DLASV2 - compute the singular value decomposition of a
2-by-2 triangular matrix [ F G ] [ 0 H ]
SYNOPSIS
SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL,
CSL )
DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR,
SSMAX, SSMIN
PURPOSE
DLASV2 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) DOUBLE PRECISION
The (1,1) element of the 2-by-2 matrix.
G (input) DOUBLE PRECISION
The (1,2) element of the 2-by-2 matrix.
H (input) DOUBLE PRECISION
The (2,2) element of the 2-by-2 matrix.
SSMIN (output) DOUBLE PRECISION
abs(SSMIN) is the smaller singular value.
SSMAX (output) DOUBLE PRECISION
abs(SSMAX) is the larger singular value.
SNL (output) DOUBLE PRECISION
CSL (output) DOUBLE PRECISION The vector (CSL,
SNL) is a unit left singular vector for the singu
lar value abs(SSMAX).
SNR (output) DOUBLE PRECISION
CSR (output) DOUBLE PRECISION The vector (CSR,
SNR) is a unit right singular vector for the sin
gular 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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