LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
 All Classes Files Functions Variables Typedefs Macros
slaic1.f File Reference

Go to the source code of this file.

Functions/Subroutines

subroutine slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
 SLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation

subroutine slaic1 ( integer  JOB,
integer  J,
real, dimension( j X,
real  SEST,
real, dimension( j W,
real  GAMMA,
real  SESTPR,
real  S,
real  C 
)

SLAIC1 applies one step of incremental condition estimation.

Download SLAIC1 + dependencies [TGZ] [ZIP] [TXT]
Purpose:
 SLAIC1 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 SLAIC1 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 REAL array, dimension (J)
          The j-vector x.
[in]SEST
          SEST is REAL
          Estimated singular value of j by j matrix L
[in]W
          W is REAL array, dimension (J)
          The j-vector w.
[in]GAMMA
          GAMMA is REAL
          The diagonal element gamma.
[out]SESTPR
          SESTPR is REAL
          Estimated singular value of (j+1) by (j+1) matrix Lhat.
[out]S
          S is REAL
          Sine needed in forming xhat.
[out]C
          C is REAL
          Cosine needed in forming xhat.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
September 2012

Definition at line 135 of file slaic1.f.

Here is the call graph for this function:

Here is the caller graph for this function: