### Navigation

- index
- modules |
- modules |
- next |
- previous |
- SciPy v0.12 Reference Guide (DRAFT) »
- Interpolation (`scipy.interpolate`) »

# scipy.interpolate.UnivariateSpline

class `scipy.interpolate.``UnivariateSpline`(x, y, w=None, bbox=[None, None], k=3, s=None)

  One-dimensional smoothing spline fit to a given set of data points.

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

  Parameters : | x : (N,) array_like 1-D array of independent input data. Must be increasing. 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 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 <= 5. 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]-s(x[i])))**2,axis=0) <= s If None (default), 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.

  See also

  `InterpolatedUnivariateSpline`
    Subclass with smoothing forced to 0
  `LSQUnivariateSpline`
    Subclass in which knots are user-selected instead of being set by smoothing condition
  `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

      >>> from numpy import linspace,exp
      >>> from numpy.random import randn
      >>> from scipy.interpolate import UnivariateSpline
      >>> x = linspace(-3, 3, 100)
      >>> y = exp(-x**2) + randn(100)/10
      >>> s = UnivariateSpline(x, y, s=1)
      >>> xs = linspace(-3, 3, 1000)
      >>> ys = s(xs)

  xs,ys is now a smoothed, super-sampled version of the noisy gaussian x,y.

  Methods

  `__call__`(x[, nu]) | Evaluate spline (or its nu-th derivative) at positions x.
  `derivatives`(x) | Return all derivatives of the spline at the point x.
  `get_coeffs`() | Return spline coefficients.
  `get_knots`() | Return positions of (boundary and interior) knots of the spline.
  `get_residual`() | Return weighted sum of squared residuals of the spline
  `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

### Navigation

- index
- modules |
- modules |
- next |
- previous |
- SciPy v0.12 Reference Guide (DRAFT) »
- Interpolation (`scipy.interpolate`) »