lapgeigv ============================================== Purpose ---------------- Computes generalized eigenvalues, left eigenvectors, and right eigenvectors for a pair of real or complex general matrices. Format ---------------- .. function:: { va1, va2, lve, rve } = lapgeigv(A, B) :param A: real or complex general matrix. :type A: NxN matrix :param B: real or complex general matrix. :type B: NxN matrix :return va1: numerator of eigenvalues. :rtype va1: Nx1 vector :return va2: denominator of eigenvalues. :rtype va2: Nx1 vector :return lve: :rtype lve: NxN left eigenvectors :return rve: :rtype rve: NxN right eigenvectors Remarks ------- *va1* and *va2* are the vectors of the numerators and denominators respectively of the eigenvalues of the solution of the generalized symmetric eigenproblem of the form :math:Aw = \lambda Bw where *A* and *B* are real or complex general matrices and :math:w = va1./va2. The generalized eigenvalues are not computed directly because some elements of *va2* may be zero, i.e., the eigenvalues may be infinite. The left and right eigenvectors diagonalize :math:U'^{-1}AU^{-1} where :math:B = U'U, that is, .. math:: \text{lve}*U'^{-1}AU^{-1}*\text{lve}' = w and .. math:: \text{rve}'*U'^{-1}AU^{-1}*\text{rve} = w This procedure calls the LAPACK routines *DGGEV* and *ZGGEV*. .. seealso:: Functions :func:lapgeig, :func:lapgeigh