math/tools/carlson_ellint_data.cpp

631 lines
18 KiB
C++

// Copyright John Maddock 2006.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
#include <boost/math/tools/test_data.hpp>
#include <boost/test/included/prg_exec_monitor.hpp>
#include <boost/math/special_functions/ellint_rj.hpp>
#include <boost/math/special_functions/ellint_rd.hpp>
#include <fstream>
#include <boost/math/tools/test_data.hpp>
#include <boost/random.hpp>
#include "mp_t.hpp"
float extern_val;
// confuse the compilers optimiser, and force a truncation to float precision:
float truncate_to_float(float const * pf)
{
extern_val = *pf;
return *pf;
}
//
// Archived here is the original implementation of this
// function by Xiaogang Zhang, we can use this to
// generate special test cases for the new version:
//
template <typename T, typename Policy>
T ellint_rj_old(T x, T y, T z, T p, const Policy& pol)
{
T value, u, lambda, alpha, beta, sigma, factor, tolerance;
T X, Y, Z, P, EA, EB, EC, E2, E3, S1, S2, S3;
unsigned long k;
BOOST_MATH_STD_USING
using namespace boost::math;
static const char* function = "boost::math::ellint_rj<%1%>(%1%,%1%,%1%)";
if(x < 0)
{
return policies::raise_domain_error<T>(function,
"Argument x must be non-negative, but got x = %1%", x, pol);
}
if(y < 0)
{
return policies::raise_domain_error<T>(function,
"Argument y must be non-negative, but got y = %1%", y, pol);
}
if(z < 0)
{
return policies::raise_domain_error<T>(function,
"Argument z must be non-negative, but got z = %1%", z, pol);
}
if(p == 0)
{
return policies::raise_domain_error<T>(function,
"Argument p must not be zero, but got p = %1%", p, pol);
}
if(x + y == 0 || y + z == 0 || z + x == 0)
{
return policies::raise_domain_error<T>(function,
"At most one argument can be zero, "
"only possible result is %1%.", std::numeric_limits<T>::quiet_NaN(), pol);
}
// error scales as the 6th power of tolerance
tolerance = pow(T(1) * tools::epsilon<T>() / 3, T(1) / 6);
// for p < 0, the integral is singular, return Cauchy principal value
if(p < 0)
{
//
// We must ensure that (z - y) * (y - x) is positive.
// Since the integral is symmetrical in x, y and z
// we can just permute the values:
//
if(x > y)
std::swap(x, y);
if(y > z)
std::swap(y, z);
if(x > y)
std::swap(x, y);
T q = -p;
T pmy = (z - y) * (y - x) / (y + q); // p - y
BOOST_ASSERT(pmy >= 0);
p = pmy + y;
value = ellint_rj_old(x, y, z, p, pol);
value *= pmy;
value -= 3 * boost::math::ellint_rf(x, y, z, pol);
value += 3 * sqrt((x * y * z) / (x * z + p * q)) * boost::math::ellint_rc(x * z + p * q, p * q, pol);
value /= (y + q);
return value;
}
// duplication
sigma = 0;
factor = 1;
k = 1;
do
{
u = (x + y + z + p + p) / 5;
X = (u - x) / u;
Y = (u - y) / u;
Z = (u - z) / u;
P = (u - p) / u;
if((tools::max)(abs(X), abs(Y), abs(Z), abs(P)) < tolerance)
break;
T sx = sqrt(x);
T sy = sqrt(y);
T sz = sqrt(z);
lambda = sy * (sx + sz) + sz * sx;
alpha = p * (sx + sy + sz) + sx * sy * sz;
alpha *= alpha;
beta = p * (p + lambda) * (p + lambda);
sigma += factor * boost::math::ellint_rc(alpha, beta, pol);
factor /= 4;
x = (x + lambda) / 4;
y = (y + lambda) / 4;
z = (z + lambda) / 4;
p = (p + lambda) / 4;
++k;
} while(k < policies::get_max_series_iterations<Policy>());
// Check to see if we gave up too soon:
policies::check_series_iterations<T>(function, k, pol);
// Taylor series expansion to the 5th order
EA = X * Y + Y * Z + Z * X;
EB = X * Y * Z;
EC = P * P;
E2 = EA - 3 * EC;
E3 = EB + 2 * P * (EA - EC);
S1 = 1 + E2 * (E2 * T(9) / 88 - E3 * T(9) / 52 - T(3) / 14);
S2 = EB * (T(1) / 6 + P * (T(-6) / 22 + P * T(3) / 26));
S3 = P * ((EA - EC) / 3 - P * EA * T(3) / 22);
value = 3 * sigma + factor * (S1 + S2 + S3) / (u * sqrt(u));
return value;
}
template <typename T, typename Policy>
T ellint_rd_imp_old(T x, T y, T z, const Policy& pol)
{
T value, u, lambda, sigma, factor, tolerance;
T X, Y, Z, EA, EB, EC, ED, EE, S1, S2;
unsigned long k;
BOOST_MATH_STD_USING
using namespace boost::math;
static const char* function = "boost::math::ellint_rd<%1%>(%1%,%1%,%1%)";
if(x < 0)
{
return policies::raise_domain_error<T>(function,
"Argument x must be >= 0, but got %1%", x, pol);
}
if(y < 0)
{
return policies::raise_domain_error<T>(function,
"Argument y must be >= 0, but got %1%", y, pol);
}
if(z <= 0)
{
return policies::raise_domain_error<T>(function,
"Argument z must be > 0, but got %1%", z, pol);
}
if(x + y == 0)
{
return policies::raise_domain_error<T>(function,
"At most one argument can be zero, but got, x + y = %1%", x + y, pol);
}
// error scales as the 6th power of tolerance
tolerance = pow(tools::epsilon<T>() / 3, T(1) / 6);
// duplication
sigma = 0;
factor = 1;
k = 1;
do
{
u = (x + y + z + z + z) / 5;
X = (u - x) / u;
Y = (u - y) / u;
Z = (u - z) / u;
if((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance)
break;
T sx = sqrt(x);
T sy = sqrt(y);
T sz = sqrt(z);
lambda = sy * (sx + sz) + sz * sx; //sqrt(x * y) + sqrt(y * z) + sqrt(z * x);
sigma += factor / (sz * (z + lambda));
factor /= 4;
x = (x + lambda) / 4;
y = (y + lambda) / 4;
z = (z + lambda) / 4;
++k;
} while(k < policies::get_max_series_iterations<Policy>());
// Check to see if we gave up too soon:
policies::check_series_iterations<T>(function, k, pol);
// Taylor series expansion to the 5th order
EA = X * Y;
EB = Z * Z;
EC = EA - EB;
ED = EA - 6 * EB;
EE = ED + EC + EC;
S1 = ED * (ED * T(9) / 88 - Z * EE * T(9) / 52 - T(3) / 14);
S2 = Z * (EE / 6 + Z * (-EC * T(9) / 22 + Z * EA * T(3) / 26));
value = 3 * sigma + factor * (1 + S1 + S2) / (u * sqrt(u));
return value;
}
template <typename T, typename Policy>
T ellint_rf_imp_old(T x, T y, T z, const Policy& pol)
{
T value, X, Y, Z, E2, E3, u, lambda, tolerance;
unsigned long k;
BOOST_MATH_STD_USING
using namespace boost::math;
static const char* function = "boost::math::ellint_rf<%1%>(%1%,%1%,%1%)";
if(x < 0 || y < 0 || z < 0)
{
return policies::raise_domain_error<T>(function,
"domain error, all arguments must be non-negative, "
"only sensible result is %1%.",
std::numeric_limits<T>::quiet_NaN(), pol);
}
if(x + y == 0 || y + z == 0 || z + x == 0)
{
return policies::raise_domain_error<T>(function,
"domain error, at most one argument can be zero, "
"only sensible result is %1%.",
std::numeric_limits<T>::quiet_NaN(), pol);
}
// Carlson scales error as the 6th power of tolerance,
// but this seems not to work for types larger than
// 80-bit reals, this heuristic seems to work OK:
if(policies::digits<T, Policy>() > 64)
{
tolerance = pow(tools::epsilon<T>(), T(1) / 4.25f);
BOOST_MATH_INSTRUMENT_VARIABLE(tolerance);
}
else
{
tolerance = pow(4 * tools::epsilon<T>(), T(1) / 6);
BOOST_MATH_INSTRUMENT_VARIABLE(tolerance);
}
// duplication
k = 1;
do
{
u = (x + y + z) / 3;
X = (u - x) / u;
Y = (u - y) / u;
Z = (u - z) / u;
// Termination condition:
if((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance)
break;
T sx = sqrt(x);
T sy = sqrt(y);
T sz = sqrt(z);
lambda = sy * (sx + sz) + sz * sx;
x = (x + lambda) / 4;
y = (y + lambda) / 4;
z = (z + lambda) / 4;
++k;
} while(k < policies::get_max_series_iterations<Policy>());
// Check to see if we gave up too soon:
policies::check_series_iterations<T>(function, k, pol);
BOOST_MATH_INSTRUMENT_VARIABLE(k);
// Taylor series expansion to the 5th order
E2 = X * Y - Z * Z;
E3 = X * Y * Z;
value = (1 + E2*(E2 / 24 - E3*T(3) / 44 - T(0.1)) + E3 / 14) / sqrt(u);
BOOST_MATH_INSTRUMENT_VARIABLE(value);
return value;
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rj_data_4e(mp_t n)
{
mp_t result = ellint_rj_old(n, n, n, n, boost::math::policies::policy<>());
return boost::math::make_tuple(n, n, n, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_3e(mp_t x, mp_t p)
{
mp_t r = ellint_rj_old(x, x, x, p, boost::math::policies::policy<>());
return boost::math::make_tuple(x, x, x, p, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_2e_1(mp_t x, mp_t y, mp_t p)
{
mp_t r = ellint_rj_old(x, x, y, p, boost::math::policies::policy<>());
return boost::math::make_tuple(x, x, y, p, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_2e_2(mp_t x, mp_t y, mp_t p)
{
mp_t r = ellint_rj_old(x, y, x, p, boost::math::policies::policy<>());
return boost::math::make_tuple(x, y, x, p, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_2e_3(mp_t x, mp_t y, mp_t p)
{
mp_t r = ellint_rj_old(y, x, x, p, boost::math::policies::policy<>());
return boost::math::make_tuple(y, x, x, p, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_2e_4(mp_t x, mp_t y, mp_t p)
{
mp_t r = ellint_rj_old(x, y, p, p, boost::math::policies::policy<>());
return boost::math::make_tuple(x, y, p, p, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_2e_1(mp_t x, mp_t y)
{
mp_t r = ellint_rd_imp_old(x, y, y, boost::math::policies::policy<>());
return boost::math::make_tuple(x, y, y, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_2e_2(mp_t x, mp_t y)
{
mp_t r = ellint_rd_imp_old(x, x, y, boost::math::policies::policy<>());
return boost::math::make_tuple(x, x, y, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_2e_3(mp_t x)
{
mp_t r = ellint_rd_imp_old(mp_t(0), x, x, boost::math::policies::policy<>());
return boost::math::make_tuple(0, x, x, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_3e(mp_t x)
{
mp_t r = ellint_rd_imp_old(x, x, x, boost::math::policies::policy<>());
return boost::math::make_tuple(x, x, x, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_0xy(mp_t x, mp_t y)
{
mp_t r = ellint_rd_imp_old(mp_t(0), x, y, boost::math::policies::policy<>());
return boost::math::make_tuple(mp_t(0), x, y, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xxx(mp_t x)
{
mp_t r = ellint_rf_imp_old(x, x, x, boost::math::policies::policy<>());
return boost::math::make_tuple(x, x, x, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xyy(mp_t x, mp_t y)
{
mp_t r = ellint_rf_imp_old(x, y, y, boost::math::policies::policy<>());
return boost::math::make_tuple(x, y, y, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xxy(mp_t x, mp_t y)
{
mp_t r = ellint_rf_imp_old(x, x, y, boost::math::policies::policy<>());
return boost::math::make_tuple(x, x, y, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xyx(mp_t x, mp_t y)
{
mp_t r = ellint_rf_imp_old(x, y, x, boost::math::policies::policy<>());
return boost::math::make_tuple(x, y, x, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_0yy(mp_t y)
{
mp_t r = ellint_rf_imp_old(mp_t(0), y, y, boost::math::policies::policy<>());
return boost::math::make_tuple(mp_t(0), y, y, r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xy0(mp_t x, mp_t y)
{
mp_t r = ellint_rf_imp_old(x, y, mp_t(0), boost::math::policies::policy<>());
return boost::math::make_tuple(x, y, mp_t(0), r);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data(mp_t n)
{
static boost::mt19937 r;
boost::uniform_real<float> ur(0, 1);
boost::uniform_int<int> ui(-100, 100);
float x = ur(r);
x = ldexp(x, ui(r));
mp_t xr(truncate_to_float(&x));
float y = ur(r);
y = ldexp(y, ui(r));
mp_t yr(truncate_to_float(&y));
float z = ur(r);
z = ldexp(z, ui(r));
mp_t zr(truncate_to_float(&z));
mp_t result = boost::math::ellint_rf(xr, yr, zr);
return boost::math::make_tuple(xr, yr, zr, result);
}
boost::math::tuple<mp_t, mp_t, mp_t> generate_rc_data(mp_t n)
{
static boost::mt19937 r;
boost::uniform_real<float> ur(0, 1);
boost::uniform_int<int> ui(-100, 100);
float x = ur(r);
x = ldexp(x, ui(r));
mp_t xr(truncate_to_float(&x));
float y = ur(r);
y = ldexp(y, ui(r));
mp_t yr(truncate_to_float(&y));
mp_t result = boost::math::ellint_rc(xr, yr);
return boost::math::make_tuple(xr, yr, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data(mp_t n)
{
static boost::mt19937 r;
boost::uniform_real<float> ur(0, 1);
boost::uniform_real<float> nur(-1, 1);
boost::uniform_int<int> ui(-100, 100);
float x = ur(r);
x = ldexp(x, ui(r));
mp_t xr(truncate_to_float(&x));
float y = ur(r);
y = ldexp(y, ui(r));
mp_t yr(truncate_to_float(&y));
float z = ur(r);
z = ldexp(z, ui(r));
mp_t zr(truncate_to_float(&z));
float p = nur(r);
p = ldexp(p, ui(r));
mp_t pr(truncate_to_float(&p));
boost::math::ellint_rj(x, y, z, p);
mp_t result = boost::math::ellint_rj(xr, yr, zr, pr);
return boost::math::make_tuple(xr, yr, zr, pr, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data(mp_t n)
{
static boost::mt19937 r;
boost::uniform_real<float> ur(0, 1);
boost::uniform_int<int> ui(-100, 100);
float x = ur(r);
x = ldexp(x, ui(r));
mp_t xr(truncate_to_float(&x));
float y = ur(r);
y = ldexp(y, ui(r));
mp_t yr(truncate_to_float(&y));
float z = ur(r);
z = ldexp(z, ui(r));
mp_t zr(truncate_to_float(&z));
mp_t result = boost::math::ellint_rd(xr, yr, zr);
return boost::math::make_tuple(xr, yr, zr, result);
}
mp_t rg_imp(mp_t x, mp_t y, mp_t z)
{
using std::swap;
// If z is zero permute so the call to RD is valid:
if(z == 0)
swap(x, z);
return (z * ellint_rf_imp_old(x, y, z, boost::math::policies::policy<>())
- (x - z) * (y - z) * ellint_rd_imp_old(x, y, z, boost::math::policies::policy<>()) / 3
+ sqrt(x * y / z)) / 2;
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_data(mp_t n)
{
static boost::mt19937 r;
boost::uniform_real<float> ur(0, 1);
boost::uniform_int<int> ui(-100, 100);
float x = ur(r);
x = ldexp(x, ui(r));
mp_t xr(truncate_to_float(&x));
float y = ur(r);
y = ldexp(y, ui(r));
mp_t yr(truncate_to_float(&y));
float z = ur(r);
z = ldexp(z, ui(r));
mp_t zr(truncate_to_float(&z));
mp_t result = rg_imp(xr, yr, zr);
return boost::math::make_tuple(xr, yr, zr, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xxx(mp_t x)
{
mp_t result = rg_imp(x, x, x);
return boost::math::make_tuple(x, x, x, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xyy(mp_t x, mp_t y)
{
mp_t result = rg_imp(x, y, y);
return boost::math::make_tuple(x, y, y, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xxy(mp_t x, mp_t y)
{
mp_t result = rg_imp(x, x, y);
return boost::math::make_tuple(x, x, y, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xyx(mp_t x, mp_t y)
{
mp_t result = rg_imp(x, y, x);
return boost::math::make_tuple(x, y, x, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_0xx(mp_t x)
{
mp_t result = rg_imp(mp_t(0), x, x);
return boost::math::make_tuple(mp_t(0), x, x, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_x0x(mp_t x)
{
mp_t result = rg_imp(x, mp_t(0), x);
return boost::math::make_tuple(x, mp_t(0), x, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xx0(mp_t x)
{
mp_t result = rg_imp(x, x, mp_t(0));
return boost::math::make_tuple(x, x, mp_t(0), result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_00x(mp_t x)
{
mp_t result = sqrt(x) / 2;
return boost::math::make_tuple(mp_t(0), mp_t(0), x, result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_0x0(mp_t x)
{
mp_t result = sqrt(x) / 2;
return boost::math::make_tuple(mp_t(0), x, mp_t(0), result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_x00(mp_t x)
{
mp_t result = sqrt(x) / 2;
return boost::math::make_tuple(x, mp_t(0), mp_t(0), result);
}
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xy0(mp_t x, mp_t y)
{
mp_t result = rg_imp(x, y, mp_t(0));
return boost::math::make_tuple(x, y, mp_t(0), result);
}
int cpp_main(int argc, char*argv[])
{
using namespace boost::math::tools;
parameter_info<mp_t> arg1, arg2, arg3;
test_data<mp_t> data;
bool cont;
std::string line;
if(argc < 1)
return 1;
do{
#if 0
int count;
std::cout << "Number of points: ";
std::cin >> count;
arg1 = make_periodic_param(mp_t(0), mp_t(1), count);
arg1.type |= dummy_param;
//
// Change this next line to get the R variant you want:
//
data.insert(&generate_rd_data, arg1);
std::cout << "Any more data [y/n]?";
std::getline(std::cin, line);
boost::algorithm::trim(line);
cont = (line == "y");
#else
get_user_parameter_info(arg1, "x");
get_user_parameter_info(arg2, "y");
//get_user_parameter_info(arg3, "p");
arg1.type |= dummy_param;
arg2.type |= dummy_param;
//arg3.type |= dummy_param;
data.insert(generate_rd_data_0xy, arg1, arg2);
std::cout << "Any more data [y/n]?";
std::getline(std::cin, line);
boost::algorithm::trim(line);
cont = (line == "y");
#endif
}while(cont);
std::cout << "Enter name of test data file [default=ellint_rf_data.ipp]";
std::getline(std::cin, line);
boost::algorithm::trim(line);
if(line == "")
line = "ellint_rf_data.ipp";
std::ofstream ofs(line.c_str());
line.erase(line.find('.'));
ofs << std::scientific << std::setprecision(40);
write_code(ofs, data, line.c_str());
return 0;
}