DLAS2 (3lapack)

compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]

SYNOPSIS

  SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )

      DOUBLE        PRECISION F, G, H, SSMAX, SSMIN

PURPOSE

  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.

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
          The smaller singular value.

  SSMAX   (output) DOUBLE PRECISION
          The larger singular value.

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.