--- rpl/lapack/lapack/dlags2.f	2010/08/06 15:32:26	1.4
+++ rpl/lapack/lapack/dlags2.f	2023/08/07 08:38:54	1.19
@@ -1,10 +1,158 @@
+*> \brief \b DLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLAGS2 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlags2.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlags2.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlags2.f">
+*> [TXT]</a>
+*> \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.
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*  =====================================================================
       SUBROUTINE DLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV,
      $                   SNV, CSQ, SNQ )
 *
-*  -- LAPACK auxiliary routine (version 3.2) --
+*  -- LAPACK auxiliary routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2006
 *
 *     .. Scalar Arguments ..
       LOGICAL            UPPER
@@ -12,65 +160,6 @@
      $                   SNU, SNV
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
-*  that if ( UPPER ) then
-*
-*            U'*A*Q = U'*( A1 A2 )*Q = ( x  0  )
-*                        ( 0  A3 )     ( x  x  )
-*  and
-*            V'*B*Q = V'*( B1 B2 )*Q = ( x  0  )
-*                        ( 0  B3 )     ( x  x  )
-*
-*  or if ( .NOT.UPPER ) then
-*
-*            U'*A*Q = U'*( A1 0  )*Q = ( x  x  )
-*                        ( A2 A3 )     ( 0  x  )
-*  and
-*            V'*B*Q = V'*( 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' 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 ..
@@ -112,8 +201,8 @@
          IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) )
      $        THEN
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**T *A and V**T *B,
+*           and (1,2) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA11R = CSL*A1
             UA12 = CSL*A2 + SNL*A3
@@ -124,7 +213,7 @@
             AUA12 = ABS( CSL )*ABS( A2 ) + ABS( SNL )*ABS( A3 )
             AVB12 = ABS( CSR )*ABS( B2 ) + ABS( SNR )*ABS( B3 )
 *
-*           zero (1,2) elements of U'*A and V'*B
+*           zero (1,2) elements of U**T *A and V**T *B
 *
             IF( ( ABS( UA11R )+ABS( UA12 ) ).NE.ZERO ) THEN
                IF( AUA12 / ( ABS( UA11R )+ABS( UA12 ) ).LE.AVB12 /
@@ -144,8 +233,8 @@
 *
          ELSE
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**T *A and V**T *B,
+*           and (2,2) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA21 = -SNL*A1
             UA22 = -SNL*A2 + CSL*A3
@@ -156,7 +245,7 @@
             AUA22 = ABS( SNL )*ABS( A2 ) + ABS( CSL )*ABS( A3 )
             AVB22 = ABS( SNR )*ABS( B2 ) + ABS( CSR )*ABS( B3 )
 *
-*           zero (2,2) elements of U'*A and V'*B, and then swap.
+*           zero (2,2) elements of U**T*A and V**T*B, and then swap.
 *
             IF( ( ABS( UA21 )+ABS( UA22 ) ).NE.ZERO ) THEN
                IF( AUA22 / ( ABS( UA21 )+ABS( UA22 ) ).LE.AVB22 /
@@ -197,8 +286,8 @@
          IF( ABS( CSR ).GE.ABS( SNR ) .OR. ABS( CSL ).GE.ABS( SNL ) )
      $        THEN
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**T *A and V**T *B,
+*           and (2,1) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA21 = -SNR*A1 + CSR*A2
             UA22R = CSR*A3
@@ -209,7 +298,7 @@
             AUA21 = ABS( SNR )*ABS( A1 ) + ABS( CSR )*ABS( A2 )
             AVB21 = ABS( SNL )*ABS( B1 ) + ABS( CSL )*ABS( B2 )
 *
-*           zero (2,1) elements of U'*A and V'*B.
+*           zero (2,1) elements of U**T *A and V**T *B.
 *
             IF( ( ABS( UA21 )+ABS( UA22R ) ).NE.ZERO ) THEN
                IF( AUA21 / ( ABS( UA21 )+ABS( UA22R ) ).LE.AVB21 /
@@ -229,8 +318,8 @@
 *
          ELSE
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**T *A and V**T *B,
+*           and (1,1) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA11 = CSR*A1 + SNR*A2
             UA12 = SNR*A3
@@ -241,7 +330,7 @@
             AUA11 = ABS( CSR )*ABS( A1 ) + ABS( SNR )*ABS( A2 )
             AVB11 = ABS( CSL )*ABS( B1 ) + ABS( SNL )*ABS( B2 )
 *
-*           zero (1,1) elements of U'*A and V'*B, and then swap.
+*           zero (1,1) elements of U**T*A and V**T*B, and then swap.
 *
             IF( ( ABS( UA11 )+ABS( UA12 ) ).NE.ZERO ) THEN
                IF( AUA11 / ( ABS( UA11 )+ABS( UA12 ) ).LE.AVB11 /