Public Types | Public Member Functions | List of all members
o2scl::mroot_hybrids_base Class Reference

Base functions for mroot_hybrids. More...

#include <mroot_hybrids.h>

Inheritance diagram for o2scl::mroot_hybrids_base:
o2scl::mroot_hybrids< func_t, vec_t, mat_t, jfunc_t > o2scl::mroot_hybrids_arma_qr_econ< func_t, vec_t, mat_t, jfunc_t > o2scl::mroot_hybrids_eigen< func_t, vec_t, mat_t, jfunc_t >

Public Types

typedef boost::numeric::ublas::vector< double > ubvector
typedef boost::numeric::ublas::matrix< double > ubmatrix

Public Member Functions

double compute_actual_reduction (double fnorm0, double fnorm1)
 Compute the actual reduction.
double compute_predicted_reduction (double fnorm0, double fnorm1)
 Compute the predicted reduction phi1p=|Q^T f + R dx|.
template<class vec2_t , class mat_t >
void compute_Rg (size_t N, const mat_t &r2, const ubvector &gradient2, vec2_t &Rg)
 Compute $ R \cdot g $ where g is the gradient.
template<class vec2_t >
void compute_wv (size_t n, const ubvector &qtdf2, const ubvector &rdx2, const vec2_t &dx2, const ubvector &diag2, double pnorm, ubvector &w2, ubvector &v2)
 Compute w and v.
template<class vec2_t , class mat_t >
void compute_rdx (size_t N, const mat_t &r2, const vec2_t &dx2, ubvector &rdx2)
 Compute $ R \cdot \mathrm{dx} $.
template<class vec2_t , class vec3_t >
double scaled_enorm (size_t n, const vec2_t &d, const vec3_t &ff)
 Compute the norm of the vector $ \vec{v} $ defined by $ v_i = d_i ff_i $.
template<class vec2_t >
double compute_delta (size_t n, ubvector &diag2, vec2_t &x2)
 Compute delta.
template<class vec2_t >
double enorm (size_t N, const vec2_t &ff)
 Compute the Euclidean norm of ff. More...
double enorm_sum (size_t n, const ubvector &a, const ubvector &b)
 Compute the Euclidean norm of the sum of a and b.
template<class vec2_t >
int compute_trial_step (size_t N, vec2_t &xl, vec2_t &dxl, vec2_t &xx_trial)
 Compute a trial step and put the result in xx_trial. More...
template<class vec2_t >
int compute_df (size_t n, const vec2_t &ff_trial, const vec2_t &fl, ubvector &dfl)
 Compute the change in the function value. More...
template<class mat2_t >
void compute_diag (size_t n, const mat2_t &J2, ubvector &diag2)
 Compute diag, the norm of the columns of the Jacobian.
template<class vec2_t , class vec3_t , class vec4_t >
void compute_qtf (size_t N, const vec2_t &q2, const vec3_t &f2, vec4_t &qtf2)
 Compute $ Q^{T} f $. More...
template<class mat2_t >
void update_diag (size_t n, const mat2_t &J2, ubvector &diag2)
 Update diag.
template<class vec2_t >
void scaled_addition (size_t N, double alpha, ubvector &newton2, double beta, ubvector &gradient2, vec2_t &pp)
 Form appropriate convex combination of the Gauss-Newton direction and the scaled gradient direction. More...
template<class mat_t >
int newton_direction (const size_t N, const mat_t &r2, const ubvector &qtf2, ubvector &p)
 Compute the Gauss-Newton direction.
template<class mat_t >
void gradient_direction (const size_t M, const size_t N, const mat_t &r2, const ubvector &qtf2, const ubvector &diag2, ubvector &g)
 Compute the gradient direction.
void minimum_step (const size_t N, double gnorm, const ubvector &diag2, ubvector &g)
 Compute the point at which the gradient is minimized.
template<class vec2_t , class mat_t >
int dogleg (size_t n, const mat_t &r2, const ubvector &qtf2, const ubvector &diag2, double delta2, ubvector &newton2, ubvector &gradient2, vec2_t &p)
 Take a dogleg step. More...

Detailed Description

Definition at line 73 of file mroot_hybrids.h.

Member Function Documentation

◆ compute_df()

template<class vec2_t >
int o2scl::mroot_hybrids_base::compute_df ( size_t  n,
const vec2_t &  ff_trial,
const vec2_t &  fl,
ubvector dfl 
Idea for Future:
Replace with daxpy?

Definition at line 215 of file mroot_hybrids.h.

◆ compute_qtf()

template<class vec2_t , class vec3_t , class vec4_t >
void o2scl::mroot_hybrids_base::compute_qtf ( size_t  N,
const vec2_t &  q2,
const vec3_t &  f2,
vec4_t &  qtf2 
Idea for Future:
This is just right-multiplication, so we could use the O2scl cblas routines instead.

Definition at line 248 of file mroot_hybrids.h.

◆ compute_trial_step()

template<class vec2_t >
int o2scl::mroot_hybrids_base::compute_trial_step ( size_t  N,
vec2_t &  xl,
vec2_t &  dxl,
vec2_t &  xx_trial 
Idea for Future:
Replace with daxpy.

Definition at line 202 of file mroot_hybrids.h.

◆ dogleg()

template<class vec2_t , class mat_t >
int o2scl::mroot_hybrids_base::dogleg ( size_t  n,
const mat_t &  r2,
const ubvector qtf2,
const ubvector diag2,
double  delta2,
ubvector newton2,
ubvector gradient2,
vec2_t &  p 

Given the QR decomposition of an n by n matrix "A", a diagonal matrix diag, a vector b, and a positive number delta, this function determines the convex combination x of the Gauss-Newton and scaled gradient directions which minimizes $ A x-b $ in the least squares sense, subject to the restriction that the Euclidean norm of $ d x $ is smaller than the value of delta.

Definition at line 361 of file mroot_hybrids.h.

◆ enorm()

template<class vec2_t >
double o2scl::mroot_hybrids_base::enorm ( size_t  N,
const vec2_t &  ff 
Idea for Future:
Replace this with dnrm2 from cblas_base.h

Definition at line 177 of file mroot_hybrids.h.

◆ scaled_addition()

template<class vec2_t >
void o2scl::mroot_hybrids_base::scaled_addition ( size_t  N,
double  alpha,
ubvector newton2,
double  beta,
ubvector gradient2,
vec2_t &  pp 

Using the Gauss-Newton direction given in newton (a vector of size N), and the gradient direction in gradient (also a vector of size N), this computes

\[ \mathrm{pp}=\alpha \mathrm{newton}+\beta \mathrm{gradient} \]

Definition at line 294 of file mroot_hybrids.h.

The documentation for this class was generated from the following file:

Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).