Morten Hjorth-Jensen
448 lines
26 KiB
HTML
448 lines
26 KiB
HTML
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._Statistics-bs001.html#___sec0" style="font-size: 80%;"> Domains and probabilities</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs002.html#___sec1" style="font-size: 80%;"> Tossing a dice</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs003.html#___sec2" style="font-size: 80%;"> Stochastic variables</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs004.html#___sec3" style="font-size: 80%;"> Stochastic variables and the main concepts, the discrete case</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs005.html#___sec4" style="font-size: 80%;"> Stochastic variables and the main concepts, the continuous case</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs006.html#___sec5" style="font-size: 80%;"> The cumulative probability</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs007.html#___sec6" style="font-size: 80%;"> Properties of PDFs</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs008.html#___sec7" style="font-size: 80%;"> Important distributions, the uniform distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs009.html#___sec8" style="font-size: 80%;"> Gaussian distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs010.html#___sec9" style="font-size: 80%;"> Exponential distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs011.html#___sec10" style="font-size: 80%;"> Expectation values</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs012.html#___sec11" style="font-size: 80%;"> Stochastic variables and the main concepts, mean values</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs013.html#___sec12" style="font-size: 80%;"> Stochastic variables and the main concepts, central moments, the variance</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs014.html#___sec13" style="font-size: 80%;"> Probability Distribution Functions</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs015.html#___sec14" style="font-size: 80%;"> Probability Distribution Functions</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs016.html#___sec15" style="font-size: 80%;"> The three famous Probability Distribution Functions</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs017.html#___sec16" style="font-size: 80%;"> Probability Distribution Functions, the normal distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs018.html#___sec17" style="font-size: 80%;"> Probability Distribution Functions, the normal distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs019.html#___sec18" style="font-size: 80%;"> Probability Distribution Functions, the cumulative distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs020.html#___sec19" style="font-size: 80%;"> Probability Distribution Functions, other important distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs021.html#___sec20" style="font-size: 80%;"> Probability Distribution Functions, the binomial distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs022.html#___sec21" style="font-size: 80%;"> Probability Distribution Functions, Poisson's distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs023.html#___sec22" style="font-size: 80%;"> Probability Distribution Functions, Poisson's distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs024.html#___sec23" style="font-size: 80%;"> Meet the covariance!</a></li>
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|
<!-- navigation toc: --> <li><a href="._Statistics-bs025.html#___sec24" style="font-size: 80%;"> Meet the covariance in matrix disguise</a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics-bs026.html#___sec25" style="font-size: 80%;"> Meet the covariance, uncorrelated events</a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics-bs027.html#___sec26" style="font-size: 80%;"> Numerical experiments and the covariance</a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics-bs028.html#___sec27" style="font-size: 80%;"> Numerical experiments and the covariance</a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics-bs029.html#___sec28" style="font-size: 80%;"> Numerical experiments and the covariance, actual situations</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs030.html#___sec29" style="font-size: 80%;"> Numerical experiments and the covariance, our observables</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs031.html#___sec30" style="font-size: 80%;"> Numerical experiments and the covariance, the sample variance</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs032.html#___sec31" style="font-size: 80%;"> Numerical experiments and the covariance, central limit theorem</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs033.html#___sec32" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs034.html#___sec33" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs035.html#___sec34" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs036.html#___sec35" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs037.html#___sec36" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation, sample variance</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs038.html#___sec37" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs039.html#___sec38" style="font-size: 80%;"><b>Random Numbers</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs040.html#___sec39" style="font-size: 80%;"><b>Random Numbers, better name: pseudo random numbers</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs041.html#___sec40" style="font-size: 80%;"><b>Random number generator RNG</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs042.html#___sec41" style="font-size: 80%;"><b>Random number generator RNG and periodic outputs</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs043.html#___sec42" style="font-size: 80%;"><b>Random number generator RNG and its period</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs044.html#___sec43" style="font-size: 80%;"><b>Random number generator RNG, other examples</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs045.html#___sec44" style="font-size: 80%;"><b>Random number generator RNG, other examples</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs046.html#___sec45" style="font-size: 80%;"><b>Random number generator RNG, RAN0</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics-bs047.html#___sec46" style="font-size: 80%;"><b>Random number generator RNG, RAN0</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs048.html#___sec47" style="font-size: 80%;"><b>Random number generator RNG, RAN0</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs049.html#___sec48" style="font-size: 80%;"><b>Random number generator RNG, RAN0</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs050.html#___sec49" style="font-size: 80%;"><b>Random number generator RNG, RAN0 code</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs051.html#___sec50" style="font-size: 80%;"> Properties of Selected Random Number Generators</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs052.html#___sec51" style="font-size: 80%;"> Properties of Selected Random Number Generators</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs053.html#___sec52" style="font-size: 80%;"> Properties of Selected Random Number Generators</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs054.html#___sec53" style="font-size: 80%;"> Simple demonstration of RNGs using python</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs055.html#___sec54" style="font-size: 80%;"> Properties of Selected Random Number Generators</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs056.html#___sec55" style="font-size: 80%;"> Correlation function and which random number generators should I use</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs057.html#___sec56" style="font-size: 80%;"> Correlation function and which random number generators should I use</a></li>
|
|
<!-- navigation toc: --> <li><a href="#___sec57" style="font-size: 80%;"><b>Which RNG should I use?</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs059.html#___sec58" style="font-size: 80%;"> How to use the Mersenne generator</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs060.html#___sec59" style="font-size: 80%;"> Why blocking?</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs061.html#___sec60" style="font-size: 80%;"> Why blocking?</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs062.html#___sec61" style="font-size: 80%;"> Code to demonstrate the calculation of the autocorrelation function</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs063.html#___sec62" style="font-size: 80%;"> What is blocking?</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs064.html#___sec63" style="font-size: 80%;"> What is blocking?</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs065.html#___sec64" style="font-size: 80%;"> What is blocking?</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics-bs066.html#___sec65" style="font-size: 80%;"> Implementation</a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics-bs067.html#___sec66" style="font-size: 80%;"> Actual implementation with code, main function</a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics-bs068.html#___sec67" style="font-size: 80%;"> The Bootstrap method</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs069.html#___sec68" style="font-size: 80%;"> Bootstrapping</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs070.html#___sec69" style="font-size: 80%;"> Bootstrapping, recipe</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs071.html#___sec70" style="font-size: 80%;"> Bootstrapping, "code":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py"</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics-bs072.html#___sec71" style="font-size: 80%;"> Jackknife, "code":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py"</a></li>
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<a name="part0058"></a>
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<!-- !split -->
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<h1 id="___sec57" class="anchor">Which RNG should I use? </h1>
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<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
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<ul>
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<li> In the library files lib.cpp and lib.h we have included four popular RNGs taken from the widely used textbook <a href="http://numerical.recipes/" target="_self">Numerical Recipes</a>. These are called ran0, ran1, ran2 and ran3.</li>
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<li> C++ has a class called <b>random</b>. The <a href="http://www.cplusplus.com/reference/random/" target="_self">random class</a> contains a large selection of RNGs and is highly recommended. Some of these RNGs have very large periods making it thereby very safe to use these RNGs in case one is performing large calculations. In particular, the <a href="http://www.cplusplus.com/reference/random/mersenne_twister_engine/" target="_self">Mersenne twister random number engine</a> has a period of \( 2^{19937} \).</li>
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