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NAME

       LAPACK-3 - computes the singular values of the 2-by-2 matrix  [ F G ]  [ 0 H ]

SYNOPSIS

       SUBROUTINE SLAS2( F, G, H, SSMIN, SSMAX )

           REAL          F, G, H, SSMAX, SSMIN

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.

ARGUMENTS

        F       (input) REAL
                The (1,1) element of the 2-by-2 matrix.

        G       (input) REAL
                The (1,2) element of the 2-by-2 matrix.

        H       (input) REAL
                The (2,2) element of the 2-by-2 matrix.

        SSMIN   (output) REAL
                The smaller singular value.

        SSMAX   (output) REAL
                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.

 LAPACK auxiliary routine (version 3.2)     April 2011                             SLAS2(3lapack)