--- rpl/lapack/lapack/dlanv2.f 2010/12/21 13:53:30 1.8 +++ rpl/lapack/lapack/dlanv2.f 2011/11/21 20:42:56 1.9 @@ -1,58 +1,141 @@ +*> \brief \b DLANV2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLANV2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric +*> matrix in standard form: +*> +*> [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ] +*> [ C D ] [ SN CS ] [ CC DD ] [-SN CS ] +*> +*> where either +*> 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or +*> 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex +*> conjugate eigenvalues. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION +*> On entry, the elements of the input matrix. +*> On exit, they are overwritten by the elements of the +*> standardised Schur form. +*> \endverbatim +*> +*> \param[out] RT1R +*> \verbatim +*> RT1R is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] RT1I +*> \verbatim +*> RT1I is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] RT2R +*> \verbatim +*> RT2R is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] RT2I +*> \verbatim +*> RT2I is DOUBLE PRECISION +*> The real and imaginary parts of the eigenvalues. If the +*> eigenvalues are a complex conjugate pair, RT1I > 0. +*> \endverbatim +*> +*> \param[out] CS +*> \verbatim +*> CS is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] SN +*> \verbatim +*> SN is DOUBLE PRECISION +*> Parameters of the rotation matrix. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> Modified by V. Sima, Research Institute for Informatics, Bucharest, +*> Romania, to reduce the risk of cancellation errors, +*> when computing real eigenvalues, and to ensure, if possible, that +*> abs(RT1R) >= abs(RT2R). +*> \endverbatim +*> +* ===================================================================== SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN ) * -* -- LAPACK auxiliary routine (version 3.2.2) -- +* -- LAPACK auxiliary routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* June 2010 +* November 2011 * * .. Scalar Arguments .. DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN * .. * -* Purpose -* ======= -* -* DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric -* matrix in standard form: -* -* [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ] -* [ C D ] [ SN CS ] [ CC DD ] [-SN CS ] -* -* where either -* 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or -* 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex -* conjugate eigenvalues. -* -* Arguments -* ========= -* -* A (input/output) DOUBLE PRECISION -* B (input/output) DOUBLE PRECISION -* C (input/output) DOUBLE PRECISION -* D (input/output) DOUBLE PRECISION -* On entry, the elements of the input matrix. -* On exit, they are overwritten by the elements of the -* standardised Schur form. -* -* RT1R (output) DOUBLE PRECISION -* RT1I (output) DOUBLE PRECISION -* RT2R (output) DOUBLE PRECISION -* RT2I (output) DOUBLE PRECISION -* The real and imaginary parts of the eigenvalues. If the -* eigenvalues are a complex conjugate pair, RT1I > 0. -* -* CS (output) DOUBLE PRECISION -* SN (output) DOUBLE PRECISION -* Parameters of the rotation matrix. -* -* Further Details -* =============== -* -* Modified by V. Sima, Research Institute for Informatics, Bucharest, -* Romania, to reduce the risk of cancellation errors, -* when computing real eigenvalues, and to ensure, if possible, that -* abs(RT1R) >= abs(RT2R). -* * ===================================================================== * * .. Parameters ..