data points.


a bivariate spline using weighted least-squares fitting


a bivariate spline over a rectangular mesh on a sphere


a smoothing bivariate spline in spherical coordinates


a bivariate spline in spherical coordinates using weighted least-squares fitting


a bivariate spline over a rectangular mesh


a function to find a bivariate B-spline representation of a surface


a function to evaluate a bivariate B-spline and its derivatives


The length of x, y and z should be at least (kx+1) * (ky+1).

If the input data is such that input dimensions have incommensurate units and differ by many orders of magnitude, the interpolant may have numerical artifacts. Consider rescaling the data before interpolating.

This routine constructs spline knot vectors automatically via the FITPACK algorithm. The spline knots may be placed away from the data points. For some data sets, this routine may fail to construct an interpolating spline, even if one is requested via s=0 parameter. In such situations, it is recommended to use bisplrep / bisplev directly instead of this routine and, if needed, increase the values of nxest and nyest parameters of bisplrep.

For linear interpolation, prefer LinearNDInterpolator. See for discussion.


__call__(x, y[, dx, dy, grid])

Evaluate the spline or its derivatives at given positions.

ev(xi, yi[, dx, dy])

Evaluate the spline at points


Return spline coefficients.


Return a tuple (tx,ty) where tx,ty contain knots positions of the spline with respect to x-, y-variable, respectively.


Return weighted sum of squared residuals of the spline approximation: sum ((w[i]*(z[i]-s(x[i],y[i])))**2,axis=0)

integral(xa, xb, ya, yb)

Evaluate the integral of the spline over area [xa,xb] x [ya,yb].

partial_derivative(dx, dy)

Construct a new spline representing a partial derivative of this spline.