# 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)

  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.

  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 interpolation.

  References

  [1]

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

  [2]

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

  [3]

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

  Examples

  Examples are given in the tutorial.