ZLAIC1 - Online Linux Manual PageSection : 1
Updated : November 2008
Source : LAPACK auxiliary routine (version 3.2)
Note : LAPACK auxiliary routine (version 3.2)

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NAMEZLAIC1 - applies one step of incremental condition estimation in its simplest version

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SYNOPSISSUBROUTINE ZLAIC1(  JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )  INTEGER J, JOB  DOUBLE PRECISION SEST, SESTPR  COMPLEX*16 C, GAMMA, S  COMPLEX*16 W( J ), X( J )

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PURPOSEZLAIC1 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' 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]' and sestpr**2 is an eigenpair of the system
    diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ]
                                          [ conjg(gamma) ] where alpha = conjg(x)'*w.

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ARGUMENTSJOB (input) INTEGER  = 1: an estimate for the largest singular value is computed.
= 2: an estimate for the smallest singular value is computed. J (input) INTEGER  Length of X and W X (input) COMPLEX*16 array, dimension (J)  The j-vector x. SEST (input) DOUBLE PRECISION  Estimated singular value of j by j matrix L W (input) COMPLEX*16 array, dimension (J)  The j-vector w. GAMMA (input) COMPLEX*16  The diagonal element gamma. SESTPR (output) DOUBLE PRECISION  Estimated singular value of (j+1) by (j+1) matrix Lhat. S (output) COMPLEX*16  Sine needed in forming xhat. C (output) COMPLEX*16  Cosine needed in forming xhat. 0

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Johanes Gumabo

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