# scipy.interpolate.LSQUnivariateSpline

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

  One-dimensional spline with explicit internal knots.

  Fits a spline y = spl(x) of degree k to the provided x, y data. t specifies the internal knots of the spline

  > Parameters: | x : (N,) array_like Input dimension of data points – must be increasing y : (N,) array_like Input dimension of data points t : (M,) array_like interior knots of the spline. Must be in ascending order and:
  >     bbox[0] < t[0] < ... < t[-1] < bbox[-1]
  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. Default is k=3, a cubic spline. 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.
  Raises: | ValueError If the interior knots do not satisfy the Schoenberg-Whitney conditions

  See also

  `UnivariateSpline`
    Superclass – knots are specified by setting a smoothing condition
  `InterpolatedUnivariateSpline`
    spline passing through all points
  `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.

  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`.

  Examples

      >>> from scipy.interpolate import LSQUnivariateSpline, UnivariateSpline
      >>> import matplotlib.pyplot as plt
      >>> x = np.linspace(-3, 3, 50)
      >>> y = np.exp(-x**2) + 0.1 * np.random.randn(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()

  (Source code)

  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()
      >>> s1 = LSQUnivariateSpline(x, x, knt[1:-1])    # Chop 1st and last knot
      >>> s1.get_knots()
      array([ 0.,  2.,  3.,  4.,  5.,  6.,  7.,  9.])

  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.