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[section iter_posv]

[heading Prototype]
There is one prototype of `iter_posv` available, please see below.
``
iter_posv( MatrixA& a, const MatrixB& b, MatrixX& x,
        int_t& iter );
``


[heading Description]

`iter_posv` (short for $FRIENDLY_NAME) provides a C++
interface to LAPACK routines DSPOSV and ZCPOSV. 
`iter_posv` 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.

`iter_posv` 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.

The selection of the LAPACK routine is done during compile-time, 
and is determined by the type of values contained in type `MatrixA`.
The type of values is obtained through the `value_type` meta-function
 `typename value_type<MatrixA>::type`.
The dispatching table below illustrates to which specific routine 
the code path will be generated. 

[table Dispatching of iter_posv
[  [ Value type of MatrixA ] [LAPACK routine] ]
[  [`double`][DSPOSV] ]
[  [`complex<double>`][ZCPOSV] ]

]


[heading Definition]
Defined in header [headerref boost/numeric/bindings/lapack/driver/iter_posv.hpp].


[heading Parameters or Requirements on Types]

[variablelist Parameters
    [[MatrixA] [The definition of term 1]]
    [[MatrixB] [The definition of term 2]]
    [[MatrixC] [
    The definition of term 3.

    Definitions may contain paragraphs.
    ]]
]


[heading Complexity]


[heading Example]
``
#include <boost/numeric/bindings/lapack/driver/iter_posv.hpp>
using namespace boost::numeric::bindings;

lapack::iter_posv( x, y, z );

``

this will output

``
[5] 0 1 2 3 4 5
``



[heading Notes]


[heading See Also]

* Originating Fortran source files [@http://www.netlib.org/lapack/double/dsposv.f dsposv.f] and [@http://www.netlib.org/lapack/complex16/zcposv.f zcposv.f] at Netlib.

[endsect]
