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author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/zlaev2.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
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Integrating Doxygen in comments
Diffstat (limited to 'SRC/zlaev2.f')
-rw-r--r-- | SRC/zlaev2.f | 152 |
1 files changed, 107 insertions, 45 deletions
diff --git a/SRC/zlaev2.f b/SRC/zlaev2.f index 1f31ff7b..8210b5fb 100644 --- a/SRC/zlaev2.f +++ b/SRC/zlaev2.f @@ -1,67 +1,129 @@ - SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) +*> \brief \b ZLAEV2 * -* -- LAPACK auxiliary routine (version 3.2) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - DOUBLE PRECISION CS1, RT1, RT2 - COMPLEX*16 A, B, C, SN1 -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION CS1, RT1, RT2 +* COMPLEX*16 A, B, C, SN1 +* .. +* * Purpose * ======= * -* ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix -* [ A B ] -* [ CONJG(B) C ]. -* On return, RT1 is the eigenvalue of larger absolute value, RT2 is the -* eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right -* eigenvector for RT1, giving the decomposition -* -* [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] -* [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. +*>\details \b Purpose: +*>\verbatim +*> +*> ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix +*> [ A B ] +*> [ CONJG(B) C ]. +*> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the +*> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right +*> eigenvector for RT1, giving the decomposition +*> +*> [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] +*> [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. +*> +*>\endverbatim * * Arguments * ========= * -* A (input) COMPLEX*16 -* The (1,1) element of the 2-by-2 matrix. -* -* B (input) COMPLEX*16 -* The (1,2) element and the conjugate of the (2,1) element of -* the 2-by-2 matrix. -* -* C (input) COMPLEX*16 -* The (2,2) element of the 2-by-2 matrix. +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 +*> The (1,1) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX*16 +*> The (1,2) element and the conjugate of the (2,1) element of +*> the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is COMPLEX*16 +*> The (2,2) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[out] RT1 +*> \verbatim +*> RT1 is DOUBLE PRECISION +*> The eigenvalue of larger absolute value. +*> \endverbatim +*> +*> \param[out] RT2 +*> \verbatim +*> RT2 is DOUBLE PRECISION +*> The eigenvalue of smaller absolute value. +*> \endverbatim +*> +*> \param[out] CS1 +*> \verbatim +*> CS1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] SN1 +*> \verbatim +*> SN1 is COMPLEX*16 +*> The vector (CS1, SN1) is a unit right eigenvector for RT1. +*> \endverbatim +*> +* +* Authors +* ======= * -* RT1 (output) DOUBLE PRECISION -* The eigenvalue of larger absolute value. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* RT2 (output) DOUBLE PRECISION -* The eigenvalue of smaller absolute value. +*> \date November 2011 * -* CS1 (output) DOUBLE PRECISION +*> \ingroup complex16OTHERauxiliary * -* SN1 (output) COMPLEX*16 -* The vector (CS1, SN1) is a unit right eigenvector for RT1. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> RT1 is accurate to a few ulps barring over/underflow. +*> +*> RT2 may be inaccurate if there is massive cancellation in the +*> determinant A*C-B*B; higher precision or correctly rounded or +*> correctly truncated arithmetic would be needed to compute RT2 +*> accurately in all cases. +*> +*> CS1 and SN1 are accurate to a few ulps barring over/underflow. +*> +*> Overflow is possible only if RT1 is within a factor of 5 of overflow. +*> Underflow is harmless if the input data is 0 or exceeds +*> underflow_threshold / macheps. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) * -* RT1 is accurate to a few ulps barring over/underflow. -* -* RT2 may be inaccurate if there is massive cancellation in the -* determinant A*C-B*B; higher precision or correctly rounded or -* correctly truncated arithmetic would be needed to compute RT2 -* accurately in all cases. -* -* CS1 and SN1 are accurate to a few ulps barring over/underflow. +* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* Overflow is possible only if RT1 is within a factor of 5 of overflow. -* Underflow is harmless if the input data is 0 or exceeds -* underflow_threshold / macheps. +* .. Scalar Arguments .. + DOUBLE PRECISION CS1, RT1, RT2 + COMPLEX*16 A, B, C, SN1 +* .. * * ===================================================================== * |