### Navigation

- index
- modules |
- next |
- previous |
- SciPy v0.7 Reference Guide (DRAFT) »
- Interpolation (`scipy.interpolate`) »

# 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.

  Description:

  > 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.

  Inputs:

  > x, y, z – Rank-1 arrays of data points. w – Rank-1 array of weights. By default w=ones(len(x)). xb, xe – End points of approximation interval in x. yb, ye – End points of approximation interval in y.

  > > By default xb, xe, yb, ye = x.min(), x.max(), y.min(), y.max()

  > kx, ky – The degrees of the spline (1 <= kx, ky <= 5). Third order
  >   (kx=ky=3) is recommended.
  > task – 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 – 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 – A threshold for determining the effective rank of an
  >   over-determined linear system of equations (0 < eps < 1) — not likely to need changing.

  > tx, ty – Rank-1 arrays of the knots of the spline for task=-1 full_output – Non-zero to return optional outputs. nxest, nyest – 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 – Non-zero to suppress printing of messages.

  Outputs: (tck, {fp, ier, msg})

  > tck – 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 – The weighted sum of squared residuals of the spline approximation. ier – 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 – A message corresponding to the integer flag, ier.

  Remarks:

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

  See also:

    splprep, splrep, splint, sproot, splev - evaluation, roots, integral UnivariateSpline, BivariateSpline - an alternative wrapping

    > of the FITPACK functions

  Notes: Based on algorithms from:

  > Dierckx P. : An algorithm for surface fitting with spline functions
  >   Ima J. Numer. Anal. 1 (1981) 267-283.
  > Dierckx P. : An algorithm for surface fitting with spline functions
  >   report tw50, Dept. Computer Science,K.U.Leuven, 1980.
  > Dierckx P. : Curve and surface fitting with splines, Monographs on
  >   Numerical Analysis, Oxford University Press, 1993.

### Navigation

- index
- modules |
- next |
- previous |
- SciPy v0.7 Reference Guide (DRAFT) »
- Interpolation (`scipy.interpolate`) »