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 B-spline representation of a 1-D curve. - Legacy - This function is considered legacy and will no longer receive updates. While we currently have no plans to remove it, we recommend that new code uses more modern alternatives instead. Specifically, we recommend using - make_splrepin new code.- Given the set of data points - (x[i], y[i])determine a smooth spline approximation of degree k on the interval- xb <= x <= xe.- Parameters:
- x, yarray_like
- The data points defining a curve - y = f(x).
- warray_like, optional
- Strictly positive rank-1 array of weights the same length as x and y. The weights are used in computing the weighted least-squares spline fit. If the errors in the y values have standard-deviation given by the vector - d, then w should be- 1/d. Default is- ones(len(x)).
- xb, xefloat, optional
- The interval to fit. If None, these default to - x[0]and- x[-1]respectively.
- kint, 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- tand- cfor a given smoothing factor, s.- If - task==1find- tand- cfor another value of the smoothing factor, s. There must have been a previous call with- task=0or- task=1for the same set of data (- twill be stored an used internally)- If - task=-1find 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.
- sfloat, optional
- A smoothing condition. The amount of smoothness is determined by satisfying the conditions: - sum((w * (y - g))**2,axis=0) <= swhere- 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 standard-deviation of y, then a good s value should be found in the range- (m-sqrt(2*m),m+sqrt(2*m))where- mis the number of datapoints in x, y, and w. default :- s=m-sqrt(2*m)if weights are supplied.- s = 0.0(interpolating) if no weights are supplied.
- tarray_like, optional
- The knots needed for - task=-1. If given then task is automatically set to- -1.
- full_outputbool, optional
- If non-zero, then return optional outputs. 
- perbool, optional
- If non-zero, data points are considered periodic with period - x[m-1]-- x[0]and a smooth periodic spline approximation is returned. Values of- y[m-1]and- w[m-1]are not used. The default is zero, corresponding to boundary condition ‘not-a-knot’.
- quietbool, optional
- Non-zero to suppress messages. 
 
- Returns:
- tcktuple
- A tuple - (t,c,k)containing the vector of knots, the B-spline coefficients, and the degree of the spline.
- fparray, optional
- The weighted sum of squared residuals of the spline approximation. 
- ierint, 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.
- msgstr, optional
- A message corresponding to the integer flag, ier. 
 
 - See also - Notes - See - splevfor evaluation of the spline and its derivatives. Uses the FORTRAN routine- curfitfrom FITPACK.- The user is responsible for assuring that the values of x are unique. Otherwise, - splrepwill not return sensible results.- If provided, knots t must satisfy the Schoenberg-Whitney conditions, i.e., there must be a subset of data points - x[j]such that- t[j] < x[j] < t[j+k+1], for- j=0, 1,...,n-k-2.- This routine zero-pads the coefficients array - cto have the same length as the array of knots- t(the trailing- k + 1coefficients are ignored by the evaluation routines,- splevand- BSpline.) This is in contrast with- splprep, which does not zero-pad the coefficients.- The default boundary condition is ‘not-a-knot’, i.e. the first and second segment at a curve end are the same polynomial. More boundary conditions are available in - CubicSpline.- References - Based on algorithms described in [1], [2], [3], and [4]: [1]- P. Dierckx, “An algorithm for smoothing, differentiation and integration of experimental data using spline functions”, J.Comp.Appl.Maths 1 (1975) 165-184. [2]- P. Dierckx, “A fast algorithm for smoothing data on a rectangular grid while using spline functions”, SIAM J.Numer.Anal. 19 (1982) 1286-1304. [3]- P. Dierckx, “An improved algorithm for curve fitting with spline functions”, report tw54, Dept. Computer Science,K.U. Leuven, 1981. [4]- P. Dierckx, “Curve and surface fitting with splines”, Monographs on Numerical Analysis, Oxford University Press, 1993. - Examples - You can interpolate 1-D points with a B-spline curve. Further examples are given in in the tutorial. - >>> import numpy as np >>> 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() 