Home Man
Search
Today's Posts
Register

Linux & Unix Commands - Search Man Pages

RedHat 9 (Linux i386) - man page for dsytrf (redhat section l)

DSYTRF(l)					)					DSYTRF(l)

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

SYNOPSIS
       SUBROUTINE DSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDA, LWORK, N

	   INTEGER	  IPIV( * )

	   DOUBLE	  PRECISION A( LDA, * ), WORK( * )

PURPOSE
       DSYTRF computes the factorization of a real symmetric matrix  A	using  the  Bunch-Kaufman
       diagonal pivoting method. The form of the factorization is

	  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, and
       D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

       This is the blocked version of the algorithm, calling Level 3 BLAS.

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

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

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the symmetric matrix A.  If UPLO = 'U', the leading N-by-N upper  trian-
	       gular  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     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       IPIV    (output) 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.

       WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The length of WORK.  LWORK >=1.	For best performance LWORK >= N*NB, where  NB  is
	       the block size returned by ILAENV.

	       If  LWORK = -1, then a workspace query is assumed; the routine only calculates the
	       optimal size of the WORK array, returns this value as the first entry of the  WORK
	       array, and no error message related to LWORK is issued by XERBLA.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       >  0:  if INFO = i, D(i,i) 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
       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 trian-
       gle 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 trian-
       gle 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).

LAPACK version 3.0			   15 June 2000 				DSYTRF(l)


All times are GMT -4. The time now is 04:10 AM.

Unix & Linux Forums Content Copyrightę1993-2018. All Rights Reserved.
UNIX.COM Login
Username:
Password:  
Show Password