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[section hesv]

[heading Prototype]
There is one prototype of `hesv` available, please see below.
``
hesv( MatrixA& a, VectorIPIV& ipiv, MatrixB& b );
``


[heading Description]

`hesv` (short for $FRIENDLY_NAME) provides a C++
interface to LAPACK routines SSYSV, DSYSV, CHESV, and ZHESV. 
`hesv` 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.

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 hesv
[  [ Value type of MatrixA ] [LAPACK routine] ]
[  [`float`][SSYSV] ]
[  [`double`][DSYSV] ]
[  [`complex<float>`][CHESV] ]
[  [`complex<double>`][ZHESV] ]

]


[heading Definition]
Defined in header [headerref boost/numeric/bindings/lapack/driver/hesv.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/hesv.hpp>
using namespace boost::numeric::bindings;

lapack::hesv( 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/single/ssysv.f ssysv.f], [@http://www.netlib.org/lapack/double/dsysv.f dsysv.f], [@http://www.netlib.org/lapack/complex/chesv.f chesv.f], and [@http://www.netlib.org/lapack/complex16/zhesv.f zhesv.f] at Netlib.

[endsect]
