dlasv2(3)

NAME

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 singu

lar 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 parame

ter.

Barring over/underflow and assuming a guard digit in sub

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 ma

chines with partial overflow, like the Cray, overflow may occur

if the largest singular value is within a factor of 2 of over

flow.)

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

DLASV2(3)