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multi_newton_time.cpp.xml @upstream/2015.00.00.7 — raw · history · blame
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xmlns:math='http://www.w3.org/1998/Math/MathML' > <head> <title>Timing Test of Multi-Threaded Newton Method</title> <meta http-equiv='Content-Type' content='text/html' charset='utf-8'/> <meta name="description" id="description" content="Timing Test of Multi-Threaded Newton Method"/> <meta name="keywords" id="keywords" content=" multi_newton_time multi_thread Newton Ad speed thread multi_newton newton timing test of multi-threaded method syntax purpose ok time_out test_time num_threads num_zero num_sub num_sum use_ad source "/> <style type='text/css'> body { color : black } body { background-color : white } A:link { color : blue } A:visited { color : purple } A:active { color : purple } </style> <script type='text/javascript' language='JavaScript' src='_multi_newton_time.cpp_xml.js'> </script> </head> <body> <table><tr> <td> <a href="http://www.coin-or.org/CppAD/" target="_top"><img border="0" src="_image.gif"/></a> </td> <td><a href="multi_newton.cpp.xml" target="_top">Prev</a> </td><td><a href="multi_newton_work.cpp.xml" target="_top">Next</a> </td><td> <select onchange='choose_across0(this)'> <option>Index-></option> <option>contents</option> <option>reference</option> <option>index</option> <option>search</option> <option>external</option> </select> </td> <td> <select onchange='choose_up0(this)'> <option>Up-></option> <option>CppAD</option> <option>multi_thread</option> <option>thread_test.cpp</option> <option>multi_newton.cpp</option> <option>multi_newton_time.cpp</option> </select> </td> <td> <select onchange='choose_down3(this)'> <option>multi_thread-></option> <option>parallel_ad</option> <option>thread_test.cpp</option> </select> </td> <td> <select onchange='choose_down2(this)'> <option>thread_test.cpp-></option> <option>a11c_openmp.cpp</option> <option>a11c_bthread.cpp</option> <option>a11c_pthread.cpp</option> <option>simple_ad_openmp.cpp</option> <option>simple_ad_bthread.cpp</option> <option>simple_ad_pthread.cpp</option> <option>team_example.cpp</option> <option>harmonic.cpp</option> <option>multi_newton.cpp</option> <option>team_thread.hpp</option> </select> </td> <td> <select onchange='choose_down1(this)'> <option>multi_newton.cpp-></option> <option>multi_newton_time.cpp</option> <option>multi_newton_work.cpp</option> </select> </td> <td>multi_newton_time.cpp</td> <td> <select onchange='choose_current0(this)'> <option>Headings-></option> <option>Syntax</option> <option>Purpose</option> <option>ok</option> <option>time_out</option> <option>test_time</option> <option>num_threads</option> <option>num_zero</option> <option>num_sub</option> <option>num_sum</option> <option>use_ad</option> <option>Source</option> </select> </td> </tr></table><br/> . <center><b><big><big>Timing Test of Multi-Threaded Newton Method</big></big></b></center> <br/> <b><big><a name="Syntax" id="Syntax">Syntax</a></big></b> <br/> <code><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'> = multi_newton_time(</span></font><i><font color="black"><span style='white-space: nowrap'>time_out</span></font></i><font color="blue"><span style='white-space: nowrap'>, </span></font><i><font color="black"><span style='white-space: nowrap'>num_threads</span></font></i><font color="blue"><span style='white-space: nowrap'>, <br/>      </span></font><i><font color="black"><span style='white-space: nowrap'>num_zero</span></font></i><font color="blue"><span style='white-space: nowrap'>, </span></font><i><font color="black"><span style='white-space: nowrap'>num_sub</span></font></i><font color="blue"><span style='white-space: nowrap'>, </span></font><i><font color="black"><span style='white-space: nowrap'>num_sum</span></font></i><font color="blue"><span style='white-space: nowrap'>, </span></font><i><font color="black"><span style='white-space: nowrap'>use_ad</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> )</span></font></code> <br/> <br/> <b><big><a name="Purpose" id="Purpose">Purpose</a></big></b> <br/> Runs correctness and timing test for a multi-threaded Newton method. This test uses Newton's method to determine all the zeros of the sine function on an interval. CppAD, or hand coded derivatives, can be used to calculate the derivatives used by Newton's method. The calculation can be done in parallel on the different sub-intervals. In addition, the calculation can be done without multi-threading. <br/> <br/> <b><big><a name="ok" id="ok">ok</a></big></b> <br/> This return value has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      bool </span></font><i><font color="black"><span style='white-space: nowrap'>ok</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> If it is true, <code><font color="blue">multi_newton_time</font></code> passed the correctness test. Otherwise it is false. <br/> <br/> <b><big><a name="time_out" id="time_out">time_out</a></big></b> <br/> This argument has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      double& </span></font><i><font color="black"><span style='white-space: nowrap'>time_out</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> The input value of the argument does not matter. Upon return it is the number of wall clock seconds required for the multi-threaded Newton method can compute all the zeros. <br/> <br/> <b><big><a name="test_time" id="test_time">test_time</a></big></b> <br/> Is the minimum amount of wall clock time that the test should take. The number of repeats for the test will be increased until this time is reached. The reported <code><i><font color="black"><span style='white-space: nowrap'>time_out</span></font></i></code> is the total wall clock time divided by the number of repeats. <br/> <br/> <b><big><a name="num_threads" id="num_threads">num_threads</a></big></b> <br/> This argument has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      size_t </span></font><i><font color="black"><span style='white-space: nowrap'>num_threads</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> It specifies the number of threads that are available for this test. If it is zero, the test is run without multi-threading and <code><font color="blue"><span style='white-space: nowrap'><br/>      1 == CppAD::thread_alloc::num_threads()<br/> </span></font></code> when <code><font color="blue">multi_newton_time</font></code> is called. If it is non-zero, the test is run with multi-threading and <code><font color="blue"><span style='white-space: nowrap'><br/>      </span></font><i><font color="black"><span style='white-space: nowrap'>num_threads</span></font></i><font color="blue"><span style='white-space: nowrap'> == CppAD::thread_alloc::num_threads()<br/> </span></font></code> when <code><font color="blue">multi_newton_time</font></code> is called. <br/> <br/> <b><big><a name="num_zero" id="num_zero">num_zero</a></big></b> <br/> This argument has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      size_t </span></font><i><font color="black"><span style='white-space: nowrap'>num_zero</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> and it must be greater than one. It specifies the actual number of zeros in the test function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi>sin</mi> <mo stretchy="false">(</mo> <mi mathvariant='italic'>x</mi> <mo stretchy="false">)</mo> </mrow></math> . To be specific, <code><font color="blue">multi_newton_time</font></code> will attempt to determine all of the values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>x</mi> </mrow></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi>sin</mi> <mo stretchy="false">(</mo> <mi mathvariant='italic'>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">=</mo> <mn>0</mn> </mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>x</mi> </mrow></math> is in the interval <code><font color="blue"><span style='white-space: nowrap'><br/>      [ 0 , (</span></font><i><font color="black"><span style='white-space: nowrap'>num_zero</span></font></i><font color="blue"><span style='white-space: nowrap'> - 1) * </span></font><i><font color="black"><span style='white-space: nowrap'>pi</span></font></i><font color="blue"><span style='white-space: nowrap'> ]<br/> </span></font></code> . <br/> <br/> <b><big><a name="num_sub" id="num_sub">num_sub</a></big></b> <br/> This argument has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      size_t </span></font><i><font color="black"><span style='white-space: nowrap'>num_sub</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> It specifies the number of sub-intervals to divide the total interval into. It must be greater than zero and should probably be greater than two times <code><i><font color="black"><span style='white-space: nowrap'>num_zero</span></font></i></code> . <br/> <br/> <b><big><a name="num_sum" id="num_sum">num_sum</a></big></b> <br/> This argument has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      size_t </span></font><i><font color="black"><span style='white-space: nowrap'>num_sum</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> and must be greater than zero. The actual function used by the Newton method is <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <mi mathvariant='italic'>f</mi> <mo stretchy="false">(</mo> <mi mathvariant='italic'>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">=</mo> <mfrac><mrow><mn>1</mn> </mrow> <mrow><mi mathvariant='italic'>n</mi> </mrow> </mfrac> <munderover><mo displaystyle='true' largeop='true'>∑</mo> <mrow><mi mathvariant='italic'>i</mi> <mo stretchy="false">=</mo> <mn>1</mn> </mrow> <mrow><mi mathvariant='italic'>n</mi> </mrow> </munderover> <mi>sin</mi> <mo stretchy="false">(</mo> <mi mathvariant='italic'>x</mi> <mo stretchy="false">)</mo> </mrow></math> where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> </mrow></math> is equal to <code><i><font color="black"><span style='white-space: nowrap'>num_sum</span></font></i></code> . Larger values of <code><i><font color="black"><span style='white-space: nowrap'>num_sum</span></font></i></code> simulate a case where the evaluation of the function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>f</mi> <mo stretchy="false">(</mo> <mi mathvariant='italic'>x</mi> <mo stretchy="false">)</mo> </mrow></math> takes more time. <br/> <br/> <b><big><a name="use_ad" id="use_ad">use_ad</a></big></b> <br/> This argument has prototype <code><font color="blue"><span style='white-space: nowrap'><br/>      bool </span></font><i><font color="black"><span style='white-space: nowrap'>user_ad</span></font></i><font color="blue"><span style='white-space: nowrap'><br/> </span></font></code> If <code><i><font color="black"><span style='white-space: nowrap'>use_ad</span></font></i></code> is <code><font color="blue">true</font></code>, then derivatives will be computed using CppAD. Note that this derivative computation includes re-taping the function for each value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>x</mi> </mrow></math> (even though re-taping is not necessary). <code><span style='white-space: nowrap'><br/> <br/> </span></code>If <code><i><font color="black"><span style='white-space: nowrap'>use_ad</span></font></i></code> is <code><font color="blue">false</font></code>, derivatives will be computed using a hand coded routine. <br/> <br/> <b><big><a name="Source" id="Source">Source</a></big></b> <code><font color="blue"> <br/> <pre style='display:inline'> # include <cppad/cppad.hpp> # include <cppad/time_test.hpp> # include <cmath> # include <cstring> # include "multi_newton.hpp" namespace { // empty namespace // values correspond to arguments in previous call to multi_newton_time size_t num_threads_;// value passed to multi_newton_time size_t num_zero_; // number of zeros of f(x) in the total interval size_t num_sub_; // number of sub-intervals to split calculation into size_t num_sum_; // larger values make f(x) take longer to calculate // value of xout corresponding to most recent call to test_once CppAD::vector<double> xout_; // either fun_ad or fun_no depending on value of use_ad void (*fun_)(double x, double& f, double& df) = 0; // A version of the sine function that can be made as slow as we like template <class Float> Float f_eval(Float x) { Float sum = 0.; size_t i; for(i = 0; i < num_sum_; i++) sum += sin(x); return sum / Float(num_sum_); } // Direct calculation of derivative with same number of floating point // operations as for f_eval. double df_direct(double x) { double sum = 0.; size_t i; for(i = 0; i < num_sum_; i++) sum += cos(x); return sum / double(num_sum_); } // AD calculation of detivative void fun_ad(double x, double& f, double& df) { // use CppAD::vector because it uses fast multi-threaded memory alloc using CppAD::vector; using CppAD::AD; vector< <a href="ad.xml" target="_top">AD</a><double> > X(1), Y(1); X[0] = x; CppAD::<a href="independent.xml" target="_top">Independent</a>(X); Y[0] = f_eval(X[0]); CppAD::<a href="funconstruct.xml" target="_top">ADFun</a><double> F(X, Y); vector<double> dx(1), dy(1); dx[0] = 1.; dy = F.<a href="forward.xml" target="_top">Forward</a>(1, dx); f = Value( Y[0] ); df = dy[0]; return; } // evaulate the function and its derivative void fun_no(double x, double& f, double& df) { f = f_eval(x); df = df_direct(x); return; } // Run computation of all the zeros once void test_once(void) { if( num_zero_ == 0 ) { std::cerr << "multi_newton_time: num_zero == 0" << std::endl; exit(1); } double pi = 4. * std::atan(1.); double xlow = 0.; double xup = (num_zero_ - 1) * pi; double eps = xup * 100. * CppAD::numeric_limits<double>::epsilon(); size_t max_itr = 20; bool ok = multi_newton( xout_ , fun_ , num_sub_ , xlow , xup , eps , max_itr , num_threads_ ); if( ! ok ) { std::cerr << "multi_newton: error" << std::endl; exit(1); } return; } // Repeat computation of all the zeros a specied number of times void test_repeat(size_t repeat) { size_t i; for(i = 0; i < repeat; i++) test_once(); return; } } // end empty namespace bool multi_newton_time( double& time_out , double test_time , size_t num_threads , size_t num_zero , size_t num_sub , size_t num_sum , bool use_ad ) { bool ok = true; using CppAD::thread_alloc; // Set local namespace environment variables num_threads_ = num_threads; num_zero_ = num_zero; num_sub_ = num_sub; num_sum_ = num_sum; if( use_ad ) fun_ = fun_ad; else fun_ = fun_no; // expect number of threads to already be set up if( num_threads > 0 ) ok &= num_threads == CppAD::thread_alloc::num_threads(); else ok &= 1 == CppAD::thread_alloc::num_threads(); // run the test case and set time return value time_out = CppAD::time_test(test_repeat, test_time); // Call test_once for a correctness check double pi = 4. * std::atan(1.); double xup = (num_zero_ - 1) * pi; double eps = xup * 100. * CppAD::numeric_limits<double>::epsilon(); ok &= (xout_.size() == num_zero); size_t i = 0; for(i = 0; i < num_zero; i++) ok &= std::fabs( xout_[i] - pi * i) <= 2 * eps; // xout_ is a static variable, so clear it to free its memory xout_.clear(); // return correctness check result return ok; } </pre> </font></code> <hr/>Input File: multi_thread/multi_newton_time.cpp </body> </html> |