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RedHat 9 (Linux i386) - man page for slasv2 (redhat section l)

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 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 over- flow. (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 per- turbations of size near the underflow threshold. LAPACK version 3.0 15 June 2000 SLASV2(l)


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