zhesv.f(3)							      LAPACK								zhesv.f(3)

NAME

       zhesv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zhesv (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
	    ZHESV computes the solution to system of linear equations A * X = B for HE matrices

Function/Subroutine Documentation
   subroutine zhesv (characterUPLO, integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex*16,
       dimension( ldb, * )B, integerLDB, complex*16, dimension( * )WORK, integerLWORK, integerINFO)
	ZHESV computes the solution to system of linear equations A * X = B for HE matrices

       Purpose:

	    ZHESV computes the solution to a complex system of linear equations
	       A * X = B,
	    where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
	    matrices.

	    The diagonal pivoting method is used to factor A as
	       A = U * D * U**H,  if UPLO = 'U', or
	       A = L * D * L**H,  if UPLO = 'L',
	    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.	The factored form of A is then
	    used to solve the system of equations A * X = B.

       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 number of linear equations, i.e., the order of the
		     matrix A.	N >= 0.

	   NRHS

		     NRHS is INTEGER
		     The number of right hand sides, i.e., the number of columns
		     of the matrix B.  NRHS >= 0.

	   A

		     A is COMPLEX*16 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, if INFO = 0, the block diagonal matrix D and the
		     multipliers used to obtain the factor U or L from the
		     factorization A = U*D*U**H or A = L*D*L**H as computed by
		     ZHETRF.

	   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, as
		     determined by ZHETRF.  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.

	   B

		     B is COMPLEX*16 array, dimension (LDB,NRHS)
		     On entry, the N-by-NRHS right hand side matrix B.
		     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

	   LDB

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

	   WORK

		     WORK is COMPLEX*16 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, and for best performance
		     LWORK >= max(1,N*NB), where NB is the optimal blocksize for
		     ZHETRF.
		     for LWORK < N, TRS will be done with Level BLAS 2
		     for LWORK >= N, TRS will be done with Level BLAS 3

		     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

		     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, so the solution could not be computed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 171 of file zhesv.f.

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

Version 3.4.1							  Sun May 26 2013							zhesv.f(3)