class scipy.interpolate.InterpolatedUnivariateSpline(x, y, w=None, bbox=[None, None], k=3, ext=0, check_finite=False)[source]

1-D interpolating spline for a given set of data points.

Fits a spline y = spl(x) of degree k to the provided x, y data. Spline function passes through all provided points. Equivalent to UnivariateSpline with s=0.

x(N,) array_like

Input dimension of data points – must be strictly increasing

y(N,) array_like

input dimension of data points

w(N,) array_like, optional

Weights for spline fitting. Must be positive. If None (default), weights are all equal.

bbox(2,) array_like, optional

2-sequence specifying the boundary of the approximation interval. If None (default), bbox=[x[0], x[-1]].

kint, optional

Degree of the smoothing spline. Must be 1 <= k <= 5.

extint 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.

The default value is 0.

check_finitebool, 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.

See also


a smooth univariate spline to fit a given set of data points.


a spline for which knots are user-selected


a smoothing bivariate spline through the given points


a bivariate spline using weighted least-squares fitting


a function to find the B-spline representation of a 1-D curve


a function to evaluate a B-spline or its derivatives


a function to find the roots of a cubic B-spline


a function to evaluate the definite integral of a B-spline between two given points


a function to evaluate all derivatives of a B-spline


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


>>> import matplotlib.pyplot as plt
>>> from scipy.interpolate import InterpolatedUnivariateSpline
>>> x = np.linspace(-3, 3, 50)
>>> y = np.exp(-x**2) + 0.1 * np.random.randn(50)
>>> spl = InterpolatedUnivariateSpline(x, y)
>>> plt.plot(x, y, 'ro', ms=5)
>>> xs = np.linspace(-3, 3, 1000)
>>> plt.plot(xs, spl(xs), 'g', lw=3, alpha=0.7)

Notice that the spl(x) interpolates y:

>>> spl.get_residual()


__call__(self, x[, nu, ext])

Evaluate spline (or its nu-th derivative) at positions x.

antiderivative(self[, n])

Construct a new spline representing the antiderivative of this spline.

derivative(self[, n])

Construct a new spline representing the derivative of this spline.

derivatives(self, x)

Return all derivatives of the spline at the point x.


Return spline coefficients.


Return positions of interior knots of the spline.


Return weighted sum of squared residuals of the spline approximation.

integral(self, a, b)

Return definite integral of the spline between two given points.


Return the zeros of the spline.

set_smoothing_factor(self, s)

Continue spline computation with the given smoothing factor s and with the knots found at the last call.