slaic1(l) [redhat man page]

SLAIC1(l)								 )								 SLAIC1(l)

NAME

       SLAIC1 - applie one step of incremental condition estimation in its simplest version

SYNOPSIS

       SUBROUTINE SLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )

	   INTEGER	  J, JOB

	   REAL 	  C, GAMMA, S, SEST, SESTPR

	   REAL 	  W( J ), X( J )

PURPOSE

       SLAIC1 applies one step of incremental condition estimation in its simplest version: Let x, twonorm(x) = 1, be an approximate singular vec-
       tor 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' 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] * [ alpha ]
						 [ gamma ]

       where  alpha =  x'*w.

ARGUMENTS

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

       SEST    (input) REAL
	       Estimated singular value of j by j matrix L

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

       GAMMA   (input) REAL
	       The diagonal element gamma.

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

       S       (output) REAL
	       Sine needed in forming xhat.

       C       (output) REAL
	       Cosine needed in forming xhat.

LAPACK version 3.0						   15 June 2000 							 SLAIC1(l)

slaic1.f(3)							      LAPACK							       slaic1.f(3)

NAME

       slaic1.f -

SYNOPSIS

   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 (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.

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

Version 3.4.2							  Tue Sep 25 2012						       slaic1.f(3)