warp.eig3#

warp.eig3( A: Matrix[Float, Literal[3], Literal[3]], ) → tuple[Matrix[Float, Literal[3], Literal[3]], Vector[Float, Literal[3]]]#

Kernel: true
Python: true
Differentiable: true

Compute the eigendecomposition of a symmetric 3x3 matrix.

Do not rely on a particular ordering of the eigenvalues, signs of the eigenvectors, or a specific eigenvector basis when eigenvalues repeat.

When eigenvalues are close or repeated, small changes in A can change Q substantially. Gradients through Q may therefore be unreliable.

The current implementation uses a fixed number of Jacobi iterations. Check reconstruction and orthogonality when accuracy is critical.

Parameters:: A – Symmetric matrix to decompose.
Returns:: A tuple (Q, d) such that A = Q * wp.diag(d) * wp.transpose(Q) up to numerical error. The columns of Q form a right-handed orthonormal eigenvector basis, paired with the corresponding eigenvalues in d.

Example

Decompose a symmetric matrix and reconstruct it from its eigenpairs:

@wp.kernel
def decompose_symmetric_matrices(
    matrices: wp.array[wp.mat33],
    eigenvectors: wp.array[wp.mat33],
    eigenvalues: wp.array[wp.vec3],
):
    i = wp.tid()
    Q, d = wp.eig3(matrices[i])
    eigenvectors[i] = Q
    eigenvalues[i] = d

matrices = wp.array(
    [wp.mat33(4.0, 1.0, 2.0, 1.0, 3.0, 1.0, 2.0, 1.0, 5.0)],
    dtype=wp.mat33,
)
eigenvectors = wp.empty(1, dtype=wp.mat33)
eigenvalues = wp.empty(1, dtype=wp.vec3)

wp.launch(
    decompose_symmetric_matrices,
    dim=1,
    inputs=[matrices],
    outputs=[eigenvectors, eigenvalues],
)

Q = eigenvectors.numpy()[0]
d = eigenvalues.numpy()[0]
print(np.round(Q @ np.diag(d) @ Q.T, 3))

[[4. 1. 2.]
 [1. 3. 1.]
 [2. 1. 5.]]

warp.eig3( A: Matrix[Float, Literal[3], Literal[3]], Q: Matrix[Float, Literal[3], Literal[3]], d: Vector[Float, Literal[3]], ) → None

Kernel: true
Python: false
Differentiable: true

Compute the eigendecomposition of a symmetric 3x3 matrix and store the eigenpairs in caller-provided output arguments.

See the return-value overload for the factorization convention, numerical behavior, and autodiff guidance.

Parameters:

A – Symmetric matrix to decompose.
Q – Output matrix whose columns are eigenvectors.
d – Output vector of the corresponding eigenvalues.

Example

Store the eigenpairs of A in Q and d:

@wp.kernel
def compute_eig3(A: wp.mat33):
    Q = wp.mat33()
    d = wp.vec3()

    wp.eig3(A, Q, d)