lapgeighv ============================================== Purpose ---------------- Computes generalized eigenvalues and eigenvectors for a pair of real symmetric or Hermitian matrices. Format ---------------- .. function:: { ve, va } = lapgeighv(A, B) :param A: real or complex symmetric or Hermitian matrix. :type A: NxN matrix :param B: real or complex positive definite symmetric or Hermitian matrix. :type B: NxN matrix :return ve: eigenvalues. :rtype ve: Nx1 vector :return va: eigenvectors. :rtype va: NxN matrix Examples ---------------- :: // Assign A A = { 3 4 5, 2 5 2, 3 2 4 }; // Assign B B = { 4 2 2, 2 6 1, 2 1 8 }; // Find the eigenvalues and corresponding // eigenvectors of the solution of the // generalized symmetric eigenproblem { ve, va } = lapgeighv(A, B); print ve; :: -0.0425 0.5082 0.8694 :: print va; :: 0.3575 -0.0996 0.9286 -0.2594 0.9446 0.2012 -0.8972 -0.3128 0.3118 Remarks ------- *ve* and *va* are the eigenvalues and eigenvectors of the solution of the generalized symmetric eigenproblem of the form :math:`Ax = λ B`. Equivalently, *va* diagonalizes :math:`U'^{-1}AU^{-1}` in the following way .. math:: va*U'^{-1}AU^{-1}*va' = ve where :math:`B = U'U`. This procedure calls the LAPACK routines *DSYGV* and *ZHEGV*. .. seealso:: Functions :func:`lapgeig`, :func:`lapgeigh`