1DLASV2(1)           LAPACK auxiliary routine (version 3.1)           DLASV2(1)
2
3
4

NAME

6       DLASV2 - the singular value decomposition of a 2-by-2 triangular matrix
7       [ F G ]  [ 0 H ]
8

SYNOPSIS

10       SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
11
12           DOUBLE         PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
13

PURPOSE

15       DLASV2 computes the singular value decomposition of a 2-by-2 triangular
16       matrix
17          [  F   G  ]
18          [   0    H   ].  On return, abs(SSMAX) is the larger singular value,
19       abs(SSMIN) is the smaller singular value, and (CSL,SNL)  and  (CSR,SNR)
20       are  the  left  and  right  singular vectors for abs(SSMAX), giving the
21       decomposition
22
23          [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
24          [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ].
25
26

ARGUMENTS

28       F       (input) DOUBLE PRECISION
29               The (1,1) element of the 2-by-2 matrix.
30
31       G       (input) DOUBLE PRECISION
32               The (1,2) element of the 2-by-2 matrix.
33
34       H       (input) DOUBLE PRECISION
35               The (2,2) element of the 2-by-2 matrix.
36
37       SSMIN   (output) DOUBLE PRECISION
38               abs(SSMIN) is the smaller singular value.
39
40       SSMAX   (output) DOUBLE PRECISION
41               abs(SSMAX) is the larger singular value.
42
43       SNL     (output) DOUBLE PRECISION
44               CSL     (output) DOUBLE PRECISION The vector (CSL,  SNL)  is  a
45               unit left singular vector for the singular value abs(SSMAX).
46
47       SNR     (output) DOUBLE PRECISION
48               CSR      (output)  DOUBLE  PRECISION The vector (CSR, SNR) is a
49               unit right singular vector for the singular value abs(SSMAX).
50

FURTHER DETAILS

52       Any input parameter may be aliased with any output parameter.
53
54       Barring over/underflow and assuming a guard digit in  subtraction,  all
55       output  quantities  are correct to within a few units in the last place
56       (ulps).
57
58       In IEEE arithmetic, the code works correctly if one matrix  element  is
59       infinite.
60
61       Overflow  will not occur unless the largest singular value itself over‐
62       flows or is within a few ulps of overflow. (On  machines  with  partial
63       overflow,  like  the  Cray,  overflow may occur if the largest singular
64       value is within a factor of 2 of overflow.)
65
66       Underflow is harmless if underflow is gradual. Otherwise,  results  may
67       correspond  to  a  matrix  modified  by  perturbations of size near the
68       underflow threshold.
69
70
71
72
73 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLASV2(1)
Impressum