Module « scipy.interpolate »

Classe « RectSphereBivariateSpline »

Informations générales

Héritage

builtins.object
    _BivariateSplineBase
        SphereBivariateSpline
            RectSphereBivariateSpline

Définition

class RectSphereBivariateSpline(SphereBivariateSpline):

Description _{[extrait de RectSphereBivariateSpline.__doc__]}

    Bivariate spline approximation over a rectangular mesh on a sphere.

    Can be used for smoothing data.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    u : array_like
        1-D array of colatitude coordinates in strictly ascending order.
        Coordinates must be given in radians and lie within the open interval
        ``(0, pi)``.
    v : array_like
        1-D array of longitude coordinates in strictly ascending order.
        Coordinates must be given in radians. First element (``v[0]``) must lie
        within the interval ``[-pi, pi)``. Last element (``v[-1]``) must satisfy
        ``v[-1] <= v[0] + 2*pi``.
    r : array_like
        2-D array of data with shape ``(u.size, v.size)``.
    s : float, optional
        Positive smoothing factor defined for estimation condition
        (``s=0`` is for interpolation).
    pole_continuity : bool or (bool, bool), optional
        Order of continuity at the poles ``u=0`` (``pole_continuity[0]``) and
        ``u=pi`` (``pole_continuity[1]``).  The order of continuity at the pole
        will be 1 or 0 when this is True or False, respectively.
        Defaults to False.
    pole_values : float or (float, float), optional
        Data values at the poles ``u=0`` and ``u=pi``.  Either the whole
        parameter or each individual element can be None.  Defaults to None.
    pole_exact : bool or (bool, bool), optional
        Data value exactness at the poles ``u=0`` and ``u=pi``.  If True, the
        value is considered to be the right function value, and it will be
        fitted exactly. If False, the value will be considered to be a data
        value just like the other data values.  Defaults to False.
    pole_flat : bool or (bool, bool), optional
        For the poles at ``u=0`` and ``u=pi``, specify whether or not the
        approximation has vanishing derivatives.  Defaults to False.

    See Also
    --------
    BivariateSpline :
        a base class for bivariate splines.
    UnivariateSpline :
        a smooth univariate spline to fit a given set of data points.
    SmoothBivariateSpline :
        a smoothing bivariate spline through the given points
    LSQBivariateSpline :
        a bivariate spline using weighted least-squares fitting
    SmoothSphereBivariateSpline :
        a smoothing bivariate spline in spherical coordinates
    LSQSphereBivariateSpline :
        a bivariate spline in spherical coordinates using weighted
        least-squares fitting
    RectBivariateSpline :
        a bivariate spline over a rectangular mesh.
    bisplrep :
        a function to find a bivariate B-spline representation of a surface
    bisplev :
        a function to evaluate a bivariate B-spline and its derivatives

    Notes
    -----
    Currently, only the smoothing spline approximation (``iopt[0] = 0`` and
    ``iopt[0] = 1`` in the FITPACK routine) is supported.  The exact
    least-squares spline approximation is not implemented yet.

    When actually performing the interpolation, the requested `v` values must
    lie within the same length 2pi interval that the original `v` values were
    chosen from.

    For more information, see the FITPACK_ site about this function.

    .. _FITPACK: http://www.netlib.org/dierckx/spgrid.f

    Examples
    --------
    Suppose we have global data on a coarse grid

    >>> lats = np.linspace(10, 170, 9) * np.pi / 180.
    >>> lons = np.linspace(0, 350, 18) * np.pi / 180.
    >>> data = np.dot(np.atleast_2d(90. - np.linspace(-80., 80., 18)).T,
    ...               np.atleast_2d(180. - np.abs(np.linspace(0., 350., 9)))).T

    We want to interpolate it to a global one-degree grid

    >>> new_lats = np.linspace(1, 180, 180) * np.pi / 180
    >>> new_lons = np.linspace(1, 360, 360) * np.pi / 180
    >>> new_lats, new_lons = np.meshgrid(new_lats, new_lons)

    We need to set up the interpolator object

    >>> from scipy.interpolate import RectSphereBivariateSpline
    >>> lut = RectSphereBivariateSpline(lats, lons, data)

    Finally we interpolate the data.  The `RectSphereBivariateSpline` object
    only takes 1-D arrays as input, therefore we need to do some reshaping.

    >>> data_interp = lut.ev(new_lats.ravel(),
    ...                      new_lons.ravel()).reshape((360, 180)).T

    Looking at the original and the interpolated data, one can see that the
    interpolant reproduces the original data very well:

    >>> import matplotlib.pyplot as plt
    >>> fig = plt.figure()
    >>> ax1 = fig.add_subplot(211)
    >>> ax1.imshow(data, interpolation='nearest')
    >>> ax2 = fig.add_subplot(212)
    >>> ax2.imshow(data_interp, interpolation='nearest')
    >>> plt.show()

    Choosing the optimal value of ``s`` can be a delicate task. Recommended
    values for ``s`` depend on the accuracy of the data values.  If the user
    has an idea of the statistical errors on the data, she can also find a
    proper estimate for ``s``. By assuming that, if she specifies the
    right ``s``, the interpolator will use a spline ``f(u,v)`` which exactly
    reproduces the function underlying the data, she can evaluate
    ``sum((r(i,j)-s(u(i),v(j)))**2)`` to find a good estimate for this ``s``.
    For example, if she knows that the statistical errors on her
    ``r(i,j)``-values are not greater than 0.1, she may expect that a good
    ``s`` should have a value not larger than ``u.size * v.size * (0.1)**2``.

    If nothing is known about the statistical error in ``r(i,j)``, ``s`` must
    be determined by trial and error.  The best is then to start with a very
    large value of ``s`` (to determine the least-squares polynomial and the
    corresponding upper bound ``fp0`` for ``s``) and then to progressively
    decrease the value of ``s`` (say by a factor 10 in the beginning, i.e.
    ``s = fp0 / 10, fp0 / 100, ...``  and more carefully as the approximation
    shows more detail) to obtain closer fits.

    The interpolation results for different values of ``s`` give some insight
    into this process:

    >>> fig2 = plt.figure()
    >>> s = [3e9, 2e9, 1e9, 1e8]
    >>> for ii in range(len(s)):
    ...     lut = RectSphereBivariateSpline(lats, lons, data, s=s[ii])
    ...     data_interp = lut.ev(new_lats.ravel(),
    ...                          new_lons.ravel()).reshape((360, 180)).T
    ...     ax = fig2.add_subplot(2, 2, ii+1)
    ...     ax.imshow(data_interp, interpolation='nearest')
    ...     ax.set_title("s = %g" % s[ii])
    >>> plt.show()

    

Constructeur(s)

Signature du constructeur	Description
__init__(self, u, v, r, s=0.0, pole_continuity=False, pole_values=None, pole_exact=False, pole_flat=False)

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Méthodes héritées de la classe SphereBivariateSpline

__init_subclass__, __subclasshook__, ev

Méthodes héritées de la classe _BivariateSplineBase

get_coeffs, get_knots, get_residual

Méthodes héritées de la classe object

__delattr__, __dir__, __format__, __getattribute__, __hash__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__