Swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation.


Computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow.


Computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel.


Computes an LU factorization of a matrix T-λ*I, where T is a general tridiagonal matrix, and λ is a scalar, using partial pivoting with row interchanges.


Performs a matrix-matrix product of the form C = alpha*A*B+beta*C, where A is a tridiagonal matrix, B and C are rectangular matrices, and alpha and beta are scalars, which may be 0, 1, or -1.


Solves the system of equations (T - lambda*I)*x = y or (T - lambda*I)T*x = y,where T is a general tridiagonal matrix and lambda is a scalar, using the LU factorization computed by ?lagtf.


Computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.


Computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.

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