1SLASV2(1)           LAPACK auxiliary routine (version 3.2)           SLASV2(1)
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NAME

6       SLASV2 - computes the singular value decomposition of a 2-by-2 triangu‐
7       lar matrix  [ 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
22          [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
23          [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ].
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ARGUMENTS

26       F       (input) REAL
27               The (1,1) element of the 2-by-2 matrix.
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29       G       (input) REAL
30               The (1,2) element of the 2-by-2 matrix.
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32       H       (input) REAL
33               The (2,2) element of the 2-by-2 matrix.
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35       SSMIN   (output) REAL
36               abs(SSMIN) is the smaller singular value.
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38       SSMAX   (output) REAL
39               abs(SSMAX) is the larger singular value.
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41       SNL     (output) REAL
42               CSL     (output) REAL The vector (CSL, SNL) is a unit left sin‐
43               gular vector for the singular value abs(SSMAX).
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45       SNR     (output) REAL
46               CSR      (output)  REAL  The  vector (CSR, SNR) is a unit right
47               singular vector for the singular value abs(SSMAX).
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FURTHER DETAILS

50       Any input parameter may be aliased with any output parameter.   Barring
51       over/underflow  and  assuming  a guard digit in subtraction, all output
52       quantities are correct to within a few units in the last place (ulps).
53       In IEEE arithmetic, the code works correctly if one matrix  element  is
54       infinite.
55       Overflow  will not occur unless the largest singular value itself over‐
56       flows or is within a few ulps of overflow. (On  machines  with  partial
57       overflow,  like  the  Cray,  overflow may occur if the largest singular
58       value is within a factor of 2 of overflow.)
59       Underflow is harmless if underflow is gradual. Otherwise,  results  may
60       correspond  to  a  matrix  modified  by  perturbations of size near the
61       underflow threshold.
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65 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLASV2(1)