scipy.interpolate.splrep¶

scipy.interpolate.
splrep
(x, y, w=None, xb=None, xe=None, k=3, task=0, s=None, t=None, full_output=0, per=0, quiet=1)[source]¶ Find the Bspline representation of 1D curve.
Given the set of data points
(x[i], y[i])
determine a smooth spline approximation of degree k on the intervalxb <= x <= xe
.Parameters:  x, y : array_like
The data points defining a curve y = f(x).
 w : array_like, optional
Strictly positive rank1 array of weights the same length as x and y. The weights are used in computing the weighted leastsquares spline fit. If the errors in the y values have standarddeviation given by the vector d, then w should be 1/d. Default is ones(len(x)).
 xb, xe : float, optional
The interval to fit. If None, these default to x[0] and x[1] respectively.
 k : int, optional
The degree of the spline fit. It is recommended to use cubic splines. Even values of k should be avoided especially with small s values. 1 <= k <= 5
 task : {1, 0, 1}, optional
If task==0 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 (t will be stored an used internally)
If task=1 find the weighted least square spline for a given set of knots, t. These should be interior knots as knots on the ends will be added automatically.
 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 datapoints in x, y, and w. default : s=msqrt(2*m) if weights are supplied. s = 0.0 (interpolating) if no weights are supplied.
 t : array_like, optional
The knots needed for task=1. If given then task is automatically set to 1.
 full_output : bool, optional
If nonzero, then return optional outputs.
 per : bool, optional
If nonzero, data points are considered periodic with period x[m1]  x[0] and a smooth periodic spline approximation is returned. Values of y[m1] and w[m1] are not used.
 quiet : bool, optional
Nonzero to suppress messages. This parameter is deprecated; use standard Python warning filters instead.
Returns:  tck : tuple
A tuple (t,c,k) containing the vector of knots, the Bspline coefficients, and the degree of the spline.
 fp : array, optional
The weighted sum of squared residuals of the spline approximation.
 ier : int, optional
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, optional
A message corresponding to the integer flag, ier.
See also
UnivariateSpline
,BivariateSpline
,splprep
,splev
,sproot
,spalde
,splint
,bisplrep
,bisplev
,BSpline
,make_interp_spline
Notes
See
splev
for evaluation of the spline and its derivatives. Uses the FORTRAN routinecurfit
from FITPACK.The user is responsible for assuring that the values of x are unique. Otherwise,
splrep
will not return sensible results.If provided, knots t must satisfy the SchoenbergWhitney conditions, i.e., there must be a subset of data points
x[j]
such thatt[j] < x[j] < t[j+k+1]
, forj=0, 1,...,nk2
.This routine zeropads the coefficients array
c
to have the same length as the array of knotst
(the trailingk + 1
coefficients are ignored by the evaluation routines,splev
andBSpline
.) This is in contrast withsplprep
, which does not zeropad the coefficients.References
Based on algorithms described in [1], [2], [3], and [4]:
[1] (1, 2) P. Dierckx, “An algorithm for smoothing, differentiation and integration of experimental data using spline functions”, J.Comp.Appl.Maths 1 (1975) 165184. [2] (1, 2) P. Dierckx, “A fast algorithm for smoothing data on a rectangular grid while using spline functions”, SIAM J.Numer.Anal. 19 (1982) 12861304. [3] (1, 2) P. Dierckx, “An improved algorithm for curve fitting with spline functions”, report tw54, Dept. Computer Science,K.U. Leuven, 1981. [4] (1, 2) P. Dierckx, “Curve and surface fitting with splines”, Monographs on Numerical Analysis, Oxford University Press, 1993. Examples
>>> import matplotlib.pyplot as plt >>> from scipy.interpolate import splev, splrep >>> x = np.linspace(0, 10, 10) >>> y = np.sin(x) >>> spl = splrep(x, y) >>> x2 = np.linspace(0, 10, 200) >>> y2 = splev(x2, spl) >>> plt.plot(x, y, 'o', x2, y2) >>> plt.show()