slasv2(3)

NAME

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 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) 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.

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

SLASV2(3)