Test vector transport and its inverse with dIntegrateTransport

[fabinsch]

Hi, I propose adding another test for the dIntegrateTransport function to check its "inverse" by using the reverse path. I use this function for vector transport along different manifolds.

[ManifoldFR]

Great contribution @fabinsch ! Can you also test for matrices ? It should still work the same

[fabinsch]

Sure, I will extend it for matrices. One point for me was to check if it actually works for a single vector (np.array), as the function doc explicitly speaks about "transporting a matrix". But as the doc string states correctly, only the row size matters and this was tested here.

In [2]: pin.dIntegrateTransport?
Docstring:
dIntegrateTransport( (Model)model, (numpy.ndarray)q, (numpy.ndarray)v, (numpy.ndarray)Jin, (ArgumentPosition)argument_position) -> numpy.ndarray :
    Takes a matrix expressed at q (+) v and uses parallel transport to express it in the tangent space at q.    This operation does the product of the matrix by the Jacobian of the integration operation, but more efficiently.Parameters:
        model: model of the kinematic tree
        q: the joint configuration vector (size model.nq)
        v: the joint velocity vector (size model.nv)
        Jin: the input matrix (row size model.nv)

[ManifoldFR]

perfect!

[jcarpent]

Does this test already exist in C++?

[fabinsch]

Does this test already exist in C++?

we are currently testing this in our cpp unittests for dIntegrateTransport which is not exactly the same as my test I think.

[jcarpent]

Could you add it in C++ instead of Python then?

[stephane-caron]

(Minor comment.)

[stephane-caron]

Shouldn't this be dIntegrateTransport(qb, v_r, tvec_at_qa, ...)?

Since we check that qa is equal to qa_r below, this line amounts to integrating $v_r$ from $qa_r$, where we will end... Somewhere else than $q_a$ or $q_b$ 😅

Meanwhile this line would fully make sense to me if we start from $q_b$: then $q_b \oplus v_r$ would land on $q_{ar} = q_a$, where we take tvec_at_qa, and transport it back to $q_b$, which is why we have the equality between tvec_at_qb and tvec_at_qa_r below. (But then, tvec_at_qa_r lies in the tangent space at $q_b$, not $q_{ar}$! 😛)

@fabinsch I understand the test passed so I must have missed something. If you can double check at some point that would be 👌

[stephane-caron]

Meanwhile I fully agree with the Python variant.