Initializes Mersenne twister RNG
- Parameters:
-
This code is translated directly from:
http://www.math.keio.ac.jp/matumoto/CODES/MT2002/mt19937ar.c
Here are the accompanying comments
A C-program for MT19937, with initialization improved 2002/1/26. Coded by Takuji Nishimura and Makoto Matsumoto.
Before using, initialize the state by using init_genrand(seed) or init_by_array(init_key, key_length).
Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. The names of its contributors may not be used to endorse or promote products derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
Any feedback is very welcome. http://www.math.keio.ac.jp/matumoto/emt.html email: matumoto@math.keio.ac.jp
Definition at line 725 of file lot.cpp.
Referenced by MT_genrand_int(), MT_init_by_array(), set_generator(), and set_seed().
![\[f(x) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}x^{a-1}(1-x)^{b-1} \]](form_0.png)
) 
)![\[ f(x) = {n \choose k}p^k(1-p)^{n-k} \]](form_70.png)
) 
)![\[ \mbox{E}(x) = np \]](form_4.png)
![\[ \mbox{Var}(x) = np(1-p) \]](form_5.png)
![\[ f(x) = \frac{1}{\pi\mbox{s} (1 + (\frac{x-\mbox{l}}{\mbox{s}})^2)} \]](form_6.png)
![\[ f(x) = \frac{1}{2^{n/2}\Gamma(n/2)}x^{n/2-1}e^{-x/2} \]](form_7.png)
![\[ \mbox{E}(x) = \mbox{n} \]](form_8.png)
![\[ \mbox{Var}(x) = 2\mbox{n} \]](form_9.png)
![\[ f({\bf x}) = \frac{\Gamma(\sum_i x_i)}{\prod_i\Gamma(x_i)}\prod_ix_i^{c_i} \]](form_73.png)
![\[ f(x) = e^{-1} \]](form_74.png)
![\[ \mbox{E}(x) = 1 \]](form_75.png)
![\[ \mbox{Var}(x) = 1 \]](form_76.png)
)![\[ f(x) = \lambda e^{-\lambda x} \]](form_96.png)
![\[ \mu = \frac{1}{\lambda} \]](form_97.png)
![\[ \sigma^2 = \left(\frac{1}{\lambda}\right)^2 \]](form_98.png)
![\[ f(x) = \frac{\Gamma((m+n)/2)}{\Gamma(m/2)\Gamma(n/2)}(m/n)^{m/2}x^{m/2-1}(1+(m/n)x)^{-(m+n)/2} \]](form_14.png)
![\[ \mbox{E}(x) = \frac{m}{m-2}, m > 2 \]](form_15.png)
![\[ \mbox{Var}(x) = \frac{2m^2(n-2)}{n(m+2)}, n > 2 \]](form_16.png)
, defaults to 1.0)![\[ f(x) = \frac{1}{\sigma^a \Gamma(a)}x^{a-1}e^{-x/\sigma} \]](form_77.png)
![\[ \mu = a\sigma \]](form_78.png)
![\[ \sigma^2 = a\sigma^2 \]](form_79.png)
![\[ f(x) = p(1-p)^x \]](form_20.png)
![\[ \mbox{E}(x) = \frac{1-p}{p} \]](form_21.png)
![\[ \mbox{Var}(x) = \frac{1-p}{p^2} \]](form_22.png)
![\[ f(x) = \frac{{w \choose x}{b \choose n-x}}{{w+b \choose n}} \]](form_80.png)
) ![\[ \mbox{E}(x) = n(\frac{w}{w+b}) \]](form_82.png)
![\[ \mbox{Var}(x) = \frac{n(\frac{w}{w+b})(1-\frac{w}{w+b})((w+b)-n)}{w+b-1} \]](form_83.png)
![\[ f(1/x) = \frac{1}{s^a \Gamma(a)}x^{a-1}e^{-x/s} \]](form_99.png)
![\[ f(y) = \frac{\lambda^a (1/y)^{a+1} e^{-\lambda/y}}{\Gamma(a)} \]](form_100.png)
![\[ \lambda = 1/s \]](form_101.png)
)![\[ \mbox{E}(x) = \frac{\lambda}{a-1} \quad , \quad a > 1 \]](form_102.png)
![\[ \mbox{Var}(x) = \frac{\lambda^2}{(a-1)^2(a-2)} \quad , \quad a > 2 \]](form_103.png)
![\[ f(x) = \frac{1}{\sigma x\sqrt{2\pi}}e^{-\frac{(\log(x) - \mu)^2}{2\sigma^2}} \]](form_33.png)
) ![\[ \mbox{E}(x) = e^{\mu + \sigma^2/2} \]](form_36.png)
![\[ \mbox{Var}(x) = e^{2\mu + \sigma^2}(e^{\sigma^2}-1) \]](form_37.png)
![\[ \mbox{mode} = \frac{e^\mu}{e^{\sigma^2}} \]](form_38.png)
![\[ \mbox{median} = e^\mu \]](form_39.png)
![\[ f(x) = \frac{1}{s}\frac{e^{\frac{x-m}{s}}}{(1 + e^{\frac{x-m}{s}})^2} \]](form_40.png)
)![\[ f(x) = \frac{1}{s}\frac{e^{\frac{-(x-m)}{s}}}{(1 + e^{\frac{-(x-m)}{s}})^2} \]](form_42.png)
) ![\[ \mbox{E}(x) = m \]](form_43.png)
![\[ \mbox{Var}(x) = \frac{\pi^2s^2}{3} \]](form_44.png)
![\[ f({\bf n}) = {\sum_i n_i \choose n_1 \dots n_I}\prod_i p_i^{n_i} \]](form_45.png)
) 
)
and 
. 
guaranteed, because ![\[ f(x) = \frac{\Gamma(x+n)}{\Gamma(n)x!}p^n(1-p)^x \]](form_46.png)
![\[ \mbox{E}(x) = \frac{x(1-p)}{p} \]](form_47.png)
![\[ \mbox{Var}(x) = \frac{x(1-p)}{p^2} \]](form_48.png)
![\[ f(x) = \frac{\lambda^x e^{-\lambda}}{x!} \]](form_52.png)
![\[ \mbox{E}(x) = \mu \]](form_50.png)
![\[ \mbox{Var}(x) = \mu \]](form_91.png)
![\[ f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} \]](form_104.png)
![\[ \mbox{Var}(x) = \sigma^2 \]](form_51.png)
![\[ f(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}} \]](form_92.png)
![\[ \mbox{E}(x) = 0 \]](form_93.png)
![\[ f(x) = \frac{\Gamma(\frac{\nu+1}{2})}{\sqrt{\pi\nu}\Gamma(\frac{\nu}{2})(1 + \frac{x^2}{\nu})^{(\nu + 1)/2}} \]](form_56.png)
)![\[ \mbox{E}(x) = 0 \quad , \quad \nu > 1 \]](form_58.png)
![\[ \mbox{Var}(x) = \frac{\nu}{\nu - 2} \quad , \quad \nu > 2 \]](form_59.png)
![\[ f(x) = (\frac{a}{b})(\frac{x}{b})^{a-1}e^{-\frac{x}{b}^a} \]](form_60.png)
![\[ \mbox{E}(x) = b\Gamma(1 + \frac{1}{a}) \]](form_61.png)
![\[ \mbox{Var}(x) = b^2(\Gamma(1+\frac{2}{a}) - \Gamma(1+\frac{1}{a})^2) \]](form_62.png)
and 
.
