pygmt.fitcircle

pygmt.fitcircle(data=None, x=None, y=None, norm=2, small_circle=False, verbose=False, **kwargs)[source]

Find mean position and great or small circle fit to points on sphere.

This method takes (longitude, latitude) values and reports the mean position and the pole to the great circle which best fits the input positions.

Two methods are available to find the mean and pole positions, depending on the value of the norm parameter.

  • norm=1 (L1 norm) approximates the minimization of the sum of absolute values of cosines of angular distances. This solution finds the mean position as the Fisher average of the data, and the pole position as the Fisher average of the cross-products between the mean and the data. Averaging cross-products gives weight to points in proportion to their distance from the mean, analogous to the “leverage” of distant points in linear regression in the plane.

  • norm=2 (L2 norm) approximates the minimization of the sum of squares of cosines of cosines of angular distances. It creates a 3 by 3 matrix of sums of squares of components of the data vectors. The eigenvectors of this matrix give the mean and pole locations. This method may be more subject to roundoff errors when there are thousands of data. The pole is given by the eigenvector corresponding to the smallest eigenvalue; it is the least-well represented factor in the data and is not easily estimated by either method.

When the data are closely grouped along a great circle both solutions are similar. If the data have large dispersion, the pole to the great circle will be less well determined than the mean. Compare both solutions as a qualitative check by calling pygmt.fitcircle`twice, once for each ``norm`.

Takes a matrix, (x, y) pairs, or a file name as input.

Must provide either data or x and y.

Full GMT docs at https://docs.generic-mapping-tools.org/6.7/fitcircle.html.

Aliases:

  • L = norm

  • S = small_circle

  • V = verbose

Parameters:

  • data (str | PathLike | dict | ndarray | DataFrame | Dataset | GeoDataFrame | None, default: None) – Pass in (longitude, latitude) values by providing a file name to an ASCII data table, a 2-D numpy.ndarray, a pandas.DataFrame, an xarray.Dataset made up of 1-D xarray.DataArray data variables, or a geopandas.GeoDataFrame containing the tabular data.

  • x/y (1-D arrays) – Arrays of x and y coordinates of the data points.

  • norm (Literal[1, 2], default: 2) – Specify the desired norm, either 1 (L1 norm, least absolute deviation) or 2 (L2 norm, least squares) [Default is 2].

  • small_circle (bool | float, default: False) – Attempt to fit a small circle instead of a great circle. The pole will be constrained to lie on the great circle connecting the pole of the best-fit great circle and the mean location of the data. Optionally set the desired fixed latitude of the small circle [Default will determine the optimal latitude].

  • verbose (Literal['quiet', 'error', 'warning', 'timing', 'info', 'compat', 'debug'] | bool, default: False) – Select verbosity level [Full usage].

Return type:

dict[str, tuple[float, float] | float]

Returns:

ret – A dictionary with the following keys, each mapping to a (longitude, latitude) tuple:

  • "flat_mean": the flat Earth mean position

  • "mean": the mean position (Fisher or eigenvalue method, depending on norm)

  • "north_pole": the north hemisphere great circle pole

  • "south_pole": the south hemisphere great circle pole

If small_circle is set, two more keys are added:

  • "small_circle_pole": the small circle pole

  • "small_circle_distance": the colatitude/distance in degrees from the small circle pole to the small circle (a float, not a tuple)