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.