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RedHat 9 (Linux i386) - man page for dlasq2 (redhat section l)

DLASQ2(l)					)					DLASQ2(l)

NAME
       DLASQ2 - compute all the eigenvalues of the symmetric positive definite tridiagonal matrix
       associated with the qd array Z to high relative accuracy are  computed  to  high  relative
       accuracy, in the absence of denormalization, underflow and overflow

SYNOPSIS
       SUBROUTINE DLASQ2( N, Z, INFO )

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION Z( * )

PURPOSE
       DLASQ2  computes all the eigenvalues of the symmetric positive definite tridiagonal matrix
       associated with the qd array Z to high relative accuracy are  computed  to  high  relative
       accuracy,  in the absence of denormalization, underflow and overflow.  To see the relation
       of Z to the tridiagonal matrix, let L be a unit lower bidiagonal matrix with  subdiagonals
       Z(2,4,6,,..)  and  let  U  be  an  upper  bidiagonal  matrix  with  1's above and diagonal
       Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the symmetric tridiagonal to which
       it is similar.

       Note  :	DLASQ2	defines  a logical variable, IEEE, which is true on machines which follow
       ieee-754 floating-point standard in their handling of infinities and NaNs, and false  oth-
       erwise. This variable is passed to DLASQ3.

ARGUMENTS
       N     (input) INTEGER
	     The number of rows and columns in the matrix. N >= 0.

       Z     (workspace) DOUBLE PRECISION array, dimension ( 4*N )
	     On  entry	Z  holds  the  qd  array. On exit, entries 1 to N hold the eigenvalues in
	     decreasing order, Z( 2*N+1 ) holds the trace, and Z( 2*N+2 ) holds the  sum  of  the
	     eigenvalues.  If  N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) holds
	     NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of shifts that failed.

       INFO  (output) INTEGER
	     = 0: successful exit
	     < 0: if the i-th argument is a scalar and had an illegal value, then INFO =  -i,  if
	     the  i-th	argument  is  an  array and the j-entry had an illegal value, then INFO =
	     -(i*100+j) > 0: the algorithm failed = 1, a split was marked by a positive value  in
	     E	=  2,  current	block of Z not diagonalized after 30*N iterations (in inner while
	     loop) = 3, termination criterion of outer while loop not met (program  created  more
	     than N unreduced blocks)

FURTHER DETAILS
       The  shifts are accumulated in SIGMA. Iteration count is in ITER.  Ping-pong is controlled
       by PP (alternates between 0 and 1).

LAPACK version 3.0			   15 June 2000 				DLASQ2(l)


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