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chetrf.f(3)				      LAPACK				      chetrf.f(3)

NAME
       chetrf.f -

SYNOPSIS
   Functions/Subroutines
       subroutine chetrf (UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
	   CHETRF

Function/Subroutine Documentation
   subroutine chetrf (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA,
       integer, dimension( * )IPIV, complex, dimension( * )WORK, integerLWORK, integerINFO)
       CHETRF

       Purpose:

	    CHETRF computes the factorization of a complex Hermitian matrix A
	    using the Bunch-Kaufman diagonal pivoting method.  The form of the
	    factorization is

	       A = U*D*U**H  or  A = L*D*L**H

	    where U (or L) is a product of permutation and unit upper (lower)
	    triangular matrices, and D is Hermitian 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.

       Parameters:
	   UPLO

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

	   N

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

	   A

		     A is COMPLEX array, dimension (LDA,N)
		     On entry, the Hermitian 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.

	   WORK

		     WORK is COMPLEX array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

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

	   INFO

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     If UPLO = 'U', then A = U*D*U**H, where
		U = P(n)*U(n)* ... <em>P(k)U(k)</em> ...,
	     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**H, where
		L = P(1)*L(1)* ... <em>P(k)*L(k)</em> ...,
	     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).

       Definition at line 178 of file chetrf.f.

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

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