Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - computes 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

**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. LAPACK auxiliary routine (version 3.2) April 2011 SLAS2(3lapack)