Object-oriented Scientific Computing Library: Version 0.910
Namespaces | Functions
householder_base.h File Reference

File for Householder transformations. More...

#include <gsl/gsl_machine.h>
#include <o2scl/err_hnd.h>
#include <o2scl/cblas.h>
#include <o2scl/permutation.h>
#include <o2scl/vec_arith.h>

Go to the source code of this file.


Detailed Description

Todo:
Better documentation for the Householder functions.

Definition in file householder_base.h.

Namespaces

namespace  o2scl_linalg
 

The namespace for linear algebra classes and functions.


Functions

template<class vec_t >
double o2scl_linalg::householder_transform (const size_t n, vec_t &v)
 Replace the vector v with a Householder vector and a coefficient tau that annihilates v[1] through v[n-1] (inclusive)
template<class mat_t >
double o2scl_linalg::householder_transform_subcol (mat_t &A, const size_t ir, const size_t ic, const size_t M)
 Compute the Householder transform of a vector formed with n rows of a column of a matrix.
template<class mat_t >
double o2scl_linalg::householder_transform_subrow (mat_t &A, const size_t ir, const size_t ic, const size_t N)
 Compute the Householder transform of a vector formed with the last n columns of a row of a matrix.
template<class vec_t , class mat_t >
void o2scl_linalg::householder_hm (const size_t M, const size_t N, double tau, const vec_t &v, mat_t &A)
 Apply a Householder transformation $ (v,\tau) $ to matrix $ A $ of size $ M $ by $ N $.
template<class mat_t >
void o2scl_linalg::householder_hm_sub (mat_t &M, const size_t ir, const size_t ic, const size_t nr, const size_t nc, const mat_t &M2, const size_t ir2, const size_t ic2, double tau)
 Apply a Householder transformation to submatrix of a larger matrix.
template<class mat1_t , class mat2_t >
void o2scl_linalg::householder_hm_sub2 (const size_t M, const size_t ic, double tau, const mat1_t &mv, mat2_t &A)
 Special version of Householder transformation for QR_unpack()
template<class vec_t , class vec2_t >
void o2scl_linalg::householder_hv (const size_t N, double tau, const vec_t &v, vec2_t &w)
 Apply a Householder transformation v to vector w.
template<class mat_t , class vec_t >
void o2scl_linalg::householder_hv_subcol (const mat_t &A, vec_t &w, double tau, const size_t ie, const size_t N)
 Apply a Householder transformation v to vector w where v is stored as a column in a matrix A.
template<class mat_t >
void o2scl_linalg::householder_hm1 (const size_t M, const size_t N, double tau, mat_t &A)
 Apply a Householder transformation $ (v,\tau) $ to a matrix being build up from the identity matrix, using the first column of A as a Householder vector.
template<class vec_t , class mat_t >
void o2scl_linalg::householder_mh (const size_t M, const size_t N, double tau, const vec_t &v, mat_t &A)
 Apply the Householder transformation (v,tau) to the right-hand side of the matrix A.
template<class mat_t , class mat2_t >
void o2scl_linalg::householder_mh_sub (mat_t &M, const size_t ir, const size_t ic, const size_t nr, const size_t nc, const mat2_t &M2, const size_t ir2, const size_t ic2, double tau)
 Apply the Householder transformation (v,tau) to the right-hand side of the matrix A.
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