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New sections of examples or cube, fifth, multiprecision and nth root finding, and comparison of timing and iterations.

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pabristow
2015-04-26 17:41:10 +01:00
parent 9b293b689d
commit e7ae689ea5
42 changed files with 3154 additions and 165 deletions
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26
example/root_finding_example.cpp
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@@ -12,10 +12,6 @@
// Note that this file contains Quickbook mark-up as well as code
// and comments, don't change any of the special comment mark-ups!
//#ifdef _MSC_VER
//# pragma warning(disable: 4180) // qualifier has no effect (in Fusion).
//#endif
//#define BOOST_MATH_INSTRUMENT
/*
@@ -27,8 +23,8 @@ It shows how use of derivatives can improve the speed.
implementation of `boost::math::cbrt`, mainly by using a better computed initial 'guess'
at `<boost/math/special_functions/cbrt.hpp>`).
Then we show how a high roots (fifth) can be computed,
and in root_finding_n_example.cpp a generic method
Then we show how a higher root (fifth) can be computed,
and in `root_finding_n_example.cpp` a generic method
for the ['n]th root that constructs the derivatives at compile-time,
These methods should be applicable to other functions that can be differentiated easily.
@@ -135,7 +131,7 @@ T cbrt_noderiv(T x)
int digits = std::numeric_limits<T>::digits; // Maximum possible binary digits accuracy for type T.
// Some fraction of digits is used to control how accurate to try to make the result.
int get_digits = (digits * 3) /4; // Near maximum (3/4) possible accuracy.
eps_tolerance<double> tol(get_digits); // Set the tolerance.
eps_tolerance<T> tol(get_digits); // Set the tolerance.
std::pair<T, T> r =
bracket_and_solve_root(cbrt_functor_noderiv<T>(x), guess, factor, is_rising, tol, it);
return r.first + (r.second - r.first)/2; // Midway between brackets.
@@ -156,12 +152,12 @@ So it may be wise to chose some reasonable estimate of how many iterations may b
if (it >= maxit)
{
std::cout << "Unable to locate solution in " << maxit << " iterations:"
" Current best guess is between " << r.first << " and " << r.second << std::endl;
std::cout << "Unable to locate solution in " << maxit << " iterations:"
" Current best guess is between " << r.first << " and " << r.second << std::endl;
}
else
{
std::cout << "Converged after " << it << " (from maximum of " << maxit << " iterations)." << std::endl;
std::cout << "Converged after " << it << " (from maximum of " << maxit << " iterations)." << std::endl;
}
for output like
@@ -200,10 +196,10 @@ To \'return\' two values, we use a `std::pair` of floating-point values:
template <class T>
struct cbrt_functor_deriv
{ // Functor also returning 1st derviative.
{ // Functor also returning 1st derivative.
cbrt_functor_deriv(T const& to_find_root_of) : a(to_find_root_of)
{ // Constructor stores value a to find root of,
// for example: calling cbrt_functor_deriv<T>(x) to use to get cube root of x.
// for example: calling cbrt_functor_deriv<T>(a) to use to get cube root of a.
}
std::pair<T, T> operator()(T const& x)
{ // Return both f(x) and f'(x).
@@ -212,7 +208,7 @@ struct cbrt_functor_deriv
return std::make_pair(fx, dx); // 'return' both fx and dx.
}
private:
T a; // to be 'cube_rooted'.
T a; // Store value to be 'cube_rooted'.
};
/*`Our cube root function is now:*/
@@ -404,8 +400,8 @@ int main()
//[root_finding_main_1
try
{
double threecubed = 27.; // value that has an exactly representable integer cube root.
double threecubedp1 = 28.; // whose cube root is *not* exactly representable.
double threecubed = 27.; // Value that has an *exactly representable* integer cube root.
double threecubedp1 = 28.; // Value whose cube root is *not* exactly representable.
std::cout << "cbrt(28) " << boost::math::cbrt(28.) << std::endl; // boost::math:: version of cbrt.
std::cout << "std::cbrt(28) " << std::cbrt(28.) << std::endl; // std:: version of cbrt.