Class mroot (o2scl)

O2scl : Class List

template<class func_t = mm_funct, class vec_t = boost::numeric::ublas::vector<double>, class jfunc_t = jac_funct>
class mroot

Multidimensional root-finding [abstract base].

The template parameters: The template parameter func_t specifies the functions to solve and should be a class containing a definition

func_t::operator()(size_t nv, const vec_t &x, vec_t &y);

where y is the value of the functions at x with parameter pa and x and y are a array-like classes defining operator[] of size nv. If the Jacobian matrix is to be specified by the user, then the parameter jfunc_t specifies the jacobian and should contain the definition

jfunc_t::operator(size_t nv, vec_t &x, vec_t &y, mat_t &j);

where x is the independent variables, y is the array of function values, and j is the Jacobian matrix. This template parameter can be ignored if only the function msolve() will be used.

There is an example for the usage of the multidimensional solver classes given in examples/ex_mroot.cpp, see the Multi-dimensional solver example.

Todo

Class mroot:

Future: Change ntrial to size_t?

Warning

Many of the routines assume that the scale of the functions and their variables is of order unity. The solution routines may lose precision if this is not the case.

Subclassed by o2scl::mroot_hybrids< mm_funct >, o2scl::mroot_hybrids< mm_funct, boost::numeric::ublas::vector< double >, boost::numeric::ublas::matrix< double >, jac_funct >, o2scl::mroot_hybrids< mm_funct, vector< double >, matrix< double >, jac_funct >, o2scl::mroot_broyden< func_t, vec_t, mat_t, jfunc_t >, o2scl::mroot_cern< func_t, vec_t, jfunc_t >, o2scl::mroot_hybrids< func_t, vec_t, mat_t, jfunc_t >

Public Functions

inline mroot()

inline virtual ~mroot()

inline virtual const char *type()

Return the type, "mroot".

virtual int msolve(size_t n, vec_t &x, func_t &func) = 0

Solve func using x as an initial guess, returning x.

inline virtual int msolve_de(size_t n, vec_t &x, func_t &func, jfunc_t &dfunc)

Solve func with derivatives dfunc using x as an initial guess, returning x.

By default, this function just calls msolve() and ignores the last argument.

template<class vec2_t, class vec3_t>
inline int print_iter(size_t n, const vec2_t &x, const vec3_t &y, int iter, double value = 0.0, double limit = 0.0, std::string comment = "")

Print out iteration information.

Depending on the value of the variable verbose, this prints out the iteration information. If verbose=0, then no information is printed, while if verbose>1, then after each iteration, the present values of x and y are output to std::cout along with the iteration number. If verbose>=2 then each iteration waits for a character.

This is implemented as a template class using a new vector type because sometimes the internal vector class is distinct from the user-specified vector class (e.g. in o2scl::mroot_hybrids).

Public Members

double tol_rel

The maximum value of the functions for success (default 1.0e-8)

double tol_abs

The minimum allowable stepsize (default 1.0e-12)

int verbose

Output control (default 0)

int ntrial

Maximum number of iterations (default 100)

int last_ntrial

The number of iterations for in the most recent minimization.

bool err_nonconv

If true, call the error handler if msolve() or msolve_de() does not converge (default true)