Fits a spline y = spl(x) of degree k to the provided x, y data. t specifies the internal knots of the spline
The number of data points must be larger than the spline degree k.
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
.
Input dimension of data points -- must be increasing
Input dimension of data points
interior knots of the spline. Must be in ascending order and:
bbox[0] < t[0] < ... < t[-1] < bbox[-1]
weights for spline fitting. Must be positive. If None (default), weights are all equal.
2-sequence specifying the boundary of the approximation interval. If None (default), bbox = [x[0], x[-1]]
.
Degree of the smoothing spline. Must be 1 <= k <= 5. Default is k = 3, a cubic spline.
Controls the extrapolation mode for elements not in the interval defined by the knot sequence.
if ext=0 or 'extrapolate', return the extrapolated value.
if ext=1 or 'zeros', return 0
if ext=2 or 'raise', raise a ValueError
if ext=3 of 'const', return the boundary value.
The default value is 0.
Whether to check that the input arrays contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination or non-sensical results) if the inputs do contain infinities or NaNs. Default is False.
If the interior knots do not satisfy the Schoenberg-Whitney conditions
1-D spline with explicit internal knots.
InterpolatedUnivariateSpline
a interpolating univariate spline for a given set of data points.
UnivariateSpline
a smooth univariate spline to fit a given set of data points.
spalde
a function to evaluate all derivatives of a B-spline
splev
a function to evaluate a B-spline or its derivatives
splint
a function to evaluate the definite integral of a B-spline between two given points
splrep
a function to find the B-spline representation of a 1-D curve
sproot
a function to find the roots of a cubic B-spline
>>> from scipy.interpolate import LSQUnivariateSpline, UnivariateSpline
... import matplotlib.pyplot as plt
... rng = np.random.default_rng()
... x = np.linspace(-3, 3, 50)
... y = np.exp(-x**2) + 0.1 * rng.standard_normal(50)
Fit a smoothing spline with a pre-defined internal knots:
>>> t = [-1, 0, 1]
... spl = LSQUnivariateSpline(x, y, t)
>>> xs = np.linspace(-3, 3, 1000)
... plt.plot(x, y, 'ro', ms=5)
... plt.plot(xs, spl(xs), 'g-', lw=3)
... plt.show()
Check the knot vector:
>>> spl.get_knots() array([-3., -1., 0., 1., 3.])
Constructing lsq spline using the knots from another spline:
>>> x = np.arange(10)
... s = UnivariateSpline(x, x, s=0)
... s.get_knots() array([ 0., 2., 3., 4., 5., 6., 7., 9.])
>>> knt = s.get_knots()See :
... s1 = LSQUnivariateSpline(x, x, knt[1:-1]) # Chop 1st and last knot
... s1.get_knots() array([ 0., 2., 3., 4., 5., 6., 7., 9.])
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.interpolate._fitpack2.InterpolatedUnivariateSpline
scipy.interpolate._fitpack2.LSQUnivariateSpline
scipy.interpolate._fitpack2.SphereBivariateSpline
scipy.interpolate._bsplines.make_lsq_spline
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