warp.spatial\_adjoint
=====================

.. currentmodule:: warp._src.lang

.. function:: spatial_adjoint(r: Matrix[Float, Literal[3], Literal[3]], s: Matrix[Float, Literal[3], Literal[3]]) -> Matrix[Float, Literal[6], Literal[6]]

   .. wp-function-tags::
      :kernel: true
      :python: false
      :differentiable: true

   Construct a 6x6 spatial matrix from the two 3x3 blocks ``r`` and ``s``.
   
   For a rigid transform ``(R, p)``, setting ``r = R`` and ``s = skew(p) * R`` constructs the
   matrix that maps twist ``(w, v)`` to ``(R * w, cross(p, R * w) + R * v)``. Wrenches transform
   differently from twists; use :func:`~warp.transform_wrench` to transform them.
   
   :param r: Block placed on both diagonals.
   :param s: Block placed in the lower-left corner.
   
   :returns: The 6x6 block matrix ``[[r, 0], [s, r]]``.
   
   .. rubric:: Example
   
   .. testcode::
   
       @wp.kernel
       def build(out: wp.array[wp.spatial_matrix]):
           r = wp.mat33(1.0, 0.0, 0.0,
                        0.0, 1.0, 0.0,
                        0.0, 0.0, 1.0)
           s = wp.mat33(0.0, -3.0, 2.0,
                        3.0, 0.0, -1.0,
                        -2.0, 1.0, 0.0)
           out[0] = wp.spatial_adjoint(r, s)
   
       out = wp.empty(1, dtype=wp.spatial_matrix)
       wp.launch(build, dim=1, outputs=[out])
       print(out.numpy()[0])
   
   .. testoutput::
   
       [[ 1.  0.  0.  0.  0.  0.]
        [ 0.  1.  0.  0.  0.  0.]
        [ 0.  0.  1.  0.  0.  0.]
        [ 0. -3.  2.  1.  0.  0.]
        [ 3.  0. -1.  0.  1.  0.]
        [-2.  1.  0.  0.  0.  1.]]