For more information, see the :None:None:`FITPACK_` site about this function.
<Unimplemented 'target' '.. _FITPACK: http://www.netlib.org/dierckx/sphere.f'>
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]
.
Positive 1-D sequence of weights.
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]
.
A threshold for determining the effective rank of an over-determined linear system of equations. :None:None:`eps` should have a value within the open interval (0, 1)
, the default is 1e-16.
Smooth bivariate spline approximation in spherical coordinates.
BivariateSpline
a base class for bivariate splines.
LSQBivariateSpline
a bivariate spline using weighted least-squares fitting
LSQSphereBivariateSpline
a bivariate spline in spherical coordinates using weighted least-squares fitting
RectBivariateSpline
a bivariate spline over a rectangular mesh.
RectSphereBivariateSpline
a bivariate spline over a rectangular mesh on a sphere
SmoothBivariateSpline
a smoothing bivariate spline through the given points
UnivariateSpline
a smooth univariate spline to fit a given set of data points.
bisplev
a function to evaluate a bivariate B-spline and its derivatives
bisplrep
a function to find a bivariate B-spline representation of a surface
Suppose we have global data on a coarse grid (the input data does not have to be on a grid):
>>> 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()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.interpolate._fitpack2.RectSphereBivariateSpline
scipy.interpolate._fitpack2.SmoothBivariateSpline
scipy.interpolate._fitpack2.BivariateSpline
scipy.interpolate._fitpack2.LSQSphereBivariateSpline
scipy.interpolate._fitpack2.RectBivariateSpline
scipy.interpolate._fitpack2.LSQBivariateSpline
scipy.interpolate._fitpack2.SmoothSphereBivariateSpline
scipy.interpolate._fitpack2.UnivariateSpline
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