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hbgvd
Prototype

There is one prototype of hbgvd available, please see below.

hbgvd( const char jobz, MatrixAB& ab, MatrixBB& bb, VectorW& w,
        MatrixZ& z );

Description

hbgvd (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SSBGVD, DSBGVD, CHBGVD, and ZHBGVD. hbgvd computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

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

Table 1.107. Dispatching of hbgvd

Value type of MatrixAB

LAPACK routine

float

SSBGVD

double

DSBGVD

complex<float>

CHBGVD

complex<double>

ZHBGVD


Definition

Defined in header boost/numeric/bindings/lapack/driver/hbgvd.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/hbgvd.hpp>
using namespace boost::numeric::bindings;

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

this will output

[5] 0 1 2 3 4 5

Notes
See Also

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