eigvalsh_tridiagonal#
- scipy.linalg.eigvalsh_tridiagonal(d, e, select='a', select_range=None, check_finite=True, tol=0.0, lapack_driver='auto')[source]#
- Solve eigenvalue problem for a real symmetric tridiagonal matrix. - Find eigenvalues w of - a:- a v[:,i] = w[i] v[:,i] v.H v = identity - For a real symmetric matrix - awith diagonal elements d and off-diagonal elements e.- Parameters:
- dndarray, shape (ndim,)
- The diagonal elements of the array. 
- endarray, shape (ndim-1,)
- The off-diagonal elements of the array. 
- select{‘a’, ‘v’, ‘i’}, optional
- Which eigenvalues to calculate - select - calculated - ‘a’ - All eigenvalues - ‘v’ - Eigenvalues in the interval (min, max] - ‘i’ - Eigenvalues with indices min <= i <= max 
- select_range(min, max), optional
- Range of selected eigenvalues 
- 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. 
- tolfloat
- The absolute tolerance to which each eigenvalue is required (only used when - lapack_driver='stebz'). An eigenvalue (or cluster) is considered to have converged if it lies in an interval of this width. If <= 0. (default), the value- eps*|a|is used where eps is the machine precision, and- |a|is the 1-norm of the matrix- a.
- lapack_driverstr
- LAPACK function to use, can be ‘auto’, ‘stemr’, ‘stebz’, ‘sterf’, or ‘stev’. When ‘auto’ (default), it will use ‘stemr’ if - select='a'and ‘stebz’ otherwise. ‘sterf’ and ‘stev’ can only be used when- select='a'.
 
- Returns:
- w(M,) ndarray
- The eigenvalues, in ascending order, each repeated according to its multiplicity. 
 
- Raises:
- LinAlgError
- If eigenvalue computation does not converge. 
 
 - See also - eigh_tridiagonal
- eigenvalues and right eiegenvectors for symmetric/Hermitian tridiagonal matrices 
 - Examples - >>> import numpy as np >>> from scipy.linalg import eigvalsh_tridiagonal, eigvalsh >>> d = 3*np.ones(4) >>> e = -1*np.ones(3) >>> w = eigvalsh_tridiagonal(d, e) >>> A = np.diag(d) + np.diag(e, k=1) + np.diag(e, k=-1) >>> w2 = eigvalsh(A) # Verify with other eigenvalue routines >>> np.allclose(w - w2, np.zeros(4)) True