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.

Download ZLAIC1 + dependencies [TGZ] [ZIP] [TXT]

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.