##### hpsvx

###### Prototype

There is one prototype of `hpsvx` available, please see below.

    hpsvx( const char fact, const MatrixAP& ap, MatrixAFP& afp,
            VectorIPIV& ipiv, const MatrixB& b, MatrixX& x, Scalar >,
            VectorFERR& ferr, VectorBERR& berr );

###### Description

`hpsvx` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SSPSVX, DSPSVX, CHPSVX, and ZHPSVX. `hpsvx` uses the diagonal pivoting factorization A = UD*U*H or A = LD*L*H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format 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 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.

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.

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 1.136. Dispatching of hpsvx

Value type of MatrixAP | LAPACK routine
--- | ---
`float` | SSPSVX
`double` | DSPSVX
`complex<float>` | CHPSVX
`complex<double>` | ZHPSVX

###### Definition

Defined in header `boost/numeric/bindings/lapack/driver/hpsvx.hpp`.

###### Parameters or Requirements on Types

Parameters

MatrixA

  The definition of term 1

MatrixB

  The definition of term 2

MatrixC

  The definition of term 3.

  Definitions may contain paragraphs.

###### Complexity

###### Example

    #include <boost/numeric/bindings/lapack/driver/hpsvx.hpp>
    using namespace boost::numeric::bindings;

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files sspsvx.f, dspsvx.f, chpsvx.f, and zhpsvx.f at Netlib.