# scipy.interpolate.LSQBivariateSpline¶

class scipy.interpolate.LSQBivariateSpline(x, y, z, tx, ty, w=None, bbox=[None, None, None, None], kx=3, ky=3, eps=None)

Weighted least-squares bivariate spline approximation.

Parameters : x, y, z : array_like 1-D sequences of data points (order is not important). tx, ty : array_like Strictly ordered 1-D sequences of knots coordinates. w : array_lie, optional Positive 1-D sequence of weights. bbox : array_like, optional Sequence of length 4 specifying the boundary of the rectangular approximation domain. By default, bbox=[min(x,tx),max(x,tx), min(y,ty),max(y,ty)]. kx, ky : ints, optional Degrees of the bivariate spline. Default is 3. s : float, 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]. eps : float, optional A threshold for determining the effective rank of an over-determined linear system of equations. eps should have a value between 0 and 1, the default is 1e-16.

UnivariateSpline
a similar class for univariate spline interpolation
SmoothUnivariateSpline
To create a BivariateSpline through the given points

Notes

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

Methods

 __call__(x, y[, mth]) Evaluate spline at positions x,y. ev(xi, yi) Evaluate spline at points (x[i], y[i]), i=0,...,len(x)-1 get_coeffs() Return spline coefficients. get_knots() Return a tuple (tx,ty) where tx,ty contain knots positions of the spline with respect to x-, y-variable, respectively. get_residual() Return weighted sum of squared residuals of the spline integral(xa, xb, ya, yb) Evaluate the integral of the spline over area [xa,xb] x [ya,yb].

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