LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dlaic1()

subroutine dlaic1 ( integer job,
integer j,
double precision, dimension( j ) x,
double precision sest,
double precision, dimension( j ) w,
double precision gamma,
double precision sestpr,
double precision s,
double precision c )

DLAIC1 applies one step of incremental condition estimation.

Download DLAIC1 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> DLAIC1 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 DLAIC1 computes sestpr, s, c such that
!> the vector
!>                 [ s*x ]
!>          xhat = [  c  ]
!> is an approximate singular vector of
!>                 [ L       0  ]
!>          Lhat = [ w**T 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]**T and sestpr**2 is an eigenpair of the system
!>
!>     diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]
!>                                           [ gamma ]
!>
!> where  alpha =  x**T*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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (J)
!>          The j-vector w.
!>
[in]GAMMA
!>          GAMMA is DOUBLE PRECISION
!>          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 DOUBLE PRECISION
!>          Sine needed in forming xhat.
!>
[out]C
!>          C is DOUBLE PRECISION
!>          Cosine needed in forming xhat.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.