Fits a spline y = spl(x) of degree k to the provided x, y data. s specifies the number of knots by specifying a smoothing condition.

Notes

The number of data points must be larger than the spline degree k.

NaN handling: If the input arrays contain nan values, the result is not useful, since the underlying spline fitting routines cannot deal with nan . A workaround is to use zero weights for not-a-number data points:

>>> from scipy.interpolate import UnivariateSpline
>>> x, y = np.array([1, 2, 3, 4]), np.array([1, np.nan, 3, 4])
>>> w = np.isnan(y)
>>> y[w] = 0.
>>> spl = UnivariateSpline(x, y, w=~w)

Notice the need to replace a nan by a numerical value (precise value does not matter as long as the corresponding weight is zero.)

Parameters

x : (N,) array_like

1-D array of independent input data. Must be increasing; must be strictly increasing if s is 0.

y : (N,) array_like

1-D array of dependent input data, of the same length as x.

w : (N,) array_like, optional

Weights for spline fitting. Must be positive. If w is None, weights are all equal. Default is None.

bbox : (2,) array_like, optional

2-sequence specifying the boundary of the approximation interval. If :None:None:`bbox` is None, bbox=[x[0], x[-1]] . Default is None.

k : int, optional

Degree of the smoothing spline. Must be 1 <= k <= 5. k = 3 is a cubic spline. Default is 3.

s : float or None, optional

Positive smoothing factor used to choose the number of knots. Number of knots will be increased until the smoothing condition is satisfied:

sum((w[i] * (y[i]-spl(x[i])))**2, axis=0) <= s

If s is None, s = len(w) which should be a good value if 1/w[i] is an estimate of the standard deviation of y[i] . If 0, spline will interpolate through all data points. Default is None.

ext : int or str, optional

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.

Default is 0.

check_finite : bool, optional

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.

1-D smoothing spline fit to a given set of data points.

See Also

BivariateSpline

a base class for bivariate splines.

InterpolatedUnivariateSpline

a interpolating univariate spline for a given set of data points.

LSQBivariateSpline

a bivariate spline using weighted least-squares fitting

LSQSphereBivariateSpline

a bivariate spline in spherical coordinates using weighted least-squares fitting

RectBivariateSpline

a bivariate spline over a rectangular mesh

RectSphereBivariateSpline

a bivariate spline over a rectangular mesh on a sphere

SmoothBivariateSpline

a smoothing bivariate spline through the given points

SmoothSphereBivariateSpline

a smoothing bivariate spline in spherical coordinates

bisplev

a function to evaluate a bivariate B-spline and its derivatives

bisplrep

a function to find a bivariate B-spline representation of a surface

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

Examples

>>> import matplotlib.pyplot as plt
... from scipy.interpolate import UnivariateSpline
... rng = np.random.default_rng()
... x = np.linspace(-3, 3, 50)
... y = np.exp(-x**2) + 0.1 * rng.standard_normal(50)
... plt.plot(x, y, 'ro', ms=5)

Use the default value for the smoothing parameter:

>>> spl = UnivariateSpline(x, y)
... xs = np.linspace(-3, 3, 1000)
... plt.plot(xs, spl(xs), 'g', lw=3)

Manually change the amount of smoothing:

>>> spl.set_smoothing_factor(0.5)
... plt.plot(xs, spl(xs), 'b', lw=3)
... plt.show()

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.interpolate._fitpack2.UnivariateSpline.integral scipy.interpolate._fitpack2.UnivariateSpline.derivatives scipy.interpolate._fitpack2.BivariateSpline scipy.interpolate._fitpack2.RectBivariateSpline scipy.interpolate._fitpack2.SphereBivariateSpline scipy.interpolate._fitpack2.SmoothBivariateSpline scipy.interpolate._fitpack2.UnivariateSpline.derivative scipy.interpolate._fitpack_impl.splint scipy.interpolate._fitpack2.UnivariateSpline.antiderivative scipy.interpolate._fitpack_impl.sproot scipy.interpolate._fitpack2.LSQUnivariateSpline scipy.interpolate._fitpack2.UnivariateSpline scipy.interpolate._fitpack2.RectSphereBivariateSpline papyri.examples.example2 scipy.interpolate._fitpack_impl.splrep scipy.special._ellip_harm.ellip_harm scipy.interpolate._fitpack2.LSQSphereBivariateSpline papyri scipy.interpolate._fitpack2.LSQBivariateSpline scipy.interpolate._fitpack2.SmoothSphereBivariateSpline scipy.interpolate._fitpack_impl.splprep scipy.interpolate._fitpack_impl.bisplrep scipy.interpolate._fitpack_py.splrep scipy.interpolate._fitpack2.InterpolatedUnivariateSpline scipy.interpolate._interpolate.interp1d scipy.interpolate._bsplines.make_interp_spline

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

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