zlaic1.f3

!>
!> 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.
!> 

JOB

!>          JOB is INTEGER
!>          = 1: an estimate for the largest singular value is computed.
!>          = 2: an estimate for the smallest singular value is computed.
!> 

J

!>          J is INTEGER
!>          Length of X and W
!> 

X

!>          X is COMPLEX*16 array, dimension (J)
!>          The j-vector x.
!> 

SEST

!>          SEST is DOUBLE PRECISION
!>          Estimated singular value of j by j matrix L
!> 

W

!>          W is COMPLEX*16 array, dimension (J)
!>          The j-vector w.
!> 

GAMMA

!>          GAMMA is COMPLEX*16
!>          The diagonal element gamma.
!> 

SESTPR

!>          SESTPR is DOUBLE PRECISION
!>          Estimated singular value of (j+1) by (j+1) matrix Lhat.
!> 

S

!>          S is COMPLEX*16
!>          Sine needed in forming xhat.
!> 

C

!>          C is COMPLEX*16
!>          Cosine needed in forming xhat.
!> 

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