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slaed3.f(3)				      LAPACK				      slaed3.f(3)

NAME
       slaed3.f -

SYNOPSIS
   Functions/Subroutines
       subroutine slaed3 (K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO)
	   SLAED3 used by sstedc. Finds the roots of the secular equation and updates the
	   eigenvectors. Used when the original matrix is tridiagonal.

Function/Subroutine Documentation
   subroutine slaed3 (integerK, integerN, integerN1, real, dimension( * )D, real, dimension( ldq,
       * )Q, integerLDQ, realRHO, real, dimension( * )DLAMDA, real, dimension( * )Q2, integer,
       dimension( * )INDX, integer, dimension( * )CTOT, real, dimension( * )W, real, dimension( *
       )S, integerINFO)
       SLAED3 used by sstedc. Finds the roots of the secular equation and updates the
       eigenvectors. Used when the original matrix is tridiagonal.

       Purpose:

	    SLAED3 finds the roots of the secular equation, as defined by the
	    values in D, W, and RHO, between 1 and K.  It makes the
	    appropriate calls to SLAED4 and then updates the eigenvectors by
	    multiplying the matrix of eigenvectors of the pair of eigensystems
	    being combined by the matrix of eigenvectors of the K-by-K system
	    which is solved here.

	    This code makes very mild assumptions about floating point
	    arithmetic. It will work on machines with a guard digit in
	    add/subtract, or on those binary machines without guard digits
	    which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
	    It could conceivably fail on hexadecimal or decimal machines
	    without guard digits, but we know of none.

       Parameters:
	   K

		     K is INTEGER
		     The number of terms in the rational function to be solved by
		     SLAED4.  K >= 0.

	   N

		     N is INTEGER
		     The number of rows and columns in the Q matrix.
		     N >= K (deflation may result in N>K).

	   N1

		     N1 is INTEGER
		     The location of the last eigenvalue in the leading submatrix.
		     min(1,N) <= N1 <= N/2.

	   D

		     D is REAL array, dimension (N)
		     D(I) contains the updated eigenvalues for
		     1 <= I <= K.

	   Q

		     Q is REAL array, dimension (LDQ,N)
		     Initially the first K columns are used as workspace.
		     On output the columns 1 to K contain
		     the updated eigenvectors.

	   LDQ

		     LDQ is INTEGER
		     The leading dimension of the array Q.  LDQ >= max(1,N).

	   RHO

		     RHO is REAL
		     The value of the parameter in the rank one update equation.
		     RHO >= 0 required.

	   DLAMDA

		     DLAMDA is REAL array, dimension (K)
		     The first K elements of this array contain the old roots
		     of the deflated updating problem.	These are the poles
		     of the secular equation. May be changed on output by
		     having lowest order bit set to zero on Cray X-MP, Cray Y-MP,
		     Cray-2, or Cray C-90, as described above.

	   Q2

		     Q2 is REAL array, dimension (LDQ2, N)
		     The first K columns of this matrix contain the non-deflated
		     eigenvectors for the split problem.

	   INDX

		     INDX is INTEGER array, dimension (N)
		     The permutation used to arrange the columns of the deflated
		     Q matrix into three groups (see SLAED2).
		     The rows of the eigenvectors found by SLAED4 must be likewise
		     permuted before the matrix multiply can take place.

	   CTOT

		     CTOT is INTEGER array, dimension (4)
		     A count of the total number of the various types of columns
		     in Q, as described in INDX.  The fourth column type is any
		     column which has been deflated.

	   W

		     W is REAL array, dimension (K)
		     The first K elements of this array contain the components
		     of the deflation-adjusted updating vector. Destroyed on
		     output.

	   S

		     S is REAL array, dimension (N1 + 1)*K
		     Will contain the eigenvectors of the repaired matrix which
		     will be multiplied by the previously accumulated eigenvectors
		     to update the system.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.
		     > 0:  if INFO = 1, an eigenvalue did not converge

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
	    Modified by Francoise Tisseur, University of Tennessee

       Definition at line 185 of file slaed3.f.

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

Version 3.4.2				 Tue Sep 25 2012			      slaed3.f(3)
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