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# 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, 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.

  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()

  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.