slasv2(3S)

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

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
     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 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.


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

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