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dsytf2_rook.f(3)		    LAPACK		      dsytf2_rook.f(3)

NAME
       dsytf2_rook.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dsytf2_rook (UPLO, N, A, LDA, IPIV, INFO)
	   DSYTF2_ROOK computes the factorization of a real symmetric
	   indefinite matrix using the bounded Bunch-Kaufman ('rook') diagonal
	   pivoting method (unblocked algorithm).

Function/Subroutine Documentation
   subroutine dsytf2_rook (characterUPLO, integerN, double precision,
       dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV,
       integerINFO)
       DSYTF2_ROOK computes the factorization of a real symmetric indefinite
       matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting
       method (unblocked algorithm).

       Purpose:

	    DSYTF2_ROOK computes the factorization of a real symmetric matrix A
	    using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:

	       A = U*D*U**T  or	 A = L*D*L**T

	    where U (or L) is a product of permutation and unit upper (lower)
	    triangular matrices, U**T is the transpose of U, and D is symmetric and
	    block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

	    This is the unblocked version of the algorithm, calling Level 2 BLAS.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     Specifies whether the upper or lower triangular part of the
		     symmetric matrix A is stored:
		     = 'U':  Upper triangular
		     = 'L':  Lower triangular

	   N

		     N is INTEGER
		     The order of the matrix A.	 N >= 0.

	   A

		     A is DOUBLE PRECISION array, dimension (LDA,N)
		     On entry, the symmetric matrix A.	If UPLO = 'U', the leading
		     n-by-n upper triangular part of A contains the upper
		     triangular part of the matrix A, and the strictly lower
		     triangular part of A is not referenced.  If UPLO = 'L', the
		     leading n-by-n lower triangular part of A contains the lower
		     triangular part of the matrix A, and the strictly upper
		     triangular part of A is not referenced.

		     On exit, the block diagonal matrix D and the multipliers used
		     to obtain the factor U or L (see below for further details).

	   LDA

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

	   IPIV

		     IPIV is INTEGER array, dimension (N)
		     Details of the interchanges and the block structure of D.

		     If UPLO = 'U':
			If IPIV(k) > 0, then rows and columns k and IPIV(k)
			were interchanged and D(k,k) is a 1-by-1 diagonal block.

			If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
			columns k and -IPIV(k) were interchanged and rows and
			columns k-1 and -IPIV(k-1) were inerchaged,
			D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

		     If UPLO = 'L':
			If IPIV(k) > 0, then rows and columns k and IPIV(k)
			were interchanged and D(k,k) is a 1-by-1 diagonal block.

			If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
			columns k and -IPIV(k) were interchanged and rows and
			columns k+1 and -IPIV(k+1) were inerchaged,
			D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

	   INFO

		     INFO is INTEGER
		     = 0: successful exit
		     < 0: if INFO = -k, the k-th argument had an illegal value
		     > 0: if INFO = k, D(k,k) is exactly zero.	The factorization
			  has been completed, but the block diagonal matrix D is
			  exactly singular, and division by zero will occur if it
			  is used to solve a system of equations.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2013

       Further Details:

	     If UPLO = 'U', then A = U*D*U**T, where
		U = P(n)*U(n)* ... *P(k)U(k)* ...,
	     i.e., U is a product of terms P(k)*U(k), where k decreases from n to
	     1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
	     and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
	     defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
	     that if the diagonal block D(k) is of order s (s = 1 or 2), then

			(   I	 v    0	  )   k-s
		U(k) =	(   0	 I    0	  )   s
			(   0	 0    I	  )   n-k
			   k-s	 s   n-k

	     If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
	     If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
	     and A(k,k), and v overwrites A(1:k-2,k-1:k).

	     If UPLO = 'L', then A = L*D*L**T, where
		L = P(1)*L(1)* ... *P(k)*L(k)* ...,
	     i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
	     n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
	     and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
	     defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
	     that if the diagonal block D(k) is of order s (s = 1 or 2), then

			(   I	 0     0   )  k-1
		L(k) =	(   0	 I     0   )  s
			(   0	 v     I   )  n-k-s+1
			   k-1	 s  n-k-s+1

	     If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
	     If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
	     and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

       Contributors:

	     November 2013,	Igor Kozachenko,
			     Computer Science Division,
			     University of California, Berkeley

	     September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
			     School of Mathematics,
			     University of Manchester

	     01-01-96 - Based on modifications by
	       J. Lewis, Boeing Computer Services Company
	       A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville abd , USA

       Definition at line 195 of file dsytf2_rook.f.

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

Version 3.4.2			Sat Nov 16 2013		      dsytf2_rook.f(3)
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