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## 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.