Lambert projection

[friedkitteh]

Description of the change

Continuation of the Gnomonic and Spherical projections already implemented.
Allows for the transformation of a vector from Cartesian coordiantes to the Lambert projection.
Also allows for transformation both ways between Gnomonic and Lambert projections.

Progress of the PR

• Docstrings for all functions
• Unit tests with pytest for all lines
• Clean style in as per black

Minimal example of the bug fix or new feature

>>> from kikuchipy.projections.lambert_projection import LambertProjection
>>># From Cartesian to Lambert
>>>my_cartesian_vector = np.array((1,1,1))
>>>my_lambert_vector = LambertProjection.project(my_cartesian_vector)
>>>
>>># From Lambert to Cartesian
>>>my_lambert_vector = np.array((1,1))
>>>my_cartesian_vector = LambertProjection.iproject(my_lambert_vector)
>>>
>>># From Lambert to Gnomonic
>>>my_lambert_vector = np.array((1,1))
>>>my_gnomonic_vector = LambertProjection.lambert_to_gnomonic(my_lambert_vector)
>>>
>>># From Gnomonic to Lambert
>>>my_gnomonic_vector = np.array((1,1))
>>>my_lambert_vector = LambertProjection.gnomonic_to_lambert(my_gnomonic_vector)
>>>

For reviewers

• Check that the PR title is short, concise, and will make sense 1 year
  later.
• Check that new functions are imported in corresponding __init__.py.
• Check that new features, API changes, and deprecations are mentioned in
  the unreleased section in doc/changelog.rst.

[hakonanes]

This is a great addition to the projection capabilities, thanks for this @friedkitteh!

Good catch with the ".py" endings in __init__.py, and the need for GnomonicProjection.project() to be a classmethod.

Let me know when you need feedback.

[friedkitteh]

Ok, finally! I think I am pretty happy with how it turned out now - it is (imo) a lot more compact, neat and clear and should be ready for review! 👍

[friedkitteh]

I can also add that it passed all 8 tests in 0.15s, I did not want to wake Travis for now..

[friedkitteh]

Numpy.where()
Vectors: 990
26 function calls in 0.002 seconds

Ordered by: standard name

ncalls tottime percall cumtime percall filename:lineno(function)
3 0.000 0.000 0.000 0.000 <array_function internals>:2(where)
1 0.000 0.000 0.002 0.002 :1()
3 0.000 0.000 0.000 0.000 multiarray.py:311(where)
4 0.000 0.000 0.000 0.000 temp_test_file_ignore.py:19(_eq_c)
1 0.000 0.000 0.002 0.002 temp_test_file_ignore.py:6(mA)
6 0.000 0.000 0.000 0.000 {built-in method builtins.abs}
1 0.000 0.000 0.002 0.002 {built-in method builtins.exec}
1 0.000 0.000 0.000 0.000 {built-in method builtins.len}
1 0.000 0.000 0.000 0.000 {built-in method builtins.print}
1 0.001 0.001 0.001 0.001 {built-in method numpy.array}
3 0.000 0.000 0.000 0.000 {built-in method numpy.core._multiarray_umath.implement_array_function}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}

For-loop
Vectors: 990
4961 function calls in 0.032 seconds

Ordered by: standard name

ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.032 0.032 :1()
1980 0.012 0.000 0.012 0.000 temp_test_file_ignore.py:19(_eq_c)
1 0.002 0.002 0.032 0.032 temp_test_file_ignore.py:24(mB)
990 0.015 0.000 0.028 0.000 temp_test_file_ignore.py:51(_setCartesian)
1980 0.000 0.000 0.000 0.000 {built-in method builtins.abs}
1 0.000 0.000 0.032 0.032 {built-in method builtins.exec}
2 0.000 0.000 0.000 0.000 {built-in method builtins.len}
1 0.000 0.000 0.000 0.000 {built-in method builtins.print}
1 0.002 0.002 0.002 0.002 {built-in method numpy.array}
3 0.000 0.000 0.000 0.000 {built-in method numpy.zeros}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}

##############################################################################################
An increase from 990 vectors to 2970 vectors:
##############################################################################################

Numpy.where()
Vectors: 2970
26 function calls in 0.043 seconds

Ordered by: standard name

ncalls tottime percall cumtime percall filename:lineno(function)
3 0.000 0.000 0.000 0.000 <array_function internals>:2(where)
1 0.000 0.000 0.043 0.043 :1()
3 0.000 0.000 0.000 0.000 multiarray.py:311(where)
4 0.000 0.000 0.000 0.000 temp_test_file_ignore.py:19(_eq_c)
1 0.001 0.001 0.043 0.043 temp_test_file_ignore.py:6(mA)
6 0.000 0.000 0.000 0.000 {built-in method builtins.abs}
1 0.000 0.000 0.043 0.043 {built-in method builtins.exec}
1 0.000 0.000 0.000 0.000 {built-in method builtins.len}
1 0.000 0.000 0.000 0.000 {built-in method builtins.print}
1 0.042 0.042 0.042 0.042 {built-in method numpy.array}
3 0.000 0.000 0.000 0.000 {built-in method numpy.core._multiarray_umath.implement_array_function}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}

For-loop
Vectors: 2970
14861 function calls in 0.586 seconds

Ordered by: standard name

ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.586 0.586 :1()
5940 0.190 0.000 0.190 0.000 temp_test_file_ignore.py:19(_eq_c)
1 0.009 0.009 0.586 0.586 temp_test_file_ignore.py:24(mB)
2970 0.380 0.000 0.571 0.000 temp_test_file_ignore.py:51(_setCartesian)
5940 0.002 0.000 0.002 0.000 {built-in method builtins.abs}
1 0.000 0.000 0.586 0.586 {built-in method builtins.exec}
2 0.000 0.000 0.000 0.000 {built-in method builtins.len}
1 0.000 0.000 0.000 0.000 {built-in method builtins.print}
1 0.005 0.005 0.005 0.005 {built-in method numpy.array}
3 0.000 0.000 0.000 0.000 {built-in method numpy.zeros}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}

[hakonanes]

Great that you timed it! Is this ready for review? I think you should be allowed to request a review from me under the "Reviewers" part of the sidebar?

[hakonanes]

Nice implementation of the Lambert projection from Callahan and De Graef (2013)! This will be used a lot. Also thankful for your fixes of other typos in the other projections.

I have three suggestions for improvements: adding a reference to the above mentioned paper, a change which might save some microseconds, and a correction of a "syntax wording". See more detailed comments below.

I have in addition some minor style comments which are unimportant and you can do with as you see fit.

After this we'll merge and I will set up a "Projections" user guide page, which you might want to add to later if you want, or I can do it if not.

[hakonanes]

@friedkitteh, I just added a commit, so you need to pull this commit before pushing I think.

I added your full name in the credits, please change if you want.

[hakonanes]

Great! Will merge after Travis passes all builds.

[hakonanes]

Congratulations on, and thanks a lot for, your first contribution, @friedkitteh! 🎊