Classe « SmoothSphereBivariateSpline »

Informations générales

Héritage

builtins.object
    _BivariateSplineBase
        SphereBivariateSpline
            SmoothSphereBivariateSpline

Définition

class SmoothSphereBivariateSpline(SphereBivariateSpline):

help(SmoothSphereBivariateSpline)

Smooth bivariate spline approximation in spherical coordinates.

.. versionadded:: 0.11.0

Parameters
----------
theta, phi, r : array_like
    1-D sequences of data points (order is not important). Coordinates
    must be given in radians. Theta must lie within the interval
    ``[0, pi]``, and phi must lie within the interval ``[0, 2pi]``.
w : array_like, optional
    Positive 1-D sequence of weights.
s : float, optional
    Positive smoothing factor defined for estimation condition:
    ``sum((w(i)*(r(i) - s(theta(i), phi(i))))**2, axis=0) <= s``
    Default ``s=len(w)`` which should be a good value if ``1/w[i]`` is an
    estimate of the standard deviation of ``r[i]``.
eps : float, optional
    A threshold for determining the effective rank of an over-determined
    linear system of equations. `eps` should have a value within the open
    interval ``(0, 1)``, the default is 1e-16.

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
RectSphereBivariateSpline :
    a bivariate spline over a rectangular mesh on a sphere
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
-----
For more information, see the FITPACK_ site about this function.

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

Examples
--------
Suppose we have global data on a coarse grid (the input data does not
have to be on a grid):

>>> import numpy as np
>>> theta = np.linspace(0., np.pi, 7)
>>> phi = np.linspace(0., 2*np.pi, 9)
>>> data = np.empty((theta.shape[0], phi.shape[0]))
>>> data[:,0], data[0,:], data[-1,:] = 0., 0., 0.
>>> data[1:-1,1], data[1:-1,-1] = 1., 1.
>>> data[1,1:-1], data[-2,1:-1] = 1., 1.
>>> data[2:-2,2], data[2:-2,-2] = 2., 2.
>>> data[2,2:-2], data[-3,2:-2] = 2., 2.
>>> data[3,3:-2] = 3.
>>> data = np.roll(data, 4, 1)

We need to set up the interpolator object

>>> lats, lons = np.meshgrid(theta, phi)
>>> from scipy.interpolate import SmoothSphereBivariateSpline
>>> lut = SmoothSphereBivariateSpline(lats.ravel(), lons.ravel(),
...                                   data.T.ravel(), s=3.5)

As a first test, we'll see what the algorithm returns when run on the
input coordinates

>>> data_orig = lut(theta, phi)

Finally we interpolate the data to a finer grid

>>> fine_lats = np.linspace(0., np.pi, 70)
>>> fine_lons = np.linspace(0., 2 * np.pi, 90)

>>> data_smth = lut(fine_lats, fine_lons)

>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(131)
>>> ax1.imshow(data, interpolation='nearest')
>>> ax2 = fig.add_subplot(132)
>>> ax2.imshow(data_orig, interpolation='nearest')
>>> ax3 = fig.add_subplot(133)
>>> ax3.imshow(data_smth, interpolation='nearest')
>>> plt.show()