Prototype

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

lalsd( const char uplo, const int_t smlsiz,
        const int_t n, VectorD& d, VectorE& e, MatrixB& b,
        const Scalar >, int_t& rank );

Description

lalsd (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SLALSD, DLALSD, CLALSD, and ZLALSD. lalsd uses the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N-by-N upper bidiagonal, and X and B are N-by-NRHS. The solution X overwrites B.

The singular values of A smaller than RCOND times the largest singular value are treated as zero in solving the least squares problem; in this case a minimum norm solution is returned. The actual singular values are returned in D in ascending order.

This code 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 XMP, Cray YMP, 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 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/auxiliary/lalsd.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/auxiliary/lalsd.hpp>
using namespace boost::numeric::bindings;

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also