zcposv.f(3)							      LAPACK							       zcposv.f(3)

NAME

       zcposv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zcposv (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO)
	    ZCPOSV computes the solution to system of linear equations A * X = B for PO matrices

Function/Subroutine Documentation
   subroutine zcposv (characterUPLO, integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B,
       integerLDB, complex*16, dimension( ldx, * )X, integerLDX, complex*16, dimension( n, * )WORK, complex, dimension( * )SWORK, double
       precision, dimension( * )RWORK, integerITER, integerINFO)
	ZCPOSV computes the solution to system of linear equations A * X = B for PO matrices

       Purpose:

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

	    ZCPOSV first attempts to factorize the matrix in COMPLEX and use this
	    factorization within an iterative refinement procedure to produce a
	    solution with COMPLEX*16 normwise backward error quality (see below).
	    If the approach fails the method switches to a COMPLEX*16
	    factorization and solve.

	    The iterative refinement is not going to be a winning strategy if
	    the ratio COMPLEX performance over COMPLEX*16 performance is too
	    small. A reasonable strategy should take the number of right-hand
	    sides and the size of the matrix into account. This might be done
	    with a call to ILAENV in the future. Up to now, we always try
	    iterative refinement.

	    The iterative refinement process is stopped if
		ITER > ITERMAX
	    or for all the RHS we have:
		RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
	    where
		o ITER is the number of the current iteration in the iterative
		  refinement process
		o RNRM is the infinity-norm of the residual
		o XNRM is the infinity-norm of the solution
		o ANRM is the infinity-operator-norm of the matrix A
		o EPS is the machine epsilon returned by DLAMCH('Epsilon')
	    The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
	    respectively.

       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.

		     Note that the imaginary parts of the diagonal
		     elements need not be set and are assumed to be zero.

		     On exit, if iterative refinement has been successfully used
		     (INFO.EQ.0 and ITER.GE.0, see description below), then A is
		     unchanged, if double precision factorization has been used
		     (INFO.EQ.0 and ITER.LT.0, see description below), then the
		     array A contains the factor U or L from the Cholesky
		     factorization A = U**H*U or A = L*L**H.

	   LDA

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

	   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, the N-by-NRHS solution matrix X.

	   LDX

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

	   WORK

		     WORK is COMPLEX*16 array, dimension (N*NRHS)
		     This array is used to hold the residual vectors.

	   SWORK

		     SWORK is COMPLEX array, dimension (N*(N+NRHS))
		     This array is used to use the single precision matrix and the
		     right-hand sides or solutions in single precision.

	   RWORK

		     RWORK is DOUBLE PRECISION array, dimension (N)

	   ITER

		     ITER is INTEGER
		     < 0: iterative refinement has failed, COMPLEX*16
			  factorization has been performed
			  -1 : the routine fell back to full precision for
			       implementation- or machine-specific reasons
			  -2 : narrowing the precision induced an overflow,
			       the routine fell back to full precision
			  -3 : failure of CPOTRF
			  -31: stop the iterative refinement after the 30th
			       iterations
		     > 0: iterative refinement has been sucessfully used.
			  Returns the number of iterations

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value
		     > 0:  if INFO = i, the leading minor of order i of
			   (COMPLEX*16) A is not positive definite, so the
			   factorization could not be completed, and the solution
			   has not been computed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 209 of file zcposv.f.

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

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