guilhem_lavaux/cosmotool
0
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Add some special math function

Browse Source
This commit is contained in:
Guilhem Lavaux 2020-10-03 20:17:07 +02:00
parent 47f2e247e9
commit 0ff1b04b3d
3 changed files with 246 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
sample/CMakeLists.txt
View File

@ -114,6 +114,9 @@ if (Boost_FOUND)
add_dependencies(graficToDensity ${all_deps}) add_dependencies(graficToDensity ${all_deps})
endif() endif()
endif() endif()
add_executable(test_special test_special.cpp)
target_link_libraries(test_special ${tolink})
endif (Boost_FOUND) endif (Boost_FOUND)
IF (ENABLE_OPENMP AND YORICK_SUPPORT) IF (ENABLE_OPENMP AND YORICK_SUPPORT)

12
sample/test_special.cpp Normal file
View File

@ -0,0 +1,12 @@
#include <iostream>
#include "special_math.hpp"
int main()
{
std::cout << CosmoTool::log1p_exp(2.0) << std::endl;
std::cout << CosmoTool::log_modified_bessel_first_kind(100.0, 0.1) << std::endl;
return 0;
}

231
src/special_math.hpp Normal file
View File

@ -0,0 +1,231 @@
// Original code derived from Boost and is distributed here
// under the Boost license (licenses/boost-license.txt)
// Copyright (c) 2006 Xiaogang Zhang
// Copyright (c) 2007, 2017 John Maddock
// Secondary code copyright by its author and is distributed here
// under the BSD-3 license (LICENSE.md). Derived from
// stan/math/prim/fun/log_modified_bessel_first_kind.hpp
#ifndef __COSMOTOOL_SPECIAL_MATH_HPP
#define __COSMOTOOL_SPECIAL_MATH_HPP
#include <CosmoTool/algo.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/math/tools/rational.hpp>
#include <cmath>
#include <limits>
// Taken and adapted from
// https://github.com/stan-dev/math/blob/develop/stan/math/prim/fun/log_modified_bessel_first_kind.hpp
namespace CosmoTool {
template <typename T> T log1p_exp(T x) {
if (x > T(0)) {
return x + std::log1p(std::exp(-x));
}
return std::log1p(std::exp(x));
}
template <typename T> T multiply_log(T a, T b) {
if (a == 0 && b == 0)
return 0;
return a * std::log(b);
}
template <typename T> T inf() { return std::numeric_limits<T>::infinity(); }
template <typename T> T log_sum_exp(T const a, T const b) {
if (a == -inf<T>()) {
return b;
}
if (a == inf<T>() && b == inf<T>()) {
return inf<T>();
}
if (a > b) {
return a + log1p_exp(b - a);
}
return b + log1p_exp(a - b);
}
/* Log of the modified Bessel function of the first kind,
* which is better known as the Bessel I function. See
* modified_bessel_first_kind.hpp for the function definition.
* The derivatives are known to be incorrect for v = 0 because a
* simple constant 0 is returned.
*
* @tparam T common type for calculation
* @param v Order, can be a non-integer but must be at least -1
* @param z Real non-negative number
* @throws std::domain_error if either v or z is NaN, z is
* negative, or v is less than -1
* @return log of Bessel I function
*/
template <typename T> T log_modified_bessel_first_kind(T const v, T const z) {
using boost::math::tools::evaluate_polynomial;
using std::log;
using std::pow;
using std::sqrt;
static const double LOG_TWO = std::log(2.0);
static const double EPSILON = std::numeric_limits<double>::epsilon();
static const double TWO_PI = 2.0 * boost::math::constants::pi<double>();
if (z == 0) {
if (v == 0) {
return 0.0;
}
if (v > 0) {
return -std::numeric_limits<T>::infinity();
}
return std::numeric_limits<T>::infinity();
}
if (std::isinf(z)) {
return z;
}
if (v == 0) {
// Modified Bessel function of the first kind of order zero
// we use the approximating forms derived in:
// "Rational Approximations for the Modified Bessel Function of the
// First Kind -- I0(x) for Computations with Double Precision"
// by Pavel Holoborodko, see
// http://www.advanpix.com/2015/11/11/rational-approximations-for-the-modified-bessel-function-of-the-first-kind-i0-computations-double-precision
// The actual coefficients used are [Boost's] own, and extend
// Pavel's work to precisions other than double.
if (z < 7.75) {
// Bessel I0 over[10 ^ -16, 7.75]
// Max error in interpolated form : 3.042e-18
// Max Error found at double precision = Poly : 5.106609e-16
// Cheb : 5.239199e-16
static const double P[] = {
1.00000000000000000e+00, 2.49999999999999909e-01,
2.77777777777782257e-02, 1.73611111111023792e-03,
6.94444444453352521e-05, 1.92901234513219920e-06,
3.93675991102510739e-08, 6.15118672704439289e-10,
7.59407002058973446e-12, 7.59389793369836367e-14,
6.27767773636292611e-16, 4.34709704153272287e-18,
2.63417742690109154e-20, 1.13943037744822825e-22,
9.07926920085624812e-25};
return log1p_exp(multiply_log(2.0, z) - log(4.0) +
log(evaluate_polynomial(P, 0.25 * square(z))));
}
if (z < 500) {
// Max error in interpolated form : 1.685e-16
// Max Error found at double precision = Poly : 2.575063e-16
// Cheb : 2.247615e+00
static const double P[] = {
3.98942280401425088e-01, 4.98677850604961985e-02,
2.80506233928312623e-02, 2.92211225166047873e-02,
4.44207299493659561e-02, 1.30970574605856719e-01,
-3.35052280231727022e+00, 2.33025711583514727e+02,
-1.13366350697172355e+04, 4.24057674317867331e+05,
-1.23157028595698731e+07, 2.80231938155267516e+08,
-5.01883999713777929e+09, 7.08029243015109113e+10,
-7.84261082124811106e+11, 6.76825737854096565e+12,
-4.49034849696138065e+13, 2.24155239966958995e+14,
-8.13426467865659318e+14, 2.02391097391687777e+15,
-3.08675715295370878e+15, 2.17587543863819074e+15};
return z + log(evaluate_polynomial(P, 1 / z)) - multiply_log(0.5, z);
}
// Max error in interpolated form : 2.437e-18
// Max Error found at double precision = Poly : 1.216719e-16
static const double P[] = {3.98942280401432905e-01, 4.98677850491434560e-02,
2.80506308916506102e-02, 2.92179096853915176e-02,
4.53371208762579442e-02};
return z + log(evaluate_polynomial(P, 1 / z)) - multiply_log(0.5, z);
}
if (v == 1) { // WARNING: will not autodiff for v = 1 correctly
// modified from Boost's bessel_i1_imp in the double precision case
// see credits above in the v == 0 case
if (z < 7.75) {
// Bessel I0 over[10 ^ -16, 7.75]
// Max error in interpolated form: 5.639e-17
// Max Error found at double precision = Poly: 1.795559e-16
static const double P[] = {
8.333333333333333803e-02, 6.944444444444341983e-03,
3.472222222225921045e-04, 1.157407407354987232e-05,
2.755731926254790268e-07, 4.920949692800671435e-09,
6.834657311305621830e-11, 7.593969849687574339e-13,
6.904822652741917551e-15, 5.220157095351373194e-17,
3.410720494727771276e-19, 1.625212890947171108e-21,
1.332898928162290861e-23};
T a = square(z) * 0.25;
T Q[3] = {1, 0.5, evaluate_polynomial(P, a)};
return log(z) + log(evaluate_polynomial(Q, a)) - LOG_TWO;
}
if (z < 500) {
// Max error in interpolated form: 1.796e-16
// Max Error found at double precision = Poly: 2.898731e-16
static const double P[] = {
3.989422804014406054e-01, -1.496033551613111533e-01,
-4.675104253598537322e-02, -4.090895951581637791e-02,
-5.719036414430205390e-02, -1.528189554374492735e-01,
3.458284470977172076e+00, -2.426181371595021021e+02,
1.178785865993440669e+04, -4.404655582443487334e+05,
1.277677779341446497e+07, -2.903390398236656519e+08,
5.192386898222206474e+09, -7.313784438967834057e+10,
8.087824484994859552e+11, -6.967602516005787001e+12,
4.614040809616582764e+13, -2.298849639457172489e+14,
8.325554073334618015e+14, -2.067285045778906105e+15,
3.146401654361325073e+15, -2.213318202179221945e+15};
return z + log(evaluate_polynomial(P, 1 / z)) - multiply_log(0.5, z);
}
// Max error in interpolated form: 1.320e-19
// Max Error found at double precision = Poly: 7.065357e-17
static const double P[] = {
3.989422804014314820e-01, -1.496033551467584157e-01,
-4.675105322571775911e-02, -4.090421597376992892e-02,
-5.843630344778927582e-02};
return z + log(evaluate_polynomial(P, 1 / z)) - multiply_log(0.5, z);
}
if (z > 100) {
// Boost does something like this in asymptotic_bessel_i_large_x
T lim = pow((square(v) + 2.5) / (2 * z), 3) / 24;
if (lim < (EPSILON * 10)) {
T s = 1;
T mu = 4 * square(v);
T ex = 8 * z;
T num = mu - 1;
T denom = ex;
s -= num / denom;
num *= mu - 9;
denom *= ex * 2;
s += num / denom;
num *= mu - 25;
denom *= ex * 3;
s -= num / denom;
s = z - log(sqrt(z * TWO_PI)) + log(s);
return s;
}
}
T log_half_z = log(0.5 * z);
T lgam = (v > -1) ? lgamma(v + 1.0) : 0;
T lcons = (2.0 + v) * log_half_z;
T out;
if (v > -1) {
out = log_sum_exp(v * log_half_z - lgam, lcons - lgamma(v + 2));
lgam += log1p(v);
} else {
out = lcons;
}
double m = 2;
double lfac = 0;
T old_out;
do {
lfac += log(m);
lgam += log(v + m);
lcons += 2 * log_half_z;
old_out = out;
out = log_sum_exp(out, lcons - lfac - lgam); // underflows eventually
m++;
} while (out > old_out || out < old_out);
return out;
}
} // namespace CosmoTool
#endif