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# scipy.interpolate.SmoothSphereBivariateSpline

class scipy.interpolate.SmoothSphereBivariateSpline(theta, phi, r, w=None, s=0.0, eps=1e-16)

  Smooth bivariate spline approximation in spherical coordinates.

  New in version 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.

  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()

  Methods

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