scipy.linalg.
hessenberg#
- scipy.linalg.hessenberg(a, calc_q=False, overwrite_a=False, check_finite=True)[source]#
- Compute Hessenberg form of a matrix. - The Hessenberg decomposition is: - A = Q H Q^H - where Q is unitary/orthogonal and H has only zero elements below the first sub-diagonal. - Parameters:
- a(M, M) array_like
- Matrix to bring into Hessenberg form. 
- calc_qbool, optional
- Whether to compute the transformation matrix. Default is False. 
- overwrite_abool, optional
- Whether to overwrite a; may improve performance. Default is False. 
- check_finitebool, optional
- Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. 
 
- Returns:
- H(M, M) ndarray
- Hessenberg form of a. 
- Q(M, M) ndarray
- Unitary/orthogonal similarity transformation matrix - A = Q H Q^H. Only returned if- calc_q=True.
 
 - Examples - >>> import numpy as np >>> from scipy.linalg import hessenberg >>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]]) >>> H, Q = hessenberg(A, calc_q=True) >>> H array([[ 2. , -11.65843866, 1.42005301, 0.25349066], [ -9.94987437, 14.53535354, -5.31022304, 2.43081618], [ 0. , -1.83299243, 0.38969961, -0.51527034], [ 0. , 0. , -3.83189513, 1.07494686]]) >>> np.allclose(Q @ H @ Q.conj().T - A, np.zeros((4, 4))) True