There is one prototype of gelsy
available, please see below.
gelsy( MatrixA& a, MatrixB& b, VectorJPVT& jpvt, const Scalar >, int_t& rank );
gelsy
(short for $FRIENDLY_NAME)
provides a C++ interface to LAPACK routines SGELSY, DGELSY, CGELSY, and
ZGELSY. gelsy
computes
the minimum-norm solution to a complex linear least squares problem:
minimize || A * X - B || using a complete orthogonal factorization of
A. A is an M-by-N matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X.
The routine first computes a QR factorization with column pivoting: A * P = Q * [ R11 R12 ] [ 0 R22 ] with R11 defined as the largest leading submatrix whose estimated condition number is less than 1/RCOND. The order of R11, RANK, is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated by unitary transformations from the right, arriving at the complete orthogonal factorization: A * P = Q * [ T11 0 ] * Z [ 0 0 ] The minimum-norm solution is then X = P * Z' [ inv(T11)*Q1'*B ] [ 0 ] where Q1 consists of the first RANK columns of Q.
This routine is basically identical to the original xGELSX except three differences: o The permutation of matrix B (the right hand side) is faster and more simple. o The call to the subroutine xGEQPF has been substituted by the the call to the subroutine xGEQP3. This subroutine is a Blas-3 version of the QR factorization with column pivoting. o Matrix B (the right hand side) is updated with Blas-3.
The selection of the LAPACK routine is done during compile-time, and
is determined by the type of values contained in type MatrixA
.
The type of values is obtained through the value_type
meta-function typename value_type<MatrixA>::type
. The dispatching table below illustrates
to which specific routine the code path will be generated.
Table 1.184. Dispatching of gelsy
Value type of MatrixA |
LAPACK routine |
---|---|
|
SGELSY |
|
DGELSY |
|
CGELSY |
|
ZGELSY |
Defined in header boost/numeric/bindings/lapack/driver/gelsy.hpp
.
Parameters
The definition of term 1
The definition of term 2
The definition of term 3.
Definitions may contain paragraphs.
#include <boost/numeric/bindings/lapack/driver/gelsy.hpp> using namespace boost::numeric::bindings; lapack::gelsy( x, y, z );
this will output
[5] 0 1 2 3 4 5