# scipy.interpolate.InterpolatedUnivariateSpline

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

  One-dimensional 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.

  Parameters:

  x : (N,) array_like

  > Input dimension of data points – must be 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]]`.

  k : int, optional

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

  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.

  > The default value 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.

  See also

  `UnivariateSpline`
    Superclass – allows knots to be selected by a smoothing condition
  `LSQUnivariateSpline`
    spline for which knots are user-selected
  `splrep`
    An older, non object-oriented wrapping of FITPACK

  `splev`, `sproot`, `splint`, `spalde`

  `BivariateSpline`
    A similar class for two-dimensional spline interpolation

  Notes

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

  Examples

      >>> 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)
      >>> plt.show()

  (Source code)

  Notice that the `spl(x)` interpolates y:

      >>> spl.get_residual()
      0.0

  Methods

  `__call__`(x[, nu, ext]) | Evaluate spline (or its nu-th derivative) at positions x.
  `antiderivative`([n]) | Construct a new spline representing the antiderivative of this spline.
  `derivative`([n]) | Construct a new spline representing the derivative of this spline.
  `derivatives`(x) | Return all derivatives of the spline at the point x.
  `get_coeffs`() | Return spline coefficients.
  `get_knots`() | Return positions of interior knots of the spline.
  `get_residual`() | Return weighted sum of squared residuals of the spline approximation.
  `integral`(a, b) | Return definite integral of the spline between two given points.
  `roots`() | Return the zeros of the spline.
  `set_smoothing_factor`(s) | Continue spline computation with the given smoothing factor s and with the knots found at the last call.