SLASV2(l) ) SLASV2(l)
SLASV2 - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [
0 H ]
SUBROUTINE SLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
REAL CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
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 singu-
lar 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 ].
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).
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)