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[section ppequ]

[heading Prototype]
There is one prototype of `ppequ` available, please see below.
``
ppequ( const MatrixAP& ap, VectorS& s, Scalar >, Scalar > );
``


[heading Description]

`ppequ` (short for $FRIENDLY_NAME) provides a C++
interface to LAPACK routines SPPEQU, DPPEQU, CPPEQU, and ZPPEQU. 
`ppequ` computes row and column scalings intended to equilibrate a
Hermitian positive definite matrix A in packed storage and reduce
its condition number (with respect to the two-norm). S contains the
scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
This choice of S puts the condition number of B within a factor N of
the smallest possible condition number over all possible diagonal
scalings.

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

[table Dispatching of ppequ
[  [ Value type of MatrixAP ] [LAPACK routine] ]
[  [`float`][SPPEQU] ]
[  [`double`][DPPEQU] ]
[  [`complex<float>`][CPPEQU] ]
[  [`complex<double>`][ZPPEQU] ]

]


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

lapack::ppequ( 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/sppequ.f sppequ.f], [@http://www.netlib.org/lapack/double/dppequ.f dppequ.f], [@http://www.netlib.org/lapack/complex/cppequ.f cppequ.f], and [@http://www.netlib.org/lapack/complex16/zppequ.f zppequ.f] at Netlib.

[endsect]
