Bug: inner_product mismatch in SpecialEuclidean

[monsij]

Describe the bug

Inner products of two vectors belonging to the tangent space of SE(2) return different values when computation is performed using point_type="vector" and point_type="matrix".

The values are significantly different, ie floating point operations may not be causing it.

Steps/Code to Reproduce

Running the script below returns False:

import numpy as np
from geomstats.geometry.special_euclidean import SpecialEuclidean

GROUP_MAT = SpecialEuclidean(n=2, point_type="matrix") 
GROUP_VECT = SpecialEuclidean(n=2, point_type="vector")

# vector form
point_vec = GROUP_VECT.random_point()
v1_vect = np.random.rand(3) # any random length 3 vector belongs to SE(2)
v2_vect = np.random.rand(3)
ip_vect = GROUP_VECT.metric.inner_product(tangent_vec_a=v1_vect, tangent_vec_b=v2_vect, base_point=point_vec)



# matrix form
point_mat = GROUP_VECT.matrix_from_vector(point_vec)
# v1_mat, v2_mat should be in the tangent space
v1_mat = GROUP_VECT.matrix_from_vector(v1_vect) 
v2_mat = GROUP_VECT.matrix_from_vector(v2_vect)
ip_mat = GROUP_MAT.metric.inner_product(tangent_vec_a=v1_mat, tangent_vec_b=v2_mat, base_point=point_mat)

print(np.allclose(ip_vect, ip_mat))

Expected Behaviour

Inner products should be about the same:
np.allclose(ip_vect, ip_mat)=True

Actual Behaviour

For example

Vector form:
<v1, v2> = 0.5463887341252732

Matrix form:
<v1, v2> = 3.2790017553516457

Your environment

Geomstats: v2.5.0
Model Name:	MacBook Pro
Processor Name:	ARM64