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claic1.f(3)				      LAPACK				      claic1.f(3)

NAME
       claic1.f -

SYNOPSIS
   Functions/Subroutines
       subroutine claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
	   CLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation
   subroutine claic1 (integerJOB, integerJ, complex, dimension( j )X, realSEST, complex,
       dimension( j )W, complexGAMMA, realSESTPR, complexS, complexC)
       CLAIC1 applies one step of incremental condition estimation.

       Purpose:

	    CLAIC1 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 CLAIC1 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 array, dimension (J)
		     The j-vector x.

	   SEST

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

	   W

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

	   GAMMA

		     GAMMA is COMPLEX
		     The diagonal element gamma.

	   SESTPR

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

	   S

		     S is COMPLEX
		     Sine needed in forming xhat.

	   C

		     C is COMPLEX
		     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 136 of file claic1.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      claic1.f(3)
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