dlasq2(l) [redhat man page]

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 otherwise. 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  (pro-
	     gram 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)

slasq2.f(3)							      LAPACK							       slasq2.f(3)

NAME

       slasq2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slasq2 (N, Z, INFO)
	   SLASQ2

Function/Subroutine Documentation
   subroutine slasq2 (integerN, real, dimension( * )Z, integerINFO)
       SLASQ2

       Purpose:

	    SLASQ2 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 : SLASQ2 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 SLASQ3.

       Parameters:
	   N

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

	   Z

		     Z is REAL 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 slasq2.f.

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

Version 3.4.1							  Sun May 26 2013						       slasq2.f(3)