Class mroot_cern (o2scl)

O2scl : Class List

template<class func_t = mm_funct, class vec_t = boost::numeric::ublas::vector<double>, class jfunc_t = jac_funct, class fp_t = double>
class mroot_cern : public o2scl::mroot<mm_funct, boost::numeric::ublas::vector<double>, jac_funct, double>

Multi-dimensional mroot-finding routine (CERNLIB)

If \( x_i \) denotes the current iteration, and \( x^{\prime}_i \) denotes the previous iteration, then the calculation is terminated if either of the following tests is successful

\[ 1:\quad \mathrm{max} | f_i(x) | \leq \mathrm{tol\_rel} \]

\[ 2:\quad \mathrm{max} |x_i-x^{\prime}_i| \leq \mathrm{tol\_abs} \times \mathrm{max} | x_i | \]

This routine treats the functions specified as a mm_funct object slightly differently than o2scl::mroot_hybrids. First the equations should be numbered (as much as is possible) in order of increasing nonlinearity. Also, instead of calculating all of the equations on each function call, only the equation specified by the size_t parameter needs to be calculated. If the equations are specified as

\[\begin{split}\begin{eqnarray*} &0=f_0(x_0,x_1,...,x_{n-1})& \\ &0=f_1(x_0,x_1,...,x_{n-1})& \\ &...& \\ &0=f_{n-1}(x_0,x_1,...,x_{n-1})& \\ \end{eqnarray*}\end{split}\]

then when the size_t argument is given as i, then only the function \( f_i \) needs to be calculated.

See the Multi-dimensional solvers section of the User’s guide for general information about the O2scl solvers. There is an example for the usage of the multidimensional solver classes given in examples/ex_mroot.cpp, see the Multi-dimensional solver example.

In class mroot_cern:

Future:

• Modify this so it handles functions which return

non-zero values. - Move some of the memory allocation out of msolve() - Give the user access to the number of function calls - Rename nier6, nier7, and nier8 to something sensible. - It may be that the o2 native Householder transformations should be used here instead of the inline version given here.

Based on the CERNLIB routines RSNLEQ and DSNLEQ, which was based on [More79] and [More80] and is documented at http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/c201/top.html

Warning

This code has not been checked to ensure that it cannot fail to solve the equations without calling the error handler and returning a non-zero value. Until then, the solution may need to be checked explicitly by the caller.

Public Functions

inline mroot_cern()

inline int get_info()

Get the value of INFO from the last call to msolve()

The value of info is assigned according to the following list. The values 1-8 are the standard behavior from CERNLIB. 0 - The function solve() has not been called. 1 - Test 1 was successful.

2 - Test 2 was successful.

3 - Both tests were successful.

4 - Number of iterations is greater than mroot_cern_root::maxf.

5 - Approximate (finite difference) Jacobian matrix is singular.

6 - Iterations are not making good progress.

7 - Iterations are diverging.

8 - Iterations are converging, but either mroot_cern_root::tol_abs is too small or the Jacobian is nearly singular or the variables are badly scaled.

9 - Either root::tol_rel or root::tol_abs is not greater than zero or the specified number of variables is \( \leq 0\).

The return values returned by msolve() corresponding to the values of INFO above are 1 - success 2 - success 3 - success 4 - exc_emaxiter 5 - exc_esing 6 - exc_enoprog 7 - exc_erunaway 8 - exc_efailed 9 - exc_einval

inline std::string get_info_string()

Get the a string corresponding to the integer returned by mroot_cern::get_info().

inline virtual const char *type()

Return the type, "mroot_cern".

inline virtual int msolve(size_t nvar, vec_t &x, func_t &func)

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

Public Members

int maxf

Maximum number of function evaluations.

If \( \mathrm{maxf}\leq 0 \) , then \( 50(\mathrm{nv}+3) \) (which is the CERNLIB default) is used. The default value of maxf is zero which then implies the default from CERNLIB.

fp_t scale

The original scale parameter from CERNLIB (default 10.0)

fp_t eps

The smallest floating point number (default \( \sim 1.49012 \times 10^{-8} \) )

The original prescription from CERNLIB for eps is given below:

#if !defined(CERNLIB_DOUBLE)
PARAMETER (EPS =  0.84293 69702 17878 97282 52636 392E-07)
#endif
#if defined(CERNLIB_IBM)
PARAMETER (EPS =  0.14901 16119 38476 562D-07)
#endif
#if defined(CERNLIB_VAX)
PARAMETER (EPS =  0.37252 90298 46191 40625D-08)
#endif
#if (defined(CERNLIB_UNIX))&&(defined(CERNLIB_DOUBLE))
PARAMETER (EPS =  0.14901 16119 38476 600D-07)
#endif

Protected Attributes

boost::numeric::ublas::matrix<fp_t> w

Desc.

int info

Internal storage for the value of info.

int mpt[289]

Store the number of function evaluations.