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 parame
ter.
traction, 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 perturba
tions of size near the underflow threshold.
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