Classe « LSQSphereBivariateSpline »

Informations générales

Héritage

builtins.object
    _BivariateSplineBase
        SphereBivariateSpline
            LSQSphereBivariateSpline

Définition

class LSQSphereBivariateSpline(SphereBivariateSpline):

help(LSQSphereBivariateSpline)

Weighted least-squares bivariate spline approximation in spherical
coordinates.

Determines a smoothing bicubic spline according to a given
set of knots in the `theta` and `phi` directions.

.. 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]``.
tt, tp : array_like
    Strictly ordered 1-D sequences of knots coordinates.
    Coordinates must satisfy ``0 < tt[i] < pi``, ``0 < tp[i] < 2*pi``.
w : array_like, optional
    Positive 1-D sequence of weights, of the same length as `theta`, `phi`
    and `r`.
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
SmoothSphereBivariateSpline :
    a smoothing bivariate spline in spherical coordinates
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):

>>> from scipy.interpolate import LSQSphereBivariateSpline
>>> import numpy as np
>>> import matplotlib.pyplot as plt

>>> theta = np.linspace(0, np.pi, num=7)
>>> phi = np.linspace(0, 2*np.pi, num=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. Here, we must also specify the
coordinates of the knots to use.

>>> lats, lons = np.meshgrid(theta, phi)
>>> knotst, knotsp = theta.copy(), phi.copy()
>>> knotst[0] += .0001
>>> knotst[-1] -= .0001
>>> knotsp[0] += .0001
>>> knotsp[-1] -= .0001
>>> lut = LSQSphereBivariateSpline(lats.ravel(), lons.ravel(),
...                                data.T.ravel(), knotst, knotsp)

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_lsq = lut(fine_lats, fine_lons)

>>> 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_lsq, interpolation='nearest')
>>> plt.show()