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# 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=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.

  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.

  See also

  `splprep`, `splrep`, `splint`, `sproot`, `splev`, `UnivariateSpline`, `BivariateSpline`

  Notes

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

  References

  [R8] | Dierckx P.:An algorithm for surface fitting with spline functions Ima J. Numer. Anal. 1 (1981) 267-283.

  [R9] | Dierckx P.:An algorithm for surface fitting with spline functions report tw50, Dept. Computer Science,K.U.Leuven, 1980.

  [R10] | Dierckx P.:Curve and surface fitting with splines, Monographs on Numerical Analysis, Oxford University Press, 1993.

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