SLASV2  -  compute  the  singular value decomposition of a
       2-by-2 triangular matrix [ F G ] [ 0 H ]


SYNOPSIS

       SUBROUTINE SLASV2( F, G, H, SSMIN, SSMAX, SNR,  CSR,  SNL,
                          CSL )

           REAL           CSL,  CSR,  F,  G,  H, SNL, SNR, SSMAX,
                          SSMIN


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
       ].


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
               abs(SSMIN) is the smaller singular value.

       SSMAX   (output) REAL
               abs(SSMAX) is the larger singular value.

       SNL     (output) REAL
               CSL      (output)  REAL The vector (CSL, SNL) is a
               unit left singular vector for the  singular  value
               abs(SSMAX).

       SNR     (output) REAL
               CSR      (output)  REAL The vector (CSR, SNR) is a
               unit right singular vector for the singular  value
               abs(SSMAX).


FURTHER DETAILS

       Any input parameter may be aliased with any output parame­
       ter.

       traction,  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  perturba­
       tions of size near the underflow threshold.


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