zlaic1()

subroutine zlaic1	(	integer	job,
		integer	j,
		complex*16, dimension( j )	x,
		double precision	sest,
		complex*16, dimension( j )	w,
		complex*16	gamma,
		double precision	sestpr,
		complex*16	s,
		complex*16	c )

ZLAIC1 applies one step of incremental condition estimation.

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Purpose:

!>
!> ZLAIC1 applies one step of incremental condition estimation in
!> its simplest version:
!>
!> Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j
!> lower triangular matrix L, such that
!>          twonorm(L*x) = sest
!> Then ZLAIC1 computes sestpr, s, c such that
!> the vector
!>                 [ s*x ]
!>          xhat = [  c  ]
!> is an approximate singular vector of
!>                 [ L       0  ]
!>          Lhat = [ w**H gamma ]
!> in the sense that
!>          twonorm(Lhat*xhat) = sestpr.
!>
!> Depending on JOB, an estimate for the largest or smallest singular
!> value is computed.
!>
!> Note that [s c]**H and sestpr**2 is an eigenpair of the system
!>
!>     diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
!>                                           [ conjg(gamma) ]
!>
!> where  alpha =  x**H * w.
!> 

Parameters

[in]	JOB	!> JOB is INTEGER !> = 1: an estimate for the largest singular value is computed. !> = 2: an estimate for the smallest singular value is computed. !>
[in]	J	!> J is INTEGER !> Length of X and W !>
[in]	X	!> X is COMPLEX*16 array, dimension (J) !> The j-vector x. !>
[in]	SEST	!> SEST is DOUBLE PRECISION !> Estimated singular value of j by j matrix L !>
[in]	W	!> W is COMPLEX*16 array, dimension (J) !> The j-vector w. !>
[in]	GAMMA	!> GAMMA is COMPLEX*16 !> The diagonal element gamma. !>
[out]	SESTPR	!> SESTPR is DOUBLE PRECISION !> Estimated singular value of (j+1) by (j+1) matrix Lhat. !>
[out]	S	!> S is COMPLEX*16 !> Sine needed in forming xhat. !>
[out]	C	!> C is COMPLEX*16 !> Cosine needed in forming xhat. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.