splrep(x, y, w=None, xb=None, xe=None, k=3, task=0, s=None, t=None, full_output=0, per=0, quiet=1)
Given the set of data points (x[i], y[i])
determine a smooth spline approximation of degree k on the interval xb <= x <= xe
.
See splev
for evaluation of the spline and its derivatives. Uses the FORTRAN routine curfit
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 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 c
to have the same length as the array of knots t
(the trailing k + 1
coefficients are ignored by the evaluation routines, splev
and BSpline
.) This is in contrast with splprep
, which does not zero-pad the coefficients.
The data points defining a curve y = f(x).
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)).
The interval to fit. If None, these default to x[0] and x[-1] respectively.
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
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.
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 standard-deviation of y, then a good s value should be found in the range (m-sqrt(2*m),m+sqrt(2*m)) where m is 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.
The knots needed for task=-1. If given then task is automatically set to -1.
If non-zero, then return optional outputs.
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.
Non-zero to suppress messages. This parameter is deprecated; use standard Python warning filters instead.
A tuple (t,c,k) containing the vector of knots, the B-spline coefficients, and the degree of the spline.
The weighted sum of squared residuals of the spline approximation.
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.
A message corresponding to the integer flag, ier.
Find the B-spline representation of a 1-D curve.
You can interpolate 1-D points with a B-spline curve. Further examples are given in in the tutorial <tutorial-interpolate_splXXX>
.
>>> 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()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.interpolate._fitpack_py.insert
scipy.interpolate._fitpack_impl.splrep
scipy.interpolate._fitpack_impl.splantider
scipy.interpolate._fitpack_py.splder
scipy.interpolate._fitpack_py.splrep
scipy.interpolate._fitpack_py.splantider
scipy.interpolate._fitpack_py.splev
scipy.interpolate._fitpack_py.sproot
scipy.interpolate._fitpack_py.splint
scipy.interpolate._fitpack_impl.splder
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