Prototype

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

bdsqr( const char uplo, const int_t n, VectorD& d,
        VectorE& e, MatrixVT& vt, MatrixU& u, MatrixC& c );

Description

bdsqr (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SBDSQR, DBDSQR, CBDSQR, and ZBDSQR. bdsqr computes the singular values and, optionally, the right and/or left singular vectors from the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B using the implicit zero-shift QR algorithm. The SVD of B has the form

B = Q * S * P**H

where S is the diagonal matrix of singular values, Q is an orthogonal matrix of left singular vectors, and P is an orthogonal matrix of right singular vectors. If left singular vectors are requested, this subroutine actually returns UQ instead of Q, and, if right singular vectors are requested, this subroutine returns PH*VT instead of P*H, for given complex input matrices U and VT. When U and VT are the unitary matrices that reduce a general matrix A to bidiagonal form: A = U*B*VT, as computed by ZGEBRD, then

A = (UQ) * S * (P*H*VT)

is the SVD of A. Optionally, the subroutine may also compute Q**H*C for a given complex input matrix C.

See "Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11, no. 5, pp. 873-912, Sept 1990) and "Accurate singular values and differential qd algorithms," by B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics Department, University of California at Berkeley, July 1992 for a detailed description of the algorithm.

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

Definition

Defined in header boost/numeric/bindings/lapack/computational/bdsqr.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/computational/bdsqr.hpp>
using namespace boost::numeric::bindings;

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also