This is documentation for an old release of SciPy (version 1.6.1). Read this page Search for this page in the documentation of the latest stable release (version 1.15.1).

scipy.interpolate.LSQSphereBivariateSpline

class scipy.interpolate.LSQSphereBivariateSpline(theta, phi, r, tt, tp, w=None, eps=1e-16)

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.

New in version 0.11.0.

Parameters

theta, phi, rarray_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, tparray_like

Strictly ordered 1-D sequences of knots coordinates. Coordinates must satisfy 0 < tt[i] < pi, 0 < tp[i] < 2*pi.

warray_like, optional

Positive 1-D sequence of weights, of the same length as theta, phi and r.

epsfloat, 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.

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 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()

Methods

__call__(self, theta, phi[, dtheta, dphi, grid])	Evaluate the spline or its derivatives at given positions.
ev(self, theta, phi[, dtheta, dphi])	Evaluate the spline at points
get_coeffs(self)	Return spline coefficients.
get_knots(self)	Return a tuple (tx,ty) where tx,ty contain knots positions of the spline with respect to x-, y-variable, respectively.
get_residual(self)	Return weighted sum of squared residuals of the spline approximation: sum ((w[i]*(z[i]-s(x[i],y[i])))**2,axis=0)