zlaic1.f man page

zlaic1.f —

Synopsis

Functions/Subroutines

subroutine zlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
ZLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation

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.  

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:

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 COMPLEX*16 array, dimension (J)
          The j-vector x.

SEST

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

W

          W is COMPLEX*16 array, dimension (J)
          The j-vector w.

GAMMA

          GAMMA is COMPLEX*16
          The diagonal element gamma.

SESTPR

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

S

          S is COMPLEX*16
          Sine needed in forming xhat.

C

          C is COMPLEX*16
          Cosine needed in forming xhat.
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 137 of file zlaic1.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zlaic1(3) is an alias of zlaic1.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK