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

zhesvx.f(3)				      LAPACK				      zhesvx.f(3)

NAME
       zhesvx.f -

SYNOPSIS
   Functions/Subroutines
       subroutine zhesvx (FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, RCOND,
	   FERR, BERR, WORK, LWORK, RWORK, INFO)
	    ZHESVX computes the solution to system of linear equations A * X = B for HE matrices

Function/Subroutine Documentation
   subroutine zhesvx (characterFACT, characterUPLO, integerN, integerNRHS, complex*16, dimension(
       lda, * )A, integerLDA, complex*16, dimension( ldaf, * )AF, integerLDAF, integer,
       dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension(
       ldx, * )X, integerLDX, double precisionRCOND, double precision, dimension( * )FERR, double
       precision, dimension( * )BERR, complex*16, dimension( * )WORK, integerLWORK, double
       precision, dimension( * )RWORK, integerINFO)
	ZHESVX computes the solution to system of linear equations A * X = B for HE matrices

       Purpose:

	    ZHESVX uses the diagonal pivoting factorization to compute 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.

	    Error bounds on the solution and a condition estimate are also
	    provided.

       Description:

	    The following steps are performed:

	    1. If FACT = 'N', the diagonal pivoting method is used to factor A.
	       The form of the factorization is
		  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.

	    2. If some D(i,i)=0, so that D is exactly singular, then the routine
	       returns with INFO = i. Otherwise, the factored form of A is used
	       to estimate the condition number of the matrix A.  If the
	       reciprocal of the condition number is less than machine precision,
	       INFO = N+1 is returned as a warning, but the routine still goes on
	       to solve for X and compute error bounds as described below.

	    3. The system of equations is solved for X using the factored form
	       of A.

	    4. Iterative refinement is applied to improve the computed solution
	       matrix and calculate error bounds and backward error estimates
	       for it.

       Parameters:
	   FACT

		     FACT is CHARACTER*1
		     Specifies whether or not the factored form of A has been
		     supplied on entry.
		     = 'F':  On entry, AF and IPIV contain the factored form
			     of A.  A, AF and IPIV will not be modified.
		     = 'N':  The matrix A will be copied to AF and factored.

	   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 matrices B and X.  NRHS >= 0.

	   A

		     A is COMPLEX*16 array, dimension (LDA,N)
		     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.

	   LDA

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

	   AF

		     AF is COMPLEX*16 array, dimension (LDAF,N)
		     If FACT = 'F', then AF is an input argument and on entry
		     contains 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.

		     If FACT = 'N', then AF is an output argument and on exit
		     returns 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.

	   LDAF

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

	   IPIV

		     IPIV is INTEGER array, dimension (N)
		     If FACT = 'F', then IPIV is an input argument and on entry
		     contains 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.

		     If FACT = 'N', then IPIV is an output argument and on exit
		     contains details of the interchanges and the block structure
		     of D, as determined by ZHETRF.

	   B

		     B is COMPLEX*16 array, dimension (LDB,NRHS)
		     The N-by-NRHS right hand side matrix B.

	   LDB

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

	   X

		     X is COMPLEX*16 array, dimension (LDX,NRHS)
		     If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.

	   LDX

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

	   RCOND

		     RCOND is DOUBLE PRECISION
		     The estimate of the reciprocal condition number of the matrix
		     A.  If RCOND is less than the machine precision (in
		     particular, if RCOND = 0), the matrix is singular to working
		     precision.  This condition is indicated by a return code of
		     INFO > 0.

	   FERR

		     FERR is DOUBLE PRECISION array, dimension (NRHS)
		     The estimated forward error bound for each solution vector
		     X(j) (the j-th column of the solution matrix X).
		     If XTRUE is the true solution corresponding to X(j), FERR(j)
		     is an estimated upper bound for the magnitude of the largest
		     element in (X(j) - XTRUE) divided by the magnitude of the
		     largest element in X(j).  The estimate is as reliable as
		     the estimate for RCOND, and is almost always a slight
		     overestimate of the true error.

	   BERR

		     BERR is DOUBLE PRECISION array, dimension (NRHS)
		     The componentwise relative backward error of each solution
		     vector X(j) (i.e., the smallest relative change in
		     any element of A or B that makes X(j) an exact solution).

	   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 >= max(1,2*N), and for best
		     performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where
		     NB is the optimal blocksize for ZHETRF.

		     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.

	   RWORK

		     RWORK is DOUBLE PRECISION array, dimension (N)

	   INFO

		     INFO is INTEGER
		     = 0: successful exit
		     < 0: if INFO = -i, the i-th argument had an illegal value
		     > 0: if INFO = i, and i is
			   <= N:  D(i,i) is exactly zero.  The factorization
				  has been completed but the factor D is exactly
				  singular, so the solution and error bounds could
				  not be computed. RCOND = 0 is returned.
			   = N+1: D is nonsingular, but RCOND is less than machine
				  precision, meaning that the matrix is singular
				  to working precision.  Nevertheless, the
				  solution and error bounds are computed because
				  there are a number of situations where the
				  computed solution can be more accurate than the
				  value of RCOND would suggest.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   April 2012

       Definition at line 284 of file zhesvx.f.

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

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


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