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 ].

F

          F is REAL


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

G

          G is REAL


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

H

          H is REAL


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

SSMIN

          SSMIN is REAL


          abs(SSMIN) is the smaller singular value.

SSMAX

          SSMAX is REAL


          abs(SSMAX) is the larger singular value.

SNL

          SNL is REAL

CSL

          CSL is REAL


          The vector (CSL, SNL) is a unit left singular vector for the


          singular value abs(SSMAX).

SNR

          SNR is REAL

CSR

          CSR is REAL


          The vector (CSR, SNR) is a unit right singular vector for the


          singular value abs(SSMAX).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

  Any input parameter may be aliased with any output parameter.


  Barring over/underflow and assuming a guard digit in subtraction, 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 perturbations of size near


  the underflow threshold.