NAME¶

DLASV2 - computes 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 singular value abs(SSMAX).

SNR (output) DOUBLE PRECISION

CSR (output) DOUBLE PRECISION 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 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.