def sym_eig(A, dt=None):
"""Compute the eigenvalues and right eigenvectors of a real symmetric matrix.
Mathematical concept refers to https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix.
2D implementation refers to :func:`taichi.lang.linalg.sym_eig2x2`.
Args:
A (ti.Matrix(n, n)): Symmetric Matrix for which the eigenvalues and right eigenvectors will be computed.
dt (DataType): The datatype for the eigenvalues and right eigenvectors.
Returns:
eigenvalues (ti.Vector(n)): The eigenvalues. Each entry store one eigen value.
eigenvectors (ti.Matrix(n, n)): The eigenvectors. Each column stores one eigenvector.
"""
assert all(A == A.transpose()), "A needs to be symmetric"
if dt is None:
dt = impl.get_runtime().default_fp
from taichi.lang import linalg
if A.n == 2:
return linalg.sym_eig2x2(A, dt)
raise Exception("Symmetric eigen solver only supports 2D matrices.")
def sym_eig(A, dt=None):
"""Compute the eigenvalues and right eigenvectors of a real symmetric matrix.
Parameters
----------
A: ti.Matrix(n, n)
Symmetric Matrix for which the eigenvalues and right eigenvectors will be computed.
dt: Optional[DataType]
The datatype for the eigenvalues and right eigenvectors
Returns
-------
eigenvalues: ti.Vector(n)
The eigenvalues. Each entry store one eigen value.
eigenvectors: ti.Matrix(n, n)
The eigenvectors. Each column stores one eigenvector.
"""
assert all(A == A.transpose()), "A needs to be symmetric"
if dt is None:
dt = impl.get_runtime().default_fp
from taichi.lang import linalg
if A.n == 2:
return linalg.sym_eig2x2(A, dt)
raise Exception("Symmetric eigen solver only supports 2D matrices.")