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version 1.8, 2011/11/21 20:43:15
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*> \brief \b ZLAEV2 |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZLAEV2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaev2.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaev2.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaev2.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) |
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* |
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* .. Scalar Arguments .. |
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* DOUBLE PRECISION CS1, RT1, RT2 |
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* COMPLEX*16 A, B, C, SN1 |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix |
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*> [ A B ] |
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*> [ CONJG(B) C ]. |
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*> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the |
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*> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right |
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*> eigenvector for RT1, giving the decomposition |
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*> |
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*> [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] |
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*> [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] A |
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*> \verbatim |
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*> A is COMPLEX*16 |
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*> The (1,1) element of the 2-by-2 matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] B |
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*> \verbatim |
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*> B is COMPLEX*16 |
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*> The (1,2) element and the conjugate of the (2,1) element of |
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*> the 2-by-2 matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] C |
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*> \verbatim |
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*> C is COMPLEX*16 |
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*> The (2,2) element of the 2-by-2 matrix. |
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*> \endverbatim |
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*> |
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*> \param[out] RT1 |
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*> \verbatim |
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*> RT1 is DOUBLE PRECISION |
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*> The eigenvalue of larger absolute value. |
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*> \endverbatim |
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*> |
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*> \param[out] RT2 |
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*> \verbatim |
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*> RT2 is DOUBLE PRECISION |
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*> The eigenvalue of smaller absolute value. |
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*> \endverbatim |
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*> |
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*> \param[out] CS1 |
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*> \verbatim |
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*> CS1 is DOUBLE PRECISION |
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*> \endverbatim |
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*> |
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*> \param[out] SN1 |
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*> \verbatim |
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*> SN1 is COMPLEX*16 |
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*> The vector (CS1, SN1) is a unit right eigenvector for RT1. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup complex16OTHERauxiliary |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> RT1 is accurate to a few ulps barring over/underflow. |
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*> |
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*> RT2 may be inaccurate if there is massive cancellation in the |
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*> determinant A*C-B*B; higher precision or correctly rounded or |
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*> correctly truncated arithmetic would be needed to compute RT2 |
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*> accurately in all cases. |
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*> |
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*> CS1 and SN1 are accurate to a few ulps barring over/underflow. |
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*> |
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*> Overflow is possible only if RT1 is within a factor of 5 of overflow. |
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*> Underflow is harmless if the input data is 0 or exceeds |
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*> underflow_threshold / macheps. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) |
SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION CS1, RT1, RT2 |
DOUBLE PRECISION CS1, RT1, RT2 |
COMPLEX*16 A, B, C, SN1 |
COMPLEX*16 A, B, C, SN1 |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix |
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* [ A B ] |
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* [ CONJG(B) C ]. |
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* On return, RT1 is the eigenvalue of larger absolute value, RT2 is the |
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* eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right |
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* eigenvector for RT1, giving the decomposition |
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* |
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* [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] |
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* [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. |
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* |
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* Arguments |
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* ========= |
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* |
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* A (input) COMPLEX*16 |
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* The (1,1) element of the 2-by-2 matrix. |
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* |
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* B (input) COMPLEX*16 |
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* The (1,2) element and the conjugate of the (2,1) element of |
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* the 2-by-2 matrix. |
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* |
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* C (input) COMPLEX*16 |
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* The (2,2) element of the 2-by-2 matrix. |
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* |
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* RT1 (output) DOUBLE PRECISION |
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* The eigenvalue of larger absolute value. |
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* |
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* RT2 (output) DOUBLE PRECISION |
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* The eigenvalue of smaller absolute value. |
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* |
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* CS1 (output) DOUBLE PRECISION |
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* SN1 (output) COMPLEX*16 |
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* The vector (CS1, SN1) is a unit right eigenvector for RT1. |
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* |
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* Further Details |
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* =============== |
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* |
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* RT1 is accurate to a few ulps barring over/underflow. |
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* |
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* RT2 may be inaccurate if there is massive cancellation in the |
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* determinant A*C-B*B; higher precision or correctly rounded or |
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* correctly truncated arithmetic would be needed to compute RT2 |
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* accurately in all cases. |
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* |
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* CS1 and SN1 are accurate to a few ulps barring over/underflow. |
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* |
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* Overflow is possible only if RT1 is within a factor of 5 of overflow. |
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* Underflow is harmless if the input data is 0 or exceeds |
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* underflow_threshold / macheps. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |