SLASV2(1) LAPACK auxiliary routine (version 3.2) SLASV2(1)NAME
SLASV2 - computes the singular value decomposition of a 2-by-2 triangu‐
lar 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 sin‐
gular 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 over‐
flows 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 (versioNovember 2008 SLASV2(1)
