slas2(3S)

NAME
     SLAS2 - compute 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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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