LAPACK  3.7.0
LAPACK: Linear Algebra PACKage

◆ slas2()

subroutine slas2 ( real  F,
real  G,
real  H,
real  SSMIN,
real  SSMAX 
)

SLAS2 computes singular values of a 2-by-2 triangular matrix.

Download SLAS2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SLAS2  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.
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
          The smaller singular value.
[out]SSMAX
          SSMAX is REAL
          The larger singular value.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016
Further Details:
  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.