+++ /dev/null
-*> \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix.
-*
-* =========== DOCUMENTATION ===========
-*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
-*
-*> \htmlonly
-*> Download DLAS2 + dependencies
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlas2.f">
-*> [TGZ]</a>
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlas2.f">
-*> [ZIP]</a>
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlas2.f">
-*> [TXT]</a>
-*> \endhtmlonly
-*
-* Definition:
-* ===========
-*
-* SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
-*
-* .. Scalar Arguments ..
-* DOUBLE PRECISION F, G, H, SSMAX, SSMIN
-* ..
-*
-*
-*> \par Purpose:
-* =============
-*>
-*> \verbatim
-*>
-*> DLAS2 computes the singular values of the 2-by-2 matrix
-*> [ F G ]
-*> [ 0 H ].
-*> On return, SSMIN is the smaller singular value and SSMAX is the
-*> larger singular value.
-*> \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
-*> The smaller singular value.
-*> \endverbatim
-*>
-*> \param[out] SSMAX
-*> \verbatim
-*> SSMAX is DOUBLE PRECISION
-*> The larger singular value.
-*> \endverbatim
-*
-* Authors:
-* ========
-*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
-*
-*> \date September 2012
-*
-*> \ingroup auxOTHERauxiliary
-*
-*> \par Further Details:
-* =====================
-*>
-*> \verbatim
-*>
-*> Barring over/underflow, all output quantities are correct to within
-*> a few units in the last place (ulps), even in the absence of a guard
-*> digit in addition/subtraction.
-*>
-*> 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 DLAS2( F, G, H, SSMIN, SSMAX )
-*
-* -- LAPACK auxiliary routine (version 3.4.2) --
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* September 2012
-*
-* .. Scalar Arguments ..
- DOUBLE PRECISION F, G, H, SSMAX, SSMIN
-* ..
-*
-* ====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ZERO
- PARAMETER ( ZERO = 0.0D0 )
- DOUBLE PRECISION ONE
- PARAMETER ( ONE = 1.0D0 )
- DOUBLE PRECISION TWO
- PARAMETER ( TWO = 2.0D0 )
-* ..
-* .. Local Scalars ..
- DOUBLE PRECISION AS, AT, AU, C, FA, FHMN, FHMX, GA, HA
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC ABS, MAX, MIN, SQRT
-* ..
-* .. Executable Statements ..
-*
- FA = ABS( F )
- GA = ABS( G )
- HA = ABS( H )
- FHMN = MIN( FA, HA )
- FHMX = MAX( FA, HA )
- IF( FHMN.EQ.ZERO ) THEN
- SSMIN = ZERO
- IF( FHMX.EQ.ZERO ) THEN
- SSMAX = GA
- ELSE
- SSMAX = MAX( FHMX, GA )*SQRT( ONE+
- $ ( MIN( FHMX, GA ) / MAX( FHMX, GA ) )**2 )
- END IF
- ELSE
- IF( GA.LT.FHMX ) THEN
- AS = ONE + FHMN / FHMX
- AT = ( FHMX-FHMN ) / FHMX
- AU = ( GA / FHMX )**2
- C = TWO / ( SQRT( AS*AS+AU )+SQRT( AT*AT+AU ) )
- SSMIN = FHMN*C
- SSMAX = FHMX / C
- ELSE
- AU = FHMX / GA
- IF( AU.EQ.ZERO ) THEN
-*
-* Avoid possible harmful underflow if exponent range
-* asymmetric (true SSMIN may not underflow even if
-* AU underflows)
-*
- SSMIN = ( FHMN*FHMX ) / GA
- SSMAX = GA
- ELSE
- AS = ONE + FHMN / FHMX
- AT = ( FHMX-FHMN ) / FHMX
- C = ONE / ( SQRT( ONE+( AS*AU )**2 )+
- $ SQRT( ONE+( AT*AU )**2 ) )
- SSMIN = ( FHMN*C )*AU
- SSMIN = SSMIN + SSMIN
- SSMAX = GA / ( C+C )
- END IF
- END IF
- END IF
- RETURN
-*
-* End of DLAS2
-*
- END
OSDN Git Service
