slaic1.f (3)

Functions/Subroutines

subroutine slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)

SLAIC1 applies one step of incremental condition estimation.

subroutine slaic1 (integerJOB, integerJ, real, dimension( j )X, realSEST, real, dimension( j )W, realGAMMA, realSESTPR, realS, realC)

SLAIC1 applies one step of incremental condition estimation.

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:

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 REAL array, dimension (J)
          The j-vector x.

SEST

          SEST is REAL
          Estimated singular value of j by j matrix L

W

          W is REAL array, dimension (J)
          The j-vector w.

GAMMA

          GAMMA is REAL
          The diagonal element gamma.

SESTPR

          SESTPR is REAL
          Estimated singular value of (j+1) by (j+1) matrix Lhat.

S

          S is REAL
          Sine needed in forming xhat.

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.

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