slartgs()

subroutine slartgs	(	real	x,
		real	y,
		real	sigma,
		real	cs,
		real	sn
	)

SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.

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Purpose:

 SLARTGS generates a plane rotation designed to introduce a bulge in
 Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD
 problem. X and Y are the top-row entries, and SIGMA is the shift.
 The computed CS and SN define a plane rotation satisfying

    [  CS  SN  ]  .  [ X^2 - SIGMA ]  =  [ R ],
    [ -SN  CS  ]     [    X * Y    ]     [ 0 ]

 with R nonnegative.  If X^2 - SIGMA and X * Y are 0, then the
 rotation is by PI/2.

Parameters

[in]	X	X is REAL The (1,1) entry of an upper bidiagonal matrix.
[in]	Y	Y is REAL The (1,2) entry of an upper bidiagonal matrix.
[in]	SIGMA	SIGMA is REAL The shift.
[out]	CS	CS is REAL The cosine of the rotation.
[out]	SN	SN is REAL The sine of the rotation.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.