--- rpl/lapack/lapack/dlags2.f 2011/07/22 07:38:06 1.8 +++ rpl/lapack/lapack/dlags2.f 2011/11/21 20:42:55 1.9 @@ -1,10 +1,161 @@ +*> \brief \b DLAGS2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAGS2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, +* SNV, CSQ, SNQ ) +* +* .. Scalar Arguments .. +* LOGICAL UPPER +* DOUBLE PRECISION A1, A2, A3, B1, B2, B3, CSQ, CSU, CSV, SNQ, +* $ SNU, SNV +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such +*> that if ( UPPER ) then +*> +*> U**T *A*Q = U**T *( A1 A2 )*Q = ( x 0 ) +*> ( 0 A3 ) ( x x ) +*> and +*> V**T*B*Q = V**T *( B1 B2 )*Q = ( x 0 ) +*> ( 0 B3 ) ( x x ) +*> +*> or if ( .NOT.UPPER ) then +*> +*> U**T *A*Q = U**T *( A1 0 )*Q = ( x x ) +*> ( A2 A3 ) ( 0 x ) +*> and +*> V**T*B*Q = V**T*( B1 0 )*Q = ( x x ) +*> ( B2 B3 ) ( 0 x ) +*> +*> The rows of the transformed A and B are parallel, where +*> +*> U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) +*> ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) +*> +*> Z**T denotes the transpose of Z. +*> +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPPER +*> \verbatim +*> UPPER is LOGICAL +*> = .TRUE.: the input matrices A and B are upper triangular. +*> = .FALSE.: the input matrices A and B are lower triangular. +*> \endverbatim +*> +*> \param[in] A1 +*> \verbatim +*> A1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] A2 +*> \verbatim +*> A2 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] A3 +*> \verbatim +*> A3 is DOUBLE PRECISION +*> On entry, A1, A2 and A3 are elements of the input 2-by-2 +*> upper (lower) triangular matrix A. +*> \endverbatim +*> +*> \param[in] B1 +*> \verbatim +*> B1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] B2 +*> \verbatim +*> B2 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] B3 +*> \verbatim +*> B3 is DOUBLE PRECISION +*> On entry, B1, B2 and B3 are elements of the input 2-by-2 +*> upper (lower) triangular matrix B. +*> \endverbatim +*> +*> \param[out] CSU +*> \verbatim +*> CSU is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] SNU +*> \verbatim +*> SNU is DOUBLE PRECISION +*> The desired orthogonal matrix U. +*> \endverbatim +*> +*> \param[out] CSV +*> \verbatim +*> CSV is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] SNV +*> \verbatim +*> SNV is DOUBLE PRECISION +*> The desired orthogonal matrix V. +*> \endverbatim +*> +*> \param[out] CSQ +*> \verbatim +*> CSQ is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] SNQ +*> \verbatim +*> SNQ is DOUBLE PRECISION +*> The desired orthogonal matrix Q. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERauxiliary +* +* ===================================================================== SUBROUTINE DLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, $ SNV, CSQ, SNQ ) * -* -- LAPACK auxiliary routine (version 3.3.1) -- +* -- 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..-- -* -- April 2011 -- +* November 2011 * * .. Scalar Arguments .. LOGICAL UPPER @@ -12,65 +163,6 @@ $ SNU, SNV * .. * -* Purpose -* ======= -* -* DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such -* that if ( UPPER ) then -* -* U**T *A*Q = U**T *( A1 A2 )*Q = ( x 0 ) -* ( 0 A3 ) ( x x ) -* and -* V**T*B*Q = V**T *( B1 B2 )*Q = ( x 0 ) -* ( 0 B3 ) ( x x ) -* -* or if ( .NOT.UPPER ) then -* -* U**T *A*Q = U**T *( A1 0 )*Q = ( x x ) -* ( A2 A3 ) ( 0 x ) -* and -* V**T*B*Q = V**T*( B1 0 )*Q = ( x x ) -* ( B2 B3 ) ( 0 x ) -* -* The rows of the transformed A and B are parallel, where -* -* U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) -* ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) -* -* Z**T denotes the transpose of Z. -* -* -* Arguments -* ========= -* -* UPPER (input) LOGICAL -* = .TRUE.: the input matrices A and B are upper triangular. -* = .FALSE.: the input matrices A and B are lower triangular. -* -* A1 (input) DOUBLE PRECISION -* A2 (input) DOUBLE PRECISION -* A3 (input) DOUBLE PRECISION -* On entry, A1, A2 and A3 are elements of the input 2-by-2 -* upper (lower) triangular matrix A. -* -* B1 (input) DOUBLE PRECISION -* B2 (input) DOUBLE PRECISION -* B3 (input) DOUBLE PRECISION -* On entry, B1, B2 and B3 are elements of the input 2-by-2 -* upper (lower) triangular matrix B. -* -* CSU (output) DOUBLE PRECISION -* SNU (output) DOUBLE PRECISION -* The desired orthogonal matrix U. -* -* CSV (output) DOUBLE PRECISION -* SNV (output) DOUBLE PRECISION -* The desired orthogonal matrix V. -* -* CSQ (output) DOUBLE PRECISION -* SNQ (output) DOUBLE PRECISION -* The desired orthogonal matrix Q. -* * ===================================================================== * * .. Parameters ..