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 ND curve.
Given a list of N rank1 arrays, x, which represent a curve in ND space parametrized by u, find a smooth approximating spline curve g(u). Uses the FORTRAN routine parcur from FITPACK.
 Parameters
 xarray_like
A list of sample vector arrays representing the curve.
 warray_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]))
. uarray_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, ueint, optional
The endpoints of the parameters interval. Defaults to u[0] and u[1].
 kint, 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. taskint, 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.
 sfloat, 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. tint, optional
The knots needed for task=1.
 full_outputint, optional
If nonzero, then return optional outputs.
 nestint, 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.
 perint, 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. quietint, optional
Nonzero to suppress messages. This parameter is deprecated; use standard Python warning filters instead.
 Returns
 tcktuple
(t,c,k) a tuple containing the vector of knots, the Bspline coefficients, and the degree of the spline.
 uarray
An array of the values of the parameter.
 fpfloat
The weighted sum of squared residuals of the spline approximation.
 ierint
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.
 msgstr
A message corresponding to the integer flag, ier.
See also
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()