gftool.matrix.Decomposition¶
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class
gftool.matrix.Decomposition(rv, xi, rv_inv)[source]¶ Decomposition of a Matrix into eigenvalues and eigenvectors.
This class holds the eigenvalues and eigenvectors of the decomposition of a matrix and offers methods to reconstruct it. The intended use case is to use the
Decompositionfor the inversion of the Green’s function to calculate it from the resolvent.The order of the attributes is always rv, xi, rv_inv, as this gives the reconstruct of the matrix: mat = (rv * xi) @ rv_inv
Attributes: - rv : (…, N, N) complex np.ndarray
The matrix of right eigenvalues.
- xi : (…, N) complex np.ndarray
The vector of eigenvalues.
- rv_inv : (…, N, N) complex np.ndarray
The inverse of
rv.
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__init__(rv, xi, rv_inv)[source] Assign the attributes obtained from a matrix digitalization.
Parameters: - rv : (…, N, N) complex np.ndarray
The matrix of right eigenvectors.
- xi : (…, N) complex np.ndarray
The vector of eigenvalues
- rv_inv : (…, N, N) complex np.ndarray
The inverse of
rv.
Methods
__init__(rv, xi, rv_inv)Assign the attributes obtained from a matrix digitalization. count(value)from_gf(gf)Decompose the inverse Green’s function matrix. from_hamiltonian(hamilton)Decompose the Hamiltonian matrix. index(value, [start, [stop]])Raises ValueError if the value is not present. reconstruct([xi, kind])Get matrix back from Decomposition.Attributes
rvrv_invxi