warp.inverse_approx#

warp.inverse_approx( a: Matrix[Float, Literal[2], Literal[2]], ) → Matrix[Float, Any, Any]#

Kernel: true
Python: false
Differentiable: true

Return an approximate inverse of a matrix.

On GPU, this function may be faster than warp.inverse(), but its result and gradients may be less accurate. For double-precision matrices, even well-conditioned inputs can yield roughly single-precision accuracy. Use warp.inverse() when double-precision accuracy matters. On CPU, both functions currently use the same inversion method.

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 before relying on the result.

Parameters:: a – Matrix to invert. Must be nonsingular.
Returns:: A matrix whose product with the input approximates the identity.

Example

Invert a matrix in a kernel and inspect the result:

@wp.kernel
def approximate_matrix_inverses(
    matrices: wp.array[wp.mat22],
    inverses: wp.array[wp.mat22],
):
    i = wp.tid()
    inverses[i] = wp.inverse_approx(matrices[i])

matrices = wp.array([wp.mat22(2.0, 1.0, 1.0, 2.0)], dtype=wp.mat22)
inverses = wp.empty_like(matrices)
wp.launch(
    approximate_matrix_inverses,
    dim=1,
    inputs=[matrices],
    outputs=[inverses],
)
inverse = inverses.numpy()[0]
print(np.round(inverse, 3))

[[ 0.667 -0.333]
 [-0.333  0.667]]

warp.inverse_approx( a: Matrix[Float, Literal[3], Literal[3]], ) → Matrix[Float, Any, Any]

Kernel: true
Python: false
Differentiable: true

Return an approximate inverse of a 3x3 matrix.

See the 2x2 overload for device behavior, numerical accuracy, and autodiff guidance.

Parameters:: a – Matrix to invert. Must be nonsingular.
Returns:: A matrix whose product with the input approximates the identity.

warp.inverse_approx( a: Matrix[Float, Literal[4], Literal[4]], ) → Matrix[Float, Any, Any]

Kernel: true
Python: false
Differentiable: true

Return an approximate inverse of a 4x4 matrix.

See the 2x2 overload for device behavior, numerical accuracy, and autodiff guidance.

Parameters:: a – Matrix to invert. Must be nonsingular.
Returns:: A matrix whose product with the input approximates the identity.