1SLASV2(1)           LAPACK auxiliary routine (version 3.1)           SLASV2(1)
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NAME

6       SLASV2 - the singular value decomposition of a 2-by-2 triangular matrix
7       [ F G ]  [ 0 H ]
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SYNOPSIS

10       SUBROUTINE SLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
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12           REAL           CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
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PURPOSE

15       SLASV2 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
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23          [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
24          [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ].
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ARGUMENTS

28       F       (input) REAL
29               The (1,1) element of the 2-by-2 matrix.
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31       G       (input) REAL
32               The (1,2) element of the 2-by-2 matrix.
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34       H       (input) REAL
35               The (2,2) element of the 2-by-2 matrix.
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37       SSMIN   (output) REAL
38               abs(SSMIN) is the smaller singular value.
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40       SSMAX   (output) REAL
41               abs(SSMAX) is the larger singular value.
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43       SNL     (output) REAL
44               CSL     (output) REAL The vector (CSL, SNL) is a unit left sin‐
45               gular vector for the singular value abs(SSMAX).
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47       SNR     (output) REAL
48               CSR      (output)  REAL  The  vector (CSR, SNR) is a unit right
49               singular vector for the singular value abs(SSMAX).
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FURTHER DETAILS

52       Any input parameter may be aliased with any output parameter.
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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).
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58       In IEEE arithmetic, the code works correctly if one matrix  element  is
59       infinite.
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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.)
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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.
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73 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLASV2(1)
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