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version 1.1, 2010/01/26 15:22:46 version 1.18, 2023/08/07 08:38:59
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   *> \brief \b DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DLASV2 + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasv2.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasv2.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasv2.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
   *
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION   CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLASV2 computes the singular value decomposition of a 2-by-2
   *> triangular matrix
   *>    [  F   G  ]
   *>    [  0   H  ].
   *> On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the
   *> smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and
   *> right singular vectors for abs(SSMAX), giving the decomposition
   *>
   *>    [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
   *>    [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ].
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] F
   *> \verbatim
   *>          F is DOUBLE PRECISION
   *>          The (1,1) element of the 2-by-2 matrix.
   *> \endverbatim
   *>
   *> \param[in] G
   *> \verbatim
   *>          G is DOUBLE PRECISION
   *>          The (1,2) element of the 2-by-2 matrix.
   *> \endverbatim
   *>
   *> \param[in] H
   *> \verbatim
   *>          H is DOUBLE PRECISION
   *>          The (2,2) element of the 2-by-2 matrix.
   *> \endverbatim
   *>
   *> \param[out] SSMIN
   *> \verbatim
   *>          SSMIN is DOUBLE PRECISION
   *>          abs(SSMIN) is the smaller singular value.
   *> \endverbatim
   *>
   *> \param[out] SSMAX
   *> \verbatim
   *>          SSMAX is DOUBLE PRECISION
   *>          abs(SSMAX) is the larger singular value.
   *> \endverbatim
   *>
   *> \param[out] SNL
   *> \verbatim
   *>          SNL is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[out] CSL
   *> \verbatim
   *>          CSL is DOUBLE PRECISION
   *>          The vector (CSL, SNL) is a unit left singular vector for the
   *>          singular value abs(SSMAX).
   *> \endverbatim
   *>
   *> \param[out] SNR
   *> \verbatim
   *>          SNR is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[out] CSR
   *> \verbatim
   *>          CSR is DOUBLE PRECISION
   *>          The vector (CSR, SNR) is a unit right singular vector for the
   *>          singular value abs(SSMAX).
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup OTHERauxiliary
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  Any input parameter may be aliased with any output parameter.
   *>
   *>  Barring over/underflow and assuming a guard digit in subtraction, all
   *>  output quantities are correct to within a few units in the last
   *>  place (ulps).
   *>
   *>  In IEEE arithmetic, the code works correctly if one matrix element is
   *>  infinite.
   *>
   *>  Overflow will not occur unless the largest singular value itself
   *>  overflows or is within a few ulps of overflow. (On machines with
   *>  partial overflow, like the Cray, overflow may occur if the largest
   *>  singular value is within a factor of 2 of overflow.)
   *>
   *>  Underflow is harmless if underflow is gradual. Otherwise, results
   *>  may correspond to a matrix modified by perturbations of size near
   *>  the underflow threshold.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )        SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine --
 *  -- 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  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION   CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN        DOUBLE PRECISION   CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLASV2 computes the singular value decomposition of a 2-by-2  
 *  triangular matrix  
 *     [  F   G  ]  
 *     [  0   H  ].  
 *  On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the  
 *  smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and  
 *  right singular vectors for abs(SSMAX), giving the decomposition  
 *  
 *     [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]  
 *     [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ].  
 *  
 *  Arguments  
 *  =========  
 *  
 *  F       (input) DOUBLE PRECISION  
 *          The (1,1) element of the 2-by-2 matrix.  
 *  
 *  G       (input) DOUBLE PRECISION  
 *          The (1,2) element of the 2-by-2 matrix.  
 *  
 *  H       (input) DOUBLE PRECISION  
 *          The (2,2) element of the 2-by-2 matrix.  
 *  
 *  SSMIN   (output) DOUBLE PRECISION  
 *          abs(SSMIN) is the smaller singular value.  
 *  
 *  SSMAX   (output) DOUBLE PRECISION  
 *          abs(SSMAX) is the larger singular value.  
 *  
 *  SNL     (output) DOUBLE PRECISION  
 *  CSL     (output) DOUBLE PRECISION  
 *          The vector (CSL, SNL) is a unit left singular vector for the  
 *          singular value abs(SSMAX).  
 *  
 *  SNR     (output) DOUBLE PRECISION  
 *  CSR     (output) DOUBLE PRECISION  
 *          The vector (CSR, SNR) is a unit right singular vector for the  
 *          singular value abs(SSMAX).  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Any input parameter may be aliased with any output parameter.  
 *  
 *  Barring over/underflow and assuming a guard digit in subtraction, all  
 *  output quantities are correct to within a few units in the last  
 *  place (ulps).  
 *  
 *  In IEEE arithmetic, the code works correctly if one matrix element is  
 *  infinite.  
 *  
 *  Overflow will not occur unless the largest singular value itself  
 *  overflows or is within a few ulps of overflow. (On machines with  
 *  partial overflow, like the Cray, overflow may occur if the largest  
 *  singular value is within a factor of 2 of overflow.)  
 *  
 *  Underflow is harmless if underflow is gradual. Otherwise, results  
 *  may correspond to a matrix modified by perturbations of size near  
 *  the underflow threshold.  
 *  
 * =====================================================================  * =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.1  
changed lines
  Added in v.1.18

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