1SLAS2(1)            LAPACK auxiliary routine (version 3.1)            SLAS2(1)
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NAME

6       SLAS2 - the singular values of the 2-by-2 matrix  [ F G ]  [ 0 H ]
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SYNOPSIS

9       SUBROUTINE SLAS2( F, G, H, SSMIN, SSMAX )
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11           REAL          F, G, H, SSMAX, SSMIN
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PURPOSE

14       SLAS2  computes the singular values of the 2-by-2 matrix
15          [  F   G  ]
16          [   0    H   ].   On return, SSMIN is the smaller singular value and
17       SSMAX is the larger singular value.
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ARGUMENTS

21       F       (input) REAL
22               The (1,1) element of the 2-by-2 matrix.
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24       G       (input) REAL
25               The (1,2) element of the 2-by-2 matrix.
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27       H       (input) REAL
28               The (2,2) element of the 2-by-2 matrix.
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30       SSMIN   (output) REAL
31               The smaller singular value.
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33       SSMAX   (output) REAL
34               The larger singular value.
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FURTHER DETAILS

37       Barring over/underflow, all output quantities are correct to  within  a
38       few  units  in  the  last  place (ulps), even in the absence of a guard
39       digit in addition/subtraction.
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41       In IEEE arithmetic, the code works correctly if one matrix  element  is
42       infinite.
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44       Overflow  will not occur unless the largest singular value itself over‐
45       flows, or is within a few ulps of overflow. (On machines  with  partial
46       overflow,  like  the  Cray,  overflow may occur if the largest singular
47       value is within a factor of 2 of overflow.)
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49       Underflow is harmless if underflow is gradual. Otherwise,  results  may
50       correspond  to  a  matrix  modified  by  perturbations of size near the
51       underflow threshold.
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56 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                        SLAS2(1)