redhat man page for slasv2

SLASV2(l)								 )								 SLASV2(l)

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  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.

LAPACK version 3.0						   15 June 2000 							 SLASV2(l)