scipy.interpolate.splprep¶

scipy.interpolate.
splprep
(x, w=None, u=None, ub=None, ue=None, k=3, task=0, s=None, t=None, full_output=0, nest=None, per=0, quiet=1)[source]¶ Find the Bspline representation of an Ndimensional curve.
Given a list of N rank1 arrays, x, which represent a curve in Ndimensional space parametrized by u, find a smooth approximating spline curve g(u). Uses the FORTRAN routine parcur from FITPACK.
Parameters:  x : array_like
A list of sample vector arrays representing the curve.
 w : array_like, optional
Strictly positive rank1 array of weights the same length as x[0]. The weights are used in computing the weighted leastsquares spline fit. If the errors in the x values have standarddeviation given by the vector d, then w should be 1/d. Default is
ones(len(x[0]))
. u : array_like, optional
An array of parameter values. If not given, these values are calculated automatically as
M = len(x[0])
, wherev[0] = 0
v[i] = v[i1] + distance(x[i], x[i1])
u[i] = v[i] / v[M1]
 ub, ue : int, optional
The endpoints of the parameters interval. Defaults to u[0] and u[1].
 k : int, optional
Degree of the spline. Cubic splines are recommended. Even values of k should be avoided especially with a small svalue.
1 <= k <= 5
, default is 3. task : int, optional
If task==0 (default), find t and c for a given smoothing factor, s. If task==1, find t and c for another value of the smoothing factor, s. There must have been a previous call with task=0 or task=1 for the same set of data. If task=1 find the weighted least square spline for a given set of knots, t.
 s : float, optional
A smoothing condition. The amount of smoothness is determined by satisfying the conditions:
sum((w * (y  g))**2,axis=0) <= s
, where g(x) is the smoothed interpolation of (x,y). The user can use s to control the tradeoff between closeness and smoothness of fit. Larger s means more smoothing while smaller values of s indicate less smoothing. Recommended values of s depend on the weights, w. If the weights represent the inverse of the standarddeviation of y, then a good s value should be found in the range(msqrt(2*m),m+sqrt(2*m))
, where m is the number of data points in x, y, and w. t : int, optional
The knots needed for task=1.
 full_output : int, optional
If nonzero, then return optional outputs.
 nest : int, optional
An overestimate of the total number of knots of the spline to help in determining the storage space. By default nest=m/2. Always large enough is nest=m+k+1.
 per : int, optional
If nonzero, data points are considered periodic with period
x[m1]  x[0]
and a smooth periodic spline approximation is returned. Values ofy[m1]
andw[m1]
are not used. quiet : int, optional
Nonzero to suppress messages. This parameter is deprecated; use standard Python warning filters instead.
Returns:  tck : tuple
(t,c,k) a tuple containing the vector of knots, the Bspline coefficients, and the degree of the spline.
 u : array
An array of the values of the parameter.
 fp : float
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
splrep
,splev
,sproot
,spalde
,splint
,bisplrep
,bisplev
,UnivariateSpline
,BivariateSpline
,BSpline
,make_interp_spline
Notes
See
splev
for evaluation of the spline and its derivatives. The number of dimensions N must be smaller than 11.The number of coefficients in the c array is
k+1
less then the number of knots,len(t)
. This is in contrast withsplrep
, which zeropads the array of coefficients to have the same length as the array of knots. These additional coefficients are ignored by evaluation routines,splev
andBSpline
.References
[1] P. Dierckx, “Algorithms for smoothing data with periodic and parametric splines, Computer Graphics and Image Processing”, 20 (1982) 171184. [2] P. Dierckx, “Algorithms for smoothing data with periodic and parametric splines”, report tw55, Dept. Computer Science, K.U.Leuven, 1981. [3] P. Dierckx, “Curve and surface fitting with splines”, Monographs on Numerical Analysis, Oxford University Press, 1993. Examples
Generate a discretization of a limacon curve in the polar coordinates:
>>> phi = np.linspace(0, 2.*np.pi, 40) >>> r = 0.5 + np.cos(phi) # polar coords >>> x, y = r * np.cos(phi), r * np.sin(phi) # convert to cartesian
And interpolate:
>>> from scipy.interpolate import splprep, splev >>> tck, u = splprep([x, y], s=0) >>> new_points = splev(u, tck)
Notice that (i) we force interpolation by using s=0, (ii) the parameterization,
u
, is generated automatically. Now plot the result:>>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> ax.plot(x, y, 'ro') >>> ax.plot(new_points[0], new_points[1], 'r') >>> plt.show()