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CentOS 7.0 - man page for dsytf2 (centos section 3)

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dsytf2.f(3)				      LAPACK				      dsytf2.f(3)

NAME
       dsytf2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dsytf2 (UPLO, N, A, LDA, IPIV, INFO)
	   DSYTF2 computes the factorization of a real symmetric indefinite matrix, using the
	   diagonal pivoting method (unblocked algorithm).

Function/Subroutine Documentation
   subroutine dsytf2 (characterUPLO, integerN, double precision, dimension( lda, * )A,
       integerLDA, integer, dimension( * )IPIV, integerINFO)
       DSYTF2 computes the factorization of a real symmetric indefinite matrix, using the
       diagonal pivoting method (unblocked algorithm).

       Purpose:

	    DSYTF2 computes the factorization of a real symmetric matrix A using
	    the Bunch-Kaufman 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 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 UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
		     columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
		     is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
		     IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
		     interchanged and 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:
	   September 2012

       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:

	     09-29-06 - patch from
	       Bobby Cheng, MathWorks

	       Replace l.204 and l.372
		    IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
	       by
		    IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN

	     01-01-96 - Based on modifications by
	       J. Lewis, Boeing Computer Services Company
	       A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
	     1-96 - Based on modifications by J. Lewis, Boeing Computer Services
		    Company

       Definition at line 186 of file dsytf2.f.

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

Version 3.4.2				 Tue Sep 25 2012			      dsytf2.f(3)
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