warp.inverse
============

.. currentmodule:: warp._src.lang

.. function:: inverse(a: Matrix[Float, Literal[2], Literal[2]]) -> Matrix[Float, Any, Any]

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

   Return the inverse of a matrix.
   
   Nearly singular inputs can amplify rounding errors and produce large
   gradients. Use a well-conditioned matrix for differentiation, and check
   that the product of the input and returned matrix is close to the identity
   when numerical accuracy is required.
   
   :param a: Matrix to invert. Must be nonsingular.
   
   :returns: The inverse matrix, whose product with the input is the identity in
             exact arithmetic.
   
   .. rubric:: Example
   
   Invert a matrix and inspect the result:
   
   .. testcode::
   
       matrix = wp.mat22(2.0, 1.0, 1.0, 2.0)
       inverse = wp.inverse(matrix)
       print(np.round(np.asarray(inverse).reshape(2, 2), 3))
   
   .. testoutput::
   
       [[ 0.667 -0.333]
        [-0.333  0.667]]
   

.. function:: inverse(a: Matrix[Float, Literal[3], Literal[3]]) -> Matrix[Float, Any, Any]
   :noindex:

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

   Return the inverse of a 3x3 matrix.
   
   See the 2x2 overload for numerical and autodiff guidance.
   
   :param a: Matrix to invert. Must be nonsingular.
   
   :returns: The inverse matrix, whose product with the input is the identity in
             exact arithmetic.
   

.. function:: inverse(a: Matrix[Float, Literal[4], Literal[4]]) -> Matrix[Float, Any, Any]
   :noindex:

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

   Return the inverse of a 4x4 matrix.
   
   See the 2x2 overload for numerical and autodiff guidance.
   
   :param a: Matrix to invert. Must be nonsingular.
   
   :returns: The inverse matrix, whose product with the input is the identity in
             exact arithmetic.