LAPACK  3.7.0
LAPACK: Linear Algebra PACKage
subroutine slasv2 ( real  F,
real  G,
real  H,
real  SSMIN,
real  SSMAX,
real  SNR,
real  CSR,
real  SNL,
real  CSL 
)

SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

Download SLASV2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SLASV2 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 REAL
          The (1,1) element of the 2-by-2 matrix.
[in]G
          G is REAL
          The (1,2) element of the 2-by-2 matrix.
[in]H
          H is REAL
          The (2,2) element of the 2-by-2 matrix.
[out]SSMIN
          SSMIN is REAL
          abs(SSMIN) is the smaller singular value.
[out]SSMAX
          SSMAX is REAL
          abs(SSMAX) is the larger singular value.
[out]SNL
          SNL is REAL
[out]CSL
          CSL is REAL
          The vector (CSL, SNL) is a unit left singular vector for the
          singular value abs(SSMAX).
[out]SNR
          SNR is REAL
[out]CSR
          CSR is REAL
          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.
Date
December 2016
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.