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36   * The eigenvalues and eigenvectors of a matrix may be complex, even when the
43 * blocks correspond to complex eigenvalue pairs \f$ u \pm iv \f$. We call
84 /** \brief Complex scalar type for #MatrixType.
86 * This is \c std::complex<Scalar> if #Scalar is real (e.g.,
88 * complex.
90 typedef std::complex<RealScalar> ComplexScalar;
160 * \returns %Matrix whose columns are the (possibly complex) eigenvectors.
336 // we have a pair of complex eigen values
394 // Complex scalar division.
396 std::complex<Scalar> cdiv(Scalar xr, Scalar xi, Scalar yr, Scalar yi)
403 return std::complex<Scalar>((xr + r*xi)/d, (xi - r*xr)/d);
409 return std::complex<Scalar>((r*xr + xi)/d, (r*xi - xr)/d);
485 else if (q < Scalar(0) && n > 0) // Complex vector
498 std::complex<Scalar> cc = cdiv<Scalar>(0.0,-m_matT.coeff(n-1,n),m_matT.coeff(n-1,n-1)-p,q);
521 std::complex<Scalar> cc = cdiv(-ra,-sa,w,q);
527 // Solve complex equations
535 std::complex<Scalar> cc = cdiv(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra,vr,vi);
560 // We handled a pair of complex conjugate eigenvalues, so need to skip them both