slasq2.f(3) [centos man page]

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

NAME

       slasq2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slasq2 (N, Z, INFO)
	   SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high
	   relative accuracy. Used by sbdsqr and sstegr.

Function/Subroutine Documentation
   subroutine slasq2 (integerN, real, dimension( * )Z, integerINFO)
       SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative
       accuracy. Used by sbdsqr and sstegr.

       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:
	   September 2012

       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 3.4.2							  Tue Sep 25 2012						       slasq2.f(3)

Check Out this Related 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)

Linux and UNIX Man Pages

slasq2.f(3) [centos man page]

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