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dsytf2(3P)		    Sun Performance Library		    dsytf2(3P)

NAME
       dsytf2  -  compute the factorization of a real symmetric matrix A using
       the Bunch-Kaufman diagonal pivoting method

SYNOPSIS
       SUBROUTINE DSYTF2(UPLO, N, A, LDA, IPIV, INFO)

       CHARACTER * 1 UPLO
       INTEGER N, LDA, INFO
       INTEGER IPIV(*)
       DOUBLE PRECISION A(LDA,*)

       SUBROUTINE DSYTF2_64(UPLO, N, A, LDA, IPIV, INFO)

       CHARACTER * 1 UPLO
       INTEGER*8 N, LDA, INFO
       INTEGER*8 IPIV(*)
       DOUBLE PRECISION A(LDA,*)

   F95 INTERFACE
       SUBROUTINE SYTF2(UPLO, [N], A, [LDA], IPIV, [INFO])

       CHARACTER(LEN=1) :: UPLO
       INTEGER :: N, LDA, INFO
       INTEGER, DIMENSION(:) :: IPIV
       REAL(8), DIMENSION(:,:) :: A

       SUBROUTINE SYTF2_64(UPLO, [N], A, [LDA], IPIV, [INFO])

       CHARACTER(LEN=1) :: UPLO
       INTEGER(8) :: N, LDA, INFO
       INTEGER(8), DIMENSION(:) :: IPIV
       REAL(8), DIMENSION(:,:) :: A

   C INTERFACE
       #include <sunperf.h>

       void dsytf2(char uplo, int n,  double  *a,  int	lda,  int  *ipiv,  int
		 *info);

       void dsytf2_64(char uplo, long n, double *a, long lda, long *ipiv, long
		 *info);

PURPOSE
       dsytf2 computes the factorization of a real symmetric  matrix  A	 using
       the Bunch-Kaufman diagonal pivoting method:

	  A = U*D*U'  or  A = L*D*L'

       where  U (or L) is a product of permutation and unit upper (lower) tri‐
       angular matrices, U' 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.

ARGUMENTS
       UPLO (input)
		 Specifies  whether  the upper or lower triangular part of the
		 symmetric matrix A is stored:
		 = 'U':	 Upper triangular
		 = 'L':	 Lower triangular

       N (input) The order of the matrix A.  N >= 0.

       A (input/output)
		 On entry, the symmetric matrix A.  If UPLO = 'U', the leading
		 n-by-n upper triangular part of A contains the upper triangu‐
		 lar 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 (input)
		 The leading dimension of the array A.	LDA >= max(1,N).

       IPIV (output)
		 Details of the interchanges and the block structure of D.  If
		 IPIV(k) > 0, then rows and columns k and IPIV(k) were	inter‐
		 changed 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 (output)
		 = 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.

FURTHER DETAILS
       1-96 - Based on modifications by J. Lewis, Boeing Computer Services
	      Company

       If UPLO = 'U', then A = U*D*U', 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', 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).

				  6 Mar 2009			    dsytf2(3P)
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