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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_like, optional

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

    bbox(4,) 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.

    eps float, 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.

  Methods

  `__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
  `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 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.

  See also

  `BivariateSpline`

    a base class for bivariate splines.

  `UnivariateSpline`

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

  `SmoothBivariateSpline`

    a smoothing bivariate spline through the given points

  `RectSphereBivariateSpline`

    a bivariate spline over a rectangular mesh on a sphere

  `SmoothSphereBivariateSpline`

    a smoothing bivariate spline in spherical coordinates

  `LSQSphereBivariateSpline`

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

  `RectBivariateSpline`

    a bivariate spline over a rectangular mesh.

  `bisplrep`

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

  `bisplev`

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

  Notes

  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.

  Array API Standard Support

  `LSQBivariateSpline` is not in-scope for support of Python Array API Standard compatible backends other than NumPy.

  See Support for the array API standard for more information.