# scipy.interpolate.LSQUnivariateSpline

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

  1-D 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`

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

  `InterpolatedUnivariateSpline`

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

  `splrep`

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

  `splev`

    a function to evaluate a B-spline or its derivatives

  `sproot`

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

  `splint`

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

  `spalde`

    a function to evaluate all derivatives of a B-spline

  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
      >>> rng = np.random.default_rng()
      >>> x = np.linspace(-3, 3, 50)
      >>> y = np.exp(-x**2) + 0.1 * rng.standard_normal(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()

  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.

  validate_input |

scipy.interpolate.InterpolatedUnivariateSpline.set_smoothing_factor scipy.interpolate.LSQUnivariateSpline.__call__