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-rw-r--r--src/boost/libs/math/test/test_toms748_solve.cpp273
1 files changed, 273 insertions, 0 deletions
diff --git a/src/boost/libs/math/test/test_toms748_solve.cpp b/src/boost/libs/math/test/test_toms748_solve.cpp
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index 00000000..5a40055c
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+++ b/src/boost/libs/math/test/test_toms748_solve.cpp
@@ -0,0 +1,273 @@
+// (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 <pch.hpp>
+
+#define BOOST_TEST_MAIN
+#include <boost/test/unit_test.hpp>
+#include <boost/test/tools/floating_point_comparison.hpp>
+
+#include <boost/math/tools/toms748_solve.hpp>
+#include <boost/math/special_functions/gamma.hpp>
+#include <boost/math/special_functions/beta.hpp>
+#include <iostream>
+#include <iomanip>
+
+//
+// Test functor implements the same test cases as used by
+// "Algorithm 748: Enclosing Zeros of Continuous Functions"
+// by G.E. Alefeld, F.A. Potra and Yixun Shi.
+//
+// Plus two more: one for inverting the incomplete gamma,
+// and one for inverting the incomplete beta.
+//
+template <class T>
+struct toms748tester
+{
+ toms748tester(unsigned i) : k(i), ip(0), a(0), b(0){}
+ toms748tester(unsigned i, int ip_) : k(i), ip(ip_), a(0), b(0){}
+ toms748tester(unsigned i, T a_, T b_) : k(i), ip(0), a(a_), b(b_){}
+
+ static unsigned total_calls()
+ {
+ return invocations;
+ }
+ static void reset()
+ {
+ invocations = 0;
+ }
+
+ T operator()(T x)
+ {
+ using namespace std;
+
+ ++invocations;
+ switch(k)
+ {
+ case 1:
+ return sin(x) - x / 2;
+ case 2:
+ {
+ T r = 0;
+ for(int i = 1; i <= 20; ++i)
+ {
+ T p = (2 * i - 5);
+ T q = x - i * i;
+ r += p * p / (q * q * q);
+ }
+ r *= -2;
+ return r;
+ }
+ case 3:
+ return a * x * exp(b * x);
+ case 4:
+ return pow(x, b) - a;
+ case 5:
+ return sin(x) - 0.5;
+ case 6:
+ return 2 * x * exp(-T(ip)) - 2 * exp(-ip * x) + 1;
+ case 7:
+ return (1 + (1 - ip) * (1 - ip)) * x - (1 - ip * x) * (1 - ip * x);
+ case 8:
+ return x * x - pow(1 - x, a);
+ case 9:
+ return (1 + (1 - ip) * (1 - ip) * (1 - ip) * (1 - ip)) * x - (1 - ip * x) * (1 - ip * x) * (1 - ip * x) * (1 - ip * x);
+ case 10:
+ return exp(-ip * x) * (x - 1) + pow(x, T(ip));
+ case 11:
+ return (ip * x - 1) / ((ip - 1) * x);
+ case 12:
+ return pow(x, T(1)/ip) - pow(T(ip), T(1)/ip);
+ case 13:
+ return x == 0 ? 0 : x * exp(-1 / (x * x));
+ case 14:
+ return x >= 0 ? (T(ip)/20) * (x / 1.5f + sin(x) - 1) : -T(ip)/20;
+ case 15:
+ {
+ T d = 2e-3f / (1+ip);
+ if(x > d)
+ return exp(1.0) - 1.859;
+ else if(x > 0)
+ return exp((ip+1)*x*1000 / 2) - 1.859;
+ return -0.859f;
+ }
+ case 16:
+ {
+ return boost::math::gamma_q(x, a) - b;
+ }
+ case 17:
+ return boost::math::ibeta(x, a, 0.5) - b;
+ }
+ return 0;
+ }
+private:
+ int k; // index of problem.
+ int ip; // integer parameter
+ T a, b; // real parameter
+
+ static unsigned invocations;
+};
+
+template <class T>
+unsigned toms748tester<T>::invocations = 0;
+
+boost::uintmax_t total = 0;
+boost::uintmax_t invocations = 0;
+
+template <class T>
+void run_test(T a, T b, int id)
+{
+ boost::uintmax_t c = 1000;
+ std::pair<double, double> r = toms748_solve(toms748tester<double>(id),
+ a,
+ b,
+ boost::math::tools::eps_tolerance<double>(std::numeric_limits<double>::digits),
+ c);
+ BOOST_CHECK_EQUAL(c, toms748tester<double>::total_calls());
+ total += c;
+ invocations += toms748tester<double>::total_calls();
+ std::cout << "Function " << id << "\nresult={" << r.first << ", " << r.second << "} total calls=" << toms748tester<double>::total_calls() << "\n\n";
+ toms748tester<double>::reset();
+}
+
+template <class T>
+void run_test(T a, T b, int id, int p)
+{
+ boost::uintmax_t c = 1000;
+ std::pair<double, double> r = toms748_solve(toms748tester<double>(id, p),
+ a,
+ b,
+ boost::math::tools::eps_tolerance<double>(std::numeric_limits<double>::digits),
+ c);
+ BOOST_CHECK_EQUAL(c, toms748tester<double>::total_calls());
+ total += c;
+ invocations += toms748tester<double>::total_calls();
+ std::cout << "Function " << id << "\nresult={" << r.first << ", " << r.second << "} total calls=" << toms748tester<double>::total_calls() << "\n\n";
+ toms748tester<double>::reset();
+}
+
+template <class T>
+void run_test(T a, T b, int id, T p1, T p2)
+{
+ boost::uintmax_t c = 1000;
+ std::pair<double, double> r = toms748_solve(toms748tester<double>(id, p1, p2),
+ a,
+ b,
+ boost::math::tools::eps_tolerance<double>(std::numeric_limits<double>::digits),
+ c);
+ BOOST_CHECK_EQUAL(c, toms748tester<double>::total_calls());
+ total += c;
+ invocations += toms748tester<double>::total_calls();
+ std::cout << "Function " << id << "\n Result={" << r.first << ", " << r.second << "} total calls=" << toms748tester<double>::total_calls() << "\n\n";
+ toms748tester<double>::reset();
+}
+
+BOOST_AUTO_TEST_CASE( test_main )
+{
+ std::cout << std::setprecision(18);
+ run_test(3.14/2, 3.14, 1);
+
+ for(int i = 1; i <= 10; i += 1)
+ {
+ run_test(i*i + 1e-9, (i+1)*(i+1) - 1e-9, 2);
+ }
+
+ run_test(-9.0, 31.0, 3, -40.0, -1.0);
+ run_test(-9.0, 31.0, 3, -100.0, -2.0);
+ run_test(-9.0, 31.0, 3, -200.0, -3.0);
+
+ for(int n = 4; n <= 12; n += 2)
+ {
+ run_test(0.0, 5.0, 4, 0.2, double(n));
+ }
+ for(int n = 4; n <= 12; n += 2)
+ {
+ run_test(0.0, 5.0, 4, 1.0, double(n));
+ }
+ for(int n = 8; n <= 14; n += 2)
+ {
+ run_test(-0.95, 4.05, 4, 1.0, double(n));
+ }
+ run_test(0.0, 1.5, 5);
+ for(int n = 1; n <= 5; ++n)
+ {
+ run_test(0.0, 1.0, 6, n);
+ }
+ for(int n = 20; n <= 100; n += 20)
+ {
+ run_test(0.0, 1.0, 6, n);
+ }
+ run_test(0.0, 1.0, 7, 5);
+ run_test(0.0, 1.0, 7, 10);
+ run_test(0.0, 1.0, 7, 20);
+ run_test(0.0, 1.0, 8, 2);
+ run_test(0.0, 1.0, 8, 5);
+ run_test(0.0, 1.0, 8, 10);
+ run_test(0.0, 1.0, 8, 15);
+ run_test(0.0, 1.0, 8, 20);
+ run_test(0.0, 1.0, 9, 1);
+ run_test(0.0, 1.0, 9, 2);
+ run_test(0.0, 1.0, 9, 4);
+ run_test(0.0, 1.0, 9, 5);
+ run_test(0.0, 1.0, 9, 8);
+ run_test(0.0, 1.0, 9, 15);
+ run_test(0.0, 1.0, 9, 20);
+ run_test(0.0, 1.0, 10, 1);
+ run_test(0.0, 1.0, 10, 5);
+ run_test(0.0, 1.0, 10, 10);
+ run_test(0.0, 1.0, 10, 15);
+ run_test(0.0, 1.0, 10, 20);
+
+ run_test(0.01, 1.0, 11, 2);
+ run_test(0.01, 1.0, 11, 5);
+ run_test(0.01, 1.0, 11, 15);
+ run_test(0.01, 1.0, 11, 20);
+
+ for(int n = 2; n <= 6; ++n)
+ run_test(1.0, 100.0, 12, n);
+ for(int n = 7; n <= 33; n+=2)
+ run_test(1.0, 100.0, 12, n);
+
+ run_test(-1.0, 4.0, 13);
+
+ for(int n = 1; n <= 40; ++n)
+ run_test(-1e4, 3.14/2, 14, n);
+
+ for(int n = 20; n <= 40; ++n)
+ run_test(-1e4, 1e-4, 15, n);
+
+ for(int n = 100; n <= 1000; n+=100)
+ run_test(-1e4, 1e-4, 15, n);
+
+ std::cout << "Total iterations consumed = " << total << std::endl;
+ std::cout << "Total function invocations consumed = " << invocations << std::endl << std::endl;
+
+ BOOST_CHECK(invocations < 3150);
+
+ std::cout << std::setprecision(18);
+
+ for(int n = 5; n <= 100; n += 10)
+ run_test(sqrt(double(n)), double(n+1), 16, (double)n, 0.4);
+
+ for(int n = 5; n <= 100; n += 10)
+ run_test(double(n / 2), double(2*n), 17, (double)n, 0.4);
+
+
+ for(int n = 4; n <= 12; n += 2)
+ {
+ boost::uintmax_t c = 1000;
+ std::pair<double, double> r = bracket_and_solve_root(toms748tester<double>(4, 0.2, double(n)),
+ 2.0,
+ 2.0,
+ true,
+ boost::math::tools::eps_tolerance<double>(std::numeric_limits<double>::digits),
+ c);
+ std::cout << std::setprecision(18);
+ std::cout << "Function " << 4 << "\n Result={" << r.first << ", " << r.second << "} total calls=" << toms748tester<double>::total_calls() << "\n\n";
+ toms748tester<double>::reset();
+ BOOST_CHECK(c < 20);
+ }
+}
+
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