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slasv2

 NAME
      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 singu-
      lar value, abs(SSMIN) is the smaller singular value, and
      (CSL,SNL) and (CSR,SNR) are the left and right singular vec-
      tors 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) entry of the 2-by-2 matrix.

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

      H       (input) REAL
              The (2,2) entry 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

      parameter.

      Barring over/underflow and assuming a guard digit in sub-
      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
      entry 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.