pypose.cummul

class pypose.cummul(input, dim, left=True)

Returns the cumulative multiplication (*) of LieTensor along a dimension.

• Left multiplication:

\[y_i = x_i * x_{i-1} * \cdots * x_1, \]

• Right multiplication:

\[y_i = x_1 * x_2 * \cdots * x_i, \]

where \(x_i,~y_i\) are the \(i\)-th LieType item along the dim dimension of input and output, respectively.

Parameters

• input (LieTensor) – the input LieTensor

• dim (int) – the dimension to do the multiplication over

• left (bool, optional) – whether perform left multiplication in cummul. If set it to False, this function performs right multiplication. Defaul: True

Returns

The LieTensor

Return type

LieTensor

Note

• The time complexity of the function is \(\mathcal{O}(\log N)\), where \(N\) is the LieTensor size along the dim dimension.

Example

• Left multiplication with \(\text{input} \in\) SE3

>>> input = pp.randn_SE3(2)
>>> pp.cummul(input, dim=0)
SE3Type LieTensor:
tensor([[-1.9615, -0.1246,  0.3666,  0.0165,  0.2853,  0.3126,  0.9059],
        [ 0.7139,  1.3988, -0.1909, -0.1780,  0.4405, -0.6571,  0.5852]])

• Left multiplication with \(\text{input} \in\) SO3

>>> input = pp.randn_SO3(1,2)
>>> pp.cummul(input, dim=1, left=False)
SO3Type LieTensor:
tensor([[[-1.8252e-01,  1.6198e-01,  8.3683e-01,  4.9007e-01],
        [ 2.0905e-04,  5.2031e-01,  8.4301e-01, -1.3642e-01]]])