dlasq2.f(3)							      LAPACK							       dlasq2.f(3)

NAME

       dlasq2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlasq2 (N, Z, INFO)
	   DLASQ2

Function/Subroutine Documentation
   subroutine dlasq2 (integerN, double precision, dimension( * )Z, integerINFO)
       DLASQ2

       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 otherwise. This variable
	    is passed to DLASQ3.

       Parameters:
	   N

		     N is INTEGER
		   The number of rows and columns in the matrix. N >= 0.

	   Z

		     Z is 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

		     INFO is 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 100*N
			      iterations (in inner while loop).  On exit Z holds
			      a qd array with the same eigenvalues as the given Z.
			 = 3, termination criterion of outer while loop not met
			      (program created more than N unreduced blocks)

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     Local Variables: I0:N0 defines a current unreduced segment of Z.
	     The shifts are accumulated in SIGMA. Iteration count is in ITER.
	     Ping-pong is controlled by PP (alternates between 0 and 1).

       Definition at line 113 of file dlasq2.f.

Author
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Version 3.4.1							  Sun May 26 2013						       dlasq2.f(3)