dlasv2()

subroutine dlasv2	(	double precision	F,
		double precision	G,
		double precision	H,
		double precision	SSMIN,
		double precision	SSMAX,
		double precision	SNR,
		double precision	CSR,
		double precision	SNL,
		double precision	CSL
	)

DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

Download DLASV2 + dependencies [TGZ] [ZIP] [TXT]

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 ].

Parameters

[in]	F	F is DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix.
[in]	G	G is DOUBLE PRECISION The (1,2) element of the 2-by-2 matrix.
[in]	H	H is DOUBLE PRECISION The (2,2) element of the 2-by-2 matrix.
[out]	SSMIN	SSMIN is DOUBLE PRECISION abs(SSMIN) is the smaller singular value.
[out]	SSMAX	SSMAX is DOUBLE PRECISION abs(SSMAX) is the larger singular value.
[out]	SNL	SNL is DOUBLE PRECISION
[out]	CSL	CSL is DOUBLE PRECISION The vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX).
[out]	SNR	SNR is DOUBLE PRECISION
[out]	CSR	CSR is DOUBLE PRECISION The vector (CSR, SNR) is a unit right singular vector for the singular value abs(SSMAX).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.

Definition at line 137 of file dlasv2.f.

*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      parameter( zero = 0.0d0 )
      DOUBLE PRECISION   HALF
      parameter( half = 0.5d0 )
      DOUBLE PRECISION   ONE
      parameter( one = 1.0d0 )
      DOUBLE PRECISION   TWO
      parameter( two = 2.0d0 )
      DOUBLE PRECISION   FOUR
      parameter( four = 4.0d0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            GASMAL, SWAP
      INTEGER            PMAX
      DOUBLE PRECISION   A, CLT, CRT, D, FA, FT, GA, GT, HA, HT, L, M,
     $                   MM, R, S, SLT, SRT, T, TEMP, TSIGN, TT
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, sign, sqrt
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           dlamch
*     ..
*     .. Executable Statements ..
*
      ft = f
      fa = abs( ft )
      ht = h
      ha = abs( h )
*
*     PMAX points to the maximum absolute element of matrix
*       PMAX = 1 if F largest in absolute values
*       PMAX = 2 if G largest in absolute values
*       PMAX = 3 if H largest in absolute values
*
      pmax = 1
      swap = ( ha.GT.fa )
      IF( swap ) THEN
         pmax = 3
         temp = ft
         ft = ht
         ht = temp
         temp = fa
         fa = ha
         ha = temp
*
*        Now FA .ge. HA
*
      END IF
      gt = g
      ga = abs( gt )
      IF( ga.EQ.zero ) THEN
*
*        Diagonal matrix
*
         ssmin = ha
         ssmax = fa
         clt = one
         crt = one
         slt = zero
         srt = zero
      ELSE
         gasmal = .true.
         IF( ga.GT.fa ) THEN
            pmax = 2
            IF( ( fa / ga ).LT.dlamch( 'EPS' ) ) THEN
*
*              Case of very large GA
*
               gasmal = .false.
               ssmax = ga
               IF( ha.GT.one ) THEN
                  ssmin = fa / ( ga / ha )
               ELSE
                  ssmin = ( fa / ga )*ha
               END IF
               clt = one
               slt = ht / gt
               srt = one
               crt = ft / gt
            END IF
         END IF
         IF( gasmal ) THEN
*
*           Normal case
*
            d = fa - ha
            IF( d.EQ.fa ) THEN
*
*              Copes with infinite F or H
*
               l = one
            ELSE
               l = d / fa
            END IF
*
*           Note that 0 .le. L .le. 1
*
            m = gt / ft
*
*           Note that abs(M) .le. 1/macheps
*
            t = two - l
*
*           Note that T .ge. 1
*
            mm = m*m
            tt = t*t
            s = sqrt( tt+mm )
*
*           Note that 1 .le. S .le. 1 + 1/macheps
*
            IF( l.EQ.zero ) THEN
               r = abs( m )
            ELSE
               r = sqrt( l*l+mm )
            END IF
*
*           Note that 0 .le. R .le. 1 + 1/macheps
*
            a = half*( s+r )
*
*           Note that 1 .le. A .le. 1 + abs(M)
*
            ssmin = ha / a
            ssmax = fa*a
            IF( mm.EQ.zero ) THEN
*
*              Note that M is very tiny
*
               IF( l.EQ.zero ) THEN
                  t = sign( two, ft )*sign( one, gt )
               ELSE
                  t = gt / sign( d, ft ) + m / t
               END IF
            ELSE
               t = ( m / ( s+t )+m / ( r+l ) )*( one+a )
            END IF
            l = sqrt( t*t+four )
            crt = two / l
            srt = t / l
            clt = ( crt+srt*m ) / a
            slt = ( ht / ft )*srt / a
         END IF
      END IF
      IF( swap ) THEN
         csl = srt
         snl = crt
         csr = slt
         snr = clt
      ELSE
         csl = clt
         snl = slt
         csr = crt
         snr = srt
      END IF
*
*     Correct signs of SSMAX and SSMIN
*
      IF( pmax.EQ.1 )
     $   tsign = sign( one, csr )*sign( one, csl )*sign( one, f )
      IF( pmax.EQ.2 )
     $   tsign = sign( one, snr )*sign( one, csl )*sign( one, g )
      IF( pmax.EQ.3 )
     $   tsign = sign( one, snr )*sign( one, snl )*sign( one, h )
      ssmax = sign( ssmax, tsign )
      ssmin = sign( ssmin, tsign*sign( one, f )*sign( one, h ) )
      RETURN
*
*     End of DLASV2
*

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