def eig(A, dt=None):
"""Compute the eigenvalues and right eigenvectors of a real matrix.
Parameters
----------
A: ti.Matrix(n, n)
2D 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.Matrix(n, 2)
The eigenvalues in complex form. Each row stores one eigenvalue. The first number
of the eigenvalue represents the real part and the second number represents the
imaginary part.
eigenvectors: ti.Matrix(n*2, n)
The eigenvectors in complex form. Each column stores one eigenvector. Each eigenvector
consists of n entries, each of which is represented by two numbers for its real part
and imaginary part.
"""
if dt is None:
dt = impl.get_runtime().default_fp
from taichi.lang import linalg
if A.n == 2:
return linalg.eig2x2(A, dt)
raise Exception("Eigen solver only supports 2D matrices.")
def eig(A, dt=None):
"""Compute the eigenvalues and right eigenvectors of a real matrix.
Mathematical concept refers to https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix.
2D implementation refers to :func:`taichi.lang.linalg.eig2x2`.
Args:
A (ti.Matrix(n, n)): 2D Matrix for which the eigenvalues and right eigenvectors will be computed.
dt (DataType): The datatype for the eigenvalues and right eigenvectors.
Returns:
eigenvalues (ti.Matrix(n, 2)): The eigenvalues in complex form. Each row stores one eigenvalue. The first number of the eigenvalue represents the real part and the second number represents the imaginary part.
eigenvectors (ti.Matrix(n*2, n)): The eigenvectors in complex form. Each column stores one eigenvector. Each eigenvector consists of n entries, each of which is represented by two numbers for its real part and imaginary part.
"""
if dt is None:
dt = impl.get_runtime().default_fp
from taichi.lang import linalg
if A.n == 2:
return linalg.eig2x2(A, dt)
raise Exception("Eigen solver only supports 2D matrices.")