Class fit_nonlin_b (o2scl)¶

O2scl : Class List

template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>> class fit_nonlin_b¶

Base routines for the nonlinear fitting classes.

Subclassed by o2scl::fit_nonlin< fit_fix_pars< bool_vec_t, gen_fit_funct<>, boost::numeric::ublas::vector< double >, boost::numeric::ublas::matrix< double > >, boost::numeric::ublas::vector< double >, boost::numeric::ublas::matrix< double > >, o2scl::fit_min< func_t, vec_t, mat_t >, o2scl::fit_nonlin< func_t, vec_t, mat_t >

Public Functions

inline fit_nonlin_b()¶

inline int test_delta_f(size_t nparm, vec_t &dx, vec_t &x, double l_epsabs, double l_epsrel)¶: Test if converged.

inline int test_gradient_f(size_t nparm, vec_t &g, double l_epsabs)¶: Test if converged.

Public Members

double tol_rel_covar¶: The relative tolerance for the computation of the covariance matrix (default 0)

Protected Functions

inline double compute_actual_reduction(double fnorm0, double fnorm1)¶: Desc.

inline size_t count_nsing(const size_t ncols, const mat_t &r2)¶: Desc.

inline void compute_newton_direction(size_t n, const mat_t &r2, const permutation &perm2, const vec_t &qtf2, vec_t &x)¶: Desc.

inline void compute_newton_bound(size_t nd, size_t np, const mat_t &r2, const vec_t &x, double dxnorm, const permutation &perm, const vec_t &diag, vec_t &w)¶: Desc.

inline void compute_gradient_direction(size_t n, const mat_t &r, const permutation &p, const vec_t &qtf2, const vec_t &diag, vec_t &g)¶: Desc.

inline void update_diag(size_t n, const mat_t &J, vec_t &diag2)¶: Desc.

inline double scaled_enorm(const vec_t &d, size_t n, const vec_t &f)¶: Euclidean norm of vector f of length n, scaled by vector d.

inline double compute_delta(vec_t &diag2, size_t n, const vec_t &x)¶: Desc.

inline void compute_rptdx(const mat_t &r2, const permutation &p, size_t N, vec_t &dx, vec_t &rptdx2)¶: Desc.

inline int qrsolv(size_t n, mat_t &r2, const permutation &p, const double lambda, const vec_t &diag2, const vec_t &qtb, vec_t &x, vec_t &sdiag2, vec_t &wa)¶

Compute the solution to a least squares system.

This function computes the solution to the least squares system

phi=[ A x=b ,lambda D x=0 ]^2

where A is an M by N matrix,D is an N by N diagonal matrix,lambda
is a scalar parameter and b is a vector of length M.

The function requires the factorization of A into A=Q R P^T,
where Q is an orthogonal matrix,R is an upper triangular matrix
with diagonal elements of non-increasing magnitude and P is a
permuation matrix. The system above is then equivalent to

[ R z=Q^T b,P^T (lambda D) P z=0 ]

where x=P z. If this system does not have full rank then a least
squares solution is obtained. On output the function also provides
an upper triangular matrix S such that

P^T (A^T A+lambda^2 D^T D) P=S^T S

Parameters,

r: On input,contains the full upper triangle of R. On output the
strict lower triangle contains the transpose of the strict upper
triangle of S,and the diagonal of S is stored in sdiag.  The full
upper triangle of R is not modified.

p: the encoded form of the permutation matrix P. column j of P is
column p[j] of the identity matrix.

lambda,diag: contains the scalar lambda and the diagonal elements
of the matrix D

qtb: contains the product Q^T b

x: on output contains the least squares solution of the system

wa: is a workspace of length N

inline void compute_newton_correction(size_t n, const mat_t &r2, const vec_t &sdiag2, const permutation &p, vec_t &x, double dxnorm, const vec_t &diag2, vec_t &w2)¶: Desc.

inline void lmpar(mat_t &r2, const permutation &perm2, const vec_t &qtf2, const vec_t &diag2, double delta2, double *par_inout, vec_t &newton2, vec_t &gradient2, vec_t &sdiag2, vec_t &x, vec_t &w2, size_t nparm, size_t ndata)¶: Determine Levenburg-Marquardt parameter.

inline void compute_trial_step(size_t N, vec_t &x, vec_t &dx, vec_t &trial)¶: Compute trial step, \( \mathrm{trial}=\mathrm{x}+\mathrm{dx} \).

inline int compute_diag(size_t nparm, size_t ndata, const mat_t &J, vec_t &diag_vec)¶

Compute the root of the sum of the squares of the columns of J.

This computes

\[ \mathrm{diag\_vec}_j = \sqrt{\sum_{i=0}^{\mathrm{ndata}-1} J_{ij}} \]

for \( 0\leq j \leq \mathrm{nparm}-1 \) . If any of the columns of J is all zero, then the corresponding entry in diag_vec is set to one instead.

inline int covariance(size_t m, size_t n, const mat_t &J, mat_t &covar, vec_t &norm, mat_t &r, vec_t &tau, permutation &perm, double epsrel)¶

Compute the covarance matrix covar given the Jacobian J.

Given a m by n Jacobian matrix J (where m must not be less than n), and a relative tolerance epsrel, this function computes the entries of the n by n covariance matrix covar. The allocation for covar must be performed beforehand.

This function is basically the equivalent of the function gsl_multifit_covar(), but rewritten for generic vector and matrix types.

The workspace work1 is used here.