Wrap fitcircle by willschlitzer · Pull Request #1550 · GenericMappingTools/pygmt

willschlitzer · 2021-09-29T07:07:54Z

This pull request wraps the module fitcircle.

Preview at https://pygmt-dev--1550.org.readthedocs.build/en/1550/api/generated/pygmt.fitcircle.html

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Run make format and make check to make sure the code follows the style guide.
Add tests for new features or tests that would have caught the bug that you're fixing.
Add new public functions/methods/classes to doc/api/index.rst.
Write detailed docstrings for all functions/methods.
If adding new functionality, add an example to docstrings or tutorials.

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seisman · 2026-08-04T12:32:52Z

+    S="small_circle",
+)
+def fitcircle(
+    data: PathLike | TableLike,


Should support parameters x/y, too.

seisman · 2026-08-04T12:40:48Z

+        $table_classes.
+    $output_type
+    $outfile
+    norm : int or bool


1, 2, 3 are not readable arguments. GMT recommends absolutes/squares/both instead.

https://github.com/GenericMappingTools/gmt/blob/d52a1e5825b73c3ad6948efce1ac8eeff01c2c93/src/longopt/fitcircle_inc.h#L32-33

As for the parameter, GMT supports norm and solution, while GMT.jl uses norm (https://www.generic-mapping-tools.org/GMTjl_doc/documentation/modules/fitcircle.html).

seisman · 2026-08-06T09:38:52Z

@willschlitzer Could you please an issue for tracking this module, using the template at https://github.com/GenericMappingTools/pygmt/blob/main/.github/ISSUE_TEMPLATE/3-module_request.md

willschlitzer · 2026-08-12T11:10:38Z

@willschlitzer Could you please an issue for tracking this module, using the template at https://github.com/GenericMappingTools/pygmt/blob/main/.github/ISSUE_TEMPLATE/3-module_request.md

@seisman Done in #4821

seisman · 2026-08-12T11:43:43Z

fitcircle has three important options:

-L: select the averaging method
-S: output small circle pole or not
-M: controls the output of columns

Their combinations can lead to quite different output formats, as shown below:

$ gmt fitcircle @sat_03.txt -L1
330.249933144   -18.4048179232  Points read: 703 Average Position (Flat Earth)
330.16910976    -18.4206421065  L1 Average Position (Fisher's Method)
52.7435567383   21.2080711967   L1 N Hemisphere Great Circle Pole (Cross-Averaged)
232.743556738   -21.2080711967  L1 S Hemisphere Great Circle Pole (Cross-Averaged)
$ gmt fitcircle @sat_03.txt -L2
330.249933144   -18.4048179232  Points read: 703 Average Position (Flat Earth)
330.169184777   -18.4206532702  L2 Average Position (Eigenval Method)
52.7451972868   21.2040074195   L2 N Hemisphere Great Circle Pole (Eigenval Method)
232.745197287   -21.2040074195  L2 S Hemisphere Great Circle Pole (Eigenval Method)
$ gmt fitcircle @sat_03.txt -L3
330.249933144   -18.4048179232  Points read: 703 Average Position (Flat Earth)
330.16910976    -18.4206421065  L1 Average Position (Fisher's Method)
52.7435567383   21.2080711967   L1 N Hemisphere Great Circle Pole (Cross-Averaged)
232.743556738   -21.2080711967  L1 S Hemisphere Great Circle Pole (Cross-Averaged)
330.169184777   -18.4206532702  L2 Average Position (Eigenval Method)
52.7451972868   21.2040074195   L2 N Hemisphere Great Circle Pole (Eigenval Method)
232.745197287   -21.2040074195  L2 S Hemisphere Great Circle Pole (Eigenval Method)
$ gmt fitcircle @sat_03.txt -L3 -S
330.249933144   -18.4048179232  Points read: 703 Average Position (Flat Earth)
330.16910976    -18.4206421065  L1 Average Position (Fisher's Method)
52.7435567383   21.2080711967   L1 N Hemisphere Great Circle Pole (Cross-Averaged)
232.743556738   -21.2080711967  L1 S Hemisphere Great Circle Pole (Cross-Averaged)
235.188595579   -22.0070525722  L1 Small Circle Pole. Distance from Pole to L1 Small Circle (degrees): 87.6019637313
330.169184777   -18.4206532702  L2 Average Position (Eigenval Method)
52.7451972868   21.2040074195   L2 N Hemisphere Great Circle Pole (Eigenval Method)
232.745197287   -21.2040074195  L2 S Hemisphere Great Circle Pole (Eigenval Method)
235.184676903   -22.0012240239  L2 Small Circle Pole.  Distance from Pole to L2 Small Circle (degrees): 87.6073161087
$ gmt fitcircle @sat_03.txt -L3 -F
330.249933144   -18.4048179232  330.16910976    -18.4206421065  52.7435567383   21.2080711967   232.743556738   -21.2080711967     330.169184777   -18.4206532702  52.7451972868   21.2040074195   232.745197287   -21.2040074195
$ gmt fitcircle @sat_03.txt -L3 -Ffmnsc -S
330.249933144   -18.4048179232  330.16910976    -18.4206421065  52.7435567383   21.2080711967   232.743556738   -21.2080711967     235.188595579   -22.0070525722  87.6019637313   330.169184777   -18.4206532702  52.7451972868   21.2040074195      232.745197287   -21.2040074195  235.184676903   -22.0012240239  87.6073161087
$ gmt fitcircle @sat_03.txt -L3 -Ff
330.249933144   -18.4048179232

The current implementation always returns a pandas.DataFrame object, which is not Pythonic, and also makes it difficult to implement the -F option later.

As mentioned in #1550 (comment), I propose

return a dictionary of tuples instead. The dictionary will look like the following for -L1/-L2:

solution = fitcircle(data="@sat_03.txt", norm=1)
>>> print(solution)
{
    "flat_mean": (330.249933144, -18.4048179232),
    "mean": (330.16910976, -18.4206421065),
    "north_pole": (52.7435567383, 21.2080711967),
    "south_pole": (232.743556738, -21.2080711967),
}

Anyone who wants both (i.e., -L3) should call pygmt.fitcircle twice.
When -S is used, the output can be:

{
    "flat_mean": (330.249933144, -18.4048179232),
    "mean": (330.16910976, -18.4206421065),
    "north_pole": (52.7435567383, 21.2080711967),
    "south_pole": (232.743556738, -21.2080711967),
    "small_circle_pole": (235.188595579, -22.0070525722),
    "small_circle_distance": 87.6019637313,
}

No need to implement the -F option, as the information is already in the dict. Anyone who wants the multi-column output can convert the dictionary manually.

Internally, we can just call fitcircle with -F and then extract the information to build the output dictionary.

Co-authored-by: Dongdong Tian <seisman.info@gmail.com>

seisman · 2026-08-21T10:13:03Z

        "@RidgeTest.prj",
        "@RidgeTest.shp",
        "@RidgeTest.shx",
+        "@sat_03.txt",


Please move this file to Line 130.

seisman · 2026-08-21T10:27:59Z

+    Setting ``norm`` to ``"absolutes"`` 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.
+
+    Setting ``norm`` to ``"squares"`` approximates the minimization of the
+    sum of squares 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.


I'm re-reading the GMT documentation and feel that norm=1/norm=2 is more understandable than norm="absolutes"/norm="squares", assuming that most readers are already familiar with L1 and L2 norms. What do you think?

Truth be told, I don't know how fitcircle would be used practically and never used the GMT module (or remember why I chose to wrap it 5 years ago). I'll defer to your judgement; my thought is absolutes and squares is more Pythonic, but if you think 1/2 is more understandable to users, that's fine with me.

seisman · 2026-08-21T10:28:30Z

+          tuple)
+    """
+    aliasdict = AliasSystem(
+        L=Alias(norm, name="norm", mapping={"absolutes": 1, "squares": 2}),


See comment https://github.com/GenericMappingTools/pygmt/pull/1550/changes#r3829465312

Suggested change

L=Alias(norm, name="norm", mapping={"absolutes": 1, "squares": 2}),

L=Alias(norm, name="norm"),

seisman · 2026-08-21T10:28:48Z

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


See comment https://github.com/GenericMappingTools/pygmt/pull/1550/changes#r3829465312. Need to check if norm is 1 or 2.

willschlitzer added 10 commits September 26, 2021 11:30

add fitcircle.py

7c1ae68

add fitcircle imports

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add test_fitcircle

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add if statements and df column names

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update formatting in fixture_data

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formatting

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add functions

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add test info to test_fitcircle_no_outfile

9bf8331

add if statement for normalize

0360abc

add tests

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willschlitzer added the feature Brand new feature label Sep 29, 2021

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Merge branch 'main' into wrap/fitcircle

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Make suggested changed for alias system and parameters

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willschlitzer mentioned this pull request Aug 12, 2026

pygmt.fitcircle: Find mean position and great [or small] circle fit to points on sphere #4821

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willschlitzer added 3 commits August 13, 2026 22:41

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	L=Alias(norm, name="norm", mapping={"absolutes": 1, "squares": 2}),
	L=Alias(norm, name="norm"),

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