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authorjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
committerjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
commite1d39294aee16fa6db9ba079b14442358217db71 (patch)
tree30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/slagv2.f
parent5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff)
Integrating Doxygen in comments
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- SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL,
- $ CSR, SNR )
-*
-* -- LAPACK auxiliary routine (version 3.2.2) --
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* June 2010
-*
-* .. Scalar Arguments ..
- INTEGER LDA, LDB
- REAL CSL, CSR, SNL, SNR
-* ..
-* .. Array Arguments ..
- REAL A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ),
- $ B( LDB, * ), BETA( 2 )
-* ..
-*
+*> \brief \b SLAGV2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition
+* ==========
+*
+* SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL,
+* CSR, SNR )
+*
+* .. Scalar Arguments ..
+* INTEGER LDA, LDB
+* REAL CSL, CSR, SNL, SNR
+* ..
+* .. Array Arguments ..
+* REAL A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ),
+* $ B( LDB, * ), BETA( 2 )
+* ..
+*
* Purpose
* =======
*
-* SLAGV2 computes the Generalized Schur factorization of a real 2-by-2
-* matrix pencil (A,B) where B is upper triangular. This routine
-* computes orthogonal (rotation) matrices given by CSL, SNL and CSR,
-* SNR such that
-*
-* 1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0
-* types), then
-*
-* [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
-* [ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]
-*
-* [ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
-* [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ],
-*
-* 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,
-* then
-*
-* [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
-* [ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]
-*
-* [ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
-* [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ]
-*
-* where b11 >= b22 > 0.
-*
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> SLAGV2 computes the Generalized Schur factorization of a real 2-by-2
+*> matrix pencil (A,B) where B is upper triangular. This routine
+*> computes orthogonal (rotation) matrices given by CSL, SNL and CSR,
+*> SNR such that
+*>
+*> 1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0
+*> types), then
+*>
+*> [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
+*> [ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]
+*>
+*> [ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
+*> [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ],
+*>
+*> 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,
+*> then
+*>
+*> [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
+*> [ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]
+*>
+*> [ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
+*> [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ]
+*>
+*> where b11 >= b22 > 0.
+*>
+*>
+*>\endverbatim
*
* Arguments
* =========
*
-* A (input/output) REAL array, dimension (LDA, 2)
-* On entry, the 2 x 2 matrix A.
-* On exit, A is overwritten by the ``A-part'' of the
-* generalized Schur form.
-*
-* LDA (input) INTEGER
-* THe leading dimension of the array A. LDA >= 2.
-*
-* B (input/output) REAL array, dimension (LDB, 2)
-* On entry, the upper triangular 2 x 2 matrix B.
-* On exit, B is overwritten by the ``B-part'' of the
-* generalized Schur form.
-*
-* LDB (input) INTEGER
-* THe leading dimension of the array B. LDB >= 2.
-*
-* ALPHAR (output) REAL array, dimension (2)
-*
-* ALPHAI (output) REAL array, dimension (2)
-*
-* BETA (output) REAL array, dimension (2)
-* (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the
-* pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may
-* be zero.
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA, 2)
+*> On entry, the 2 x 2 matrix A.
+*> On exit, A is overwritten by the ``A-part'' of the
+*> generalized Schur form.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> THe leading dimension of the array A. LDA >= 2.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is REAL array, dimension (LDB, 2)
+*> On entry, the upper triangular 2 x 2 matrix B.
+*> On exit, B is overwritten by the ``B-part'' of the
+*> generalized Schur form.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> THe leading dimension of the array B. LDB >= 2.
+*> \endverbatim
+*>
+*> \param[out] ALPHAR
+*> \verbatim
+*> ALPHAR is REAL array, dimension (2)
+*> \endverbatim
+*>
+*> \param[out] ALPHAI
+*> \verbatim
+*> ALPHAI is REAL array, dimension (2)
+*> \endverbatim
+*>
+*> \param[out] BETA
+*> \verbatim
+*> BETA is REAL array, dimension (2)
+*> (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the
+*> pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may
+*> be zero.
+*> \endverbatim
+*>
+*> \param[out] CSL
+*> \verbatim
+*> CSL is REAL
+*> The cosine of the left rotation matrix.
+*> \endverbatim
+*>
+*> \param[out] SNL
+*> \verbatim
+*> SNL is REAL
+*> The sine of the left rotation matrix.
+*> \endverbatim
+*>
+*> \param[out] CSR
+*> \verbatim
+*> CSR is REAL
+*> The cosine of the right rotation matrix.
+*> \endverbatim
+*>
+*> \param[out] SNR
+*> \verbatim
+*> SNR is REAL
+*> The sine of the right rotation matrix.
+*> \endverbatim
+*>
+*
+* Authors
+* =======
*
-* CSL (output) REAL
-* The cosine of the left rotation matrix.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-* SNL (output) REAL
-* The sine of the left rotation matrix.
+*> \date November 2011
*
-* CSR (output) REAL
-* The cosine of the right rotation matrix.
+*> \ingroup realOTHERauxiliary
*
-* SNR (output) REAL
-* The sine of the right rotation matrix.
*
* Further Details
* ===============
+*>\details \b Further \b Details
+*> \verbatim
+*>
+*> Based on contributions by
+*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+*>
+*> \endverbatim
+*>
+* =====================================================================
+ SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL,
+ $ CSR, SNR )
*
-* Based on contributions by
-* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+* -- LAPACK auxiliary routine (version 3.2.2) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
+*
+* .. Scalar Arguments ..
+ INTEGER LDA, LDB
+ REAL CSL, CSR, SNL, SNR
+* ..
+* .. Array Arguments ..
+ REAL A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ),
+ $ B( LDB, * ), BETA( 2 )
+* ..
*
* =====================================================================
*