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.- The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details. - 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’, ‘stev’, or ‘stevd’. When ‘auto’ (default), it will use ‘stevd’ 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