Find the B-spline representation of 1-D curve.
Description:
Given the set of data points (x[i], y[i]) determine a smooth spline approximation of degree k on the interval xb <= x <= xe. The coefficients, c, and the knot points, t, are returned. Uses the FORTRAN routine curfit from FITPACK.
Inputs:
x, y – The data points defining a curve y = f(x). w – 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, xe – The interval to fit. If None, these default to x[0] and x[-1]
- respectively.
- k – The order of the spline fit. It is recommended to use cubic splines.
- Even order splines should be avoided especially with small s values. 1 <= k <= 5
- task – 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 – 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.- t – The knots needed for task=-1. If given then task is automatically
- set to -1.
full_output – If non-zero, then return optional outputs. per – 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.quiet – Non-zero to suppress messages.
Outputs: (tck, {fp, ier, msg})
- tck – (t,c,k) a tuple containing the vector of knots, the B-spline
- coefficients, and the degree of the spline.
fp – The weighted sum of squared residuals of the spline approximation. ier – 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 – A message corresponding to the integer flag, ier.
Remarks:
See splev for evaluation of the spline and its derivatives.
Example:
x = linspace(0, 10, 10) y = sin(x) tck = splrep(x, y) x2 = linspace(0, 10, 200) y2 = splev(x2, tck) plot(x, y, ‘o’, x2, y2)
splprep, splev, sproot, spalde, splint - evaluation, roots, integral bisplrep, bisplev - bivariate splines UnivariateSpline, BivariateSpline - an alternative wrapping
of the FITPACK functions
Notes: