code: def test_lambert_equal_area_projection_cart():
      xyz = np.array(
          [
              [1, 0, 0],
              [0, 1, 0],
              [0, 0, 1],
              [-1, 0, 0],
              [0, -1, 0],
              [0, 0, -1],
          ]
      )
      # points sit on +/-1 on all 3 axes
  
      r, theta, phi = cart2sphere(*xyz.T)
  
      leap = lambert_equal_area_projection_polar(theta, phi)
      r2 = np.sqrt(2)
      assert_array_almost_equal(
          np.sqrt(np.sum(leap**2, axis=1)),
          np.array([r2, r2, 0, r2, r2, 2]),
      )
  
imports: import numpy
  import random
  from dipy.core.geometry import sphere2cart, cart2sphere, nearest_pos_semi_def, sphere_distance, cart_distance, vector_cosine, lambert_equal_area_projection_polar, circumradius, vec2vec_rotmat, vector_norm, compose_transformations, compose_matrix, decompose_matrix, perpendicular_directions, dist_to_corner, is_hemispherical
  from numpy.testing import assert_array_equal, assert_array_almost_equal, assert_equal, assert_raises, assert_almost_equal
  from dipy.testing.spherepoints import sphere_points
  from dipy.testing.decorators import set_random_number_generator
  from dipy.core.sphere_stats import random_uniform_on_sphere
  from itertools import permutations
label_desc: Use image node_id 9 for calling a global function with example usage: test_lambert_equal_area_projection_cart() without return types