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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/dlaic1.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/dlaic1.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/dlaic1.f

SYNOPSIS

Functions/Subroutines


subroutine DLAIC1 (job, j, x, sest, w, gamma, sestpr, s, c)
DLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation

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.

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

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 DOUBLE PRECISION array, dimension (J)
!>          The j-vector x.
!>

SEST

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

W

!>          W is DOUBLE PRECISION array, dimension (J)
!>          The j-vector w.
!>

GAMMA

!>          GAMMA is DOUBLE PRECISION
!>          The diagonal element gamma.
!>

SESTPR

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

S

!>          S is DOUBLE PRECISION
!>          Sine needed in forming xhat.
!>

C

!>          C is DOUBLE PRECISION
!>          Cosine needed in forming xhat.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 133 of file dlaic1.f.

Author

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Version 3.12.0 LAPACK