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List: boost-commit
Subject: [Boost-commit] svn:boost r73460 -
From: e_float () yahoo ! com
Date: 2011-07-31 11:59:05
Message-ID: 20110731115905.6771D2F81DB () wowbagger ! osl ! iu ! edu
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Author: christopher_kormanyos
Date: 2011-07-31 07:59:03 EDT (Sun, 31 Jul 2011)
New Revision: 73460
URL: http://svn.boost.org/trac/boost/changeset/73460
Log:
- Corrected spelling in filename guass --> gauss
Added:
sandbox/e_float/libs/e_float/example/example_008_gauss_laguerre.cpp
- copied unchanged from r73459, \
/sandbox/e_float/libs/e_float/example/example_008_guass_laguerre.cpp Removed:
sandbox/e_float/libs/e_float/example/example_008_guass_laguerre.cpp
Deleted: sandbox/e_float/libs/e_float/example/example_008_guass_laguerre.cpp
==============================================================================
--- sandbox/e_float/libs/e_float/example/example_008_guass_laguerre.cpp 2011-07-31 \
07:59:03 EDT (Sun, 31 Jul 2011)
+++ (empty file)
@@ -1,313 +0,0 @@
-
-// Copyright Christopher Kormanyos 2002 - 2011.
-// Distributed under 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)
-
-// This work is based on an earlier work:
-// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function \
Calculations",
-// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. \
http://doi.acm.org/10.1145/1916461.1916469
-
-#include <vector>
-
-#include <e_float/e_float.hpp>
-#include <e_float/e_float_functions.hpp>
-
-#include "examples.h"
-#include "../src/utility/util_digit_scale.h"
-#include "../src/utility/util_find_root_newton_raphson.h"
-#include "../src/utility/util_lexical_cast.h"
-#include "../src/utility/util_noncopyable.h"
-#include "../src/utility/util_point.h"
-
-namespace examples
-{
- namespace nr_008
- {
- class GaussQuadAbscissasAndWeights : private Util::noncopyable
- {
- protected:
-
- const INT32 N;
- std::vector<e_float> xi;
- std::vector<e_float> wi;
-
- protected:
-
- GaussQuadAbscissasAndWeights(const INT32 n) : N (n),
- xi(0u),
- wi(0u) { }
-
- public:
-
- virtual ~GaussQuadAbscissasAndWeights() { }
-
- public:
-
- const std::vector<e_float>& abscissas(void) const { return xi; }
- const std::vector<e_float>& weights (void) const { return wi; }
- };
-
- class GuassLaguerreAbscissasAndWeights : public GaussQuadAbscissasAndWeights
- {
- private:
-
- const e_float alpha;
-
- public:
-
- GuassLaguerreAbscissasAndWeights(const INT32 n, const e_float& a = \
ef::zero());
-
- virtual ~GuassLaguerreAbscissasAndWeights() { }
-
- private:
-
- class FindRootLaguerre : public Util::FindRootNewtonRaphson<e_float>
- {
- private:
-
- static const e_float& my_tol(void)
- {
- static const e_float val = e_float("1E-" + Util::lexical_cast(ef::tol() - \
static_cast<INT64>(3)));
- return val;
- }
-
- const INT32 N;
- const e_float alpha;
- mutable e_float my_d;
- mutable e_float my_p2;
-
- public:
-
- FindRootLaguerre(const INT32 n,
- const e_float& a,
- const e_float& lo,
- const e_float& hi) : \
Util::FindRootNewtonRaphson<e_float>(lo, hi, my_tol()),
- N (n),
- alpha(a),
- my_d (static_cast<UINT32>(0u)),
- my_p2(static_cast<UINT32>(0u)) { }
-
- virtual ~FindRootLaguerre() { }
-
- const e_float& poly_p2(void) const { return my_p2; }
-
- private:
-
- virtual void my_function_derivative(const e_float& x, e_float& f, e_float& \
d) const;
-
- virtual e_float my_function(const e_float& x) const;
- };
-
- e_float my_laguerre(const e_float& x) const
- {
- static const FindRootLaguerre rl(N, alpha, ef::zero(), ef::million());
- return rl.function(x);
- }
- };
- }
-}
-
-examples::nr_008::GuassLaguerreAbscissasAndWeights::GuassLaguerreAbscissasAndWeights(const \
INT32 n,
- \
const e_float& a) : GaussQuadAbscissasAndWeights(n),
- \
alpha(a)
-{
- // Walk through the function using a step-size of dynamic width
- // to find the zero crossings of the Laguerre function.
- // Store these zero crossings as bracketed root estimates.
- std::vector<Util::point<e_float> > xlo_xhi_points;
-
- // Estimate first Laguerre zero using the approximation of x1
- // from Stroud and Secrest.
- const double alf = ef::to_double(alpha);
- const double x1 = ((1.0 + alf) * (3.0 + (0.92 * alf))) / (1.0 + (2.4 * \
static_cast<double>(N)) + (1.8 * alf));
-
- e_float delta(x1 / 10.0);
- e_float x = delta;
-
- bool bo_is_neg = ef::isneg(my_laguerre(ef::zero()));
-
- std::cout << "finding approximate roots..." << std::endl;
-
- while(static_cast<INT32>(xlo_xhi_points.size()) < N)
- {
- x += delta;
-
- if(ef::isneg(my_laguerre(x)) != bo_is_neg)
- {
- // Refine the approximate root with 16 bisection iteration steps.
- e_float dx;
- e_float rt;
- e_float hi = x;
- e_float lo = x - delta;
-
- if(my_laguerre(lo) < ef::zero())
- {
- dx = hi - lo;
- rt = lo;
- }
- else
- {
- dx = lo - hi;
- rt = hi;
- }
-
- // Here are the 16 bisection iteration steps.
- for(UINT32 j = static_cast<UINT32>(0u); j < static_cast<UINT32>(16u); j++)
- {
- dx /= static_cast<INT32>(2);
-
- const e_float x_mid = rt + dx;
- const e_float f_mid = my_laguerre(x_mid);
-
- if(f_mid <= ef::zero())
- {
- rt = x_mid;
- }
- }
-
- // Store the refined approximate root as a bracketed point.
- xlo_xhi_points.push_back(Util::point<e_float>(rt - dx, rt + dx));
-
- if(xlo_xhi_points.size() > static_cast<std::size_t>(1u))
- {
- const e_float new_delta2 = (xlo_xhi_points.end() - \
static_cast<std::size_t>(1u))->x
- - (xlo_xhi_points.end() - \
static_cast<std::size_t>(2u))->x;
-
- // Dynamically adjust and set the new step-size.
- delta = new_delta2 / static_cast<INT32>(2);
- }
-
- bo_is_neg = !bo_is_neg;
- }
- }
-
- // Calculate the abscissas and weights to full precision.
- for(std::size_t i = static_cast<std::size_t>(0u); i < xlo_xhi_points.size(); i++)
- {
- std::cout << "calculating abscissa and weight for index: " << i << std::endl;
-
- // Find the abscissas using Newton-Raphson iteration.
- const FindRootLaguerre rooti(N, alpha, xlo_xhi_points[i].x, \
xlo_xhi_points[i].y);
- const e_float ri = rooti.operation();
-
- if(!rooti.success())
- {
- break;
- }
-
- // Calculate the weights.
- e_float f;
- e_float d;
- rooti.function_derivative(ri, f, d);
-
- // Store abscissas and weights.
- xi.push_back(ri);
-
- if(ef::iszero(alpha))
- {
- wi.push_back(-ef::one() / ((d * N) * rooti.poly_p2()));
- }
- else
- {
- const e_float norm_g = ef::gamma(alpha + N) / \
ef::factorial(static_cast<UINT32>(N - static_cast<INT32>(1)));
- wi.push_back(-norm_g / ((d * N) * rooti.poly_p2()));
- }
- }
-}
-
-void examples::nr_008::GuassLaguerreAbscissasAndWeights::FindRootLaguerre::my_function_derivative(const \
e_float& x, e_float& f, e_float& d) const
-{
- f = my_function(x);
- d = my_d;
-}
-
-e_float examples::nr_008::GuassLaguerreAbscissasAndWeights::FindRootLaguerre::my_function(const \
e_float& x) const
-{
- e_float p1(1);
- e_float p2(0);
-
- for(INT32 j = static_cast<INT32>(0); j < N; j++)
- {
- const e_float p3(p2);
- p2 = p1;
-
- const INT32 j_plus_one = static_cast<INT32>(j + static_cast<INT32>(1));
- const INT32 two_j_plus_one = static_cast<INT32>(j + j_plus_one);
-
- p1 = (((two_j_plus_one + (alpha - x)) * p2) - ((j + alpha) * p3)) / j_plus_one;
- }
-
- my_d = ((N * p1) - ((N + alpha) * p2)) / x;
- my_p2 = p2;
-
- return p1;
-}
-
-namespace examples
-{
- namespace nr_008
- {
- struct GaussLaguerreAi : public Util::Function<e_float>
- {
- private:
-
- const e_float x;
- const e_float zeta;
- const e_float one_over_zeta;
- e_float factor;
-
- public:
-
- GaussLaguerreAi(const e_float& X) : x(X),
- zeta(ef::two_third() * (ef::sqrt(x) * x)),
- one_over_zeta(ef::one() / zeta),
- factor(0u)
- {
- const e_float zeta_times_48_pow_sixth = ef::rootn(zeta * \
static_cast<INT32>(48), static_cast<INT32>(6));
- factor = ef::one() / ((ef::sqrt_pi() * zeta_times_48_pow_sixth) * \
(ef::exp(zeta) * ef::gamma(ef::five() / static_cast<INT32>(6))));
- }
-
- virtual ~GaussLaguerreAi() { }
-
- private:
-
- virtual e_float my_function(const e_float& t) const
- {
- return factor / ef::rootn(ef::two() + (t * one_over_zeta), \
static_cast<INT32>(6));
- }
- };
- }
-}
-
-e_float examples::nr_008::gauss_laguerre_airy_a(const e_float& x)
-{
- static const INT32 n_terms = static_cast<INT32>(Util::DigitScale() * 400.0);
-
- static const GuassLaguerreAbscissasAndWeights aw(n_terms, -ef::one() / \
static_cast<INT32>(6));
-
- static const std::size_t sz = aw.weights().size();
-
- const GaussLaguerreAi ai(x);
-
- e_float sum(0);
-
- for(std::size_t i = static_cast<std::size_t>(0u); i < sz; i++)
- {
- const e_float fi = ai.function(aw.abscissas()[i]);
- const e_float wi = aw.weights()[i];
-
- const e_float term = wi * fi;
-
- const INT64 order_check = static_cast<INT64>(term.order() - sum.order());
-
- if((i > static_cast<INT32>(20)) && (order_check < -ef::tol()))
- {
- break;
- }
-
- sum += term;
- }
-
- return sum;
-}
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