.. highlightlang:: us

.. index:: rand

.. _rand:

rand
====

.. us.tag  rand GERMAN math-rand math-create-mat Changed5140

:ref:`rand` berechnet gleichverteilte Zufallszahlen.

.. function::  rmRand = rand()
    rmRand = rand(ssGenerator)
    rmRand = rand(nRows, nColumns)
    rmRand = rand(nRows, nColumns, ssGenerator)
    rmRand = rand(rvSize)
    rmRand = rand(rvSize, ssGenerator)

.. us.return

**Returnwert**

*rmRand* ist eine reelle Matrix.

.. us.params

**Parameter**

.. uparam:: nRows

   *nr* ist die Anzahl an Zeilen.

.. uparam:: nColumns

   *nc* ist die Anzahl an Spalten.

.. uparam:: rvSize

   *rvSize* ist ein Vektor mit zwei Elementen. *rvSize[1]* ist die Anzahl an
   Zeilen, *rvSize[2]* ist die Anzahl an Spalten.

.. uparam:: ssGenerator

   Ist einer der folgenden Strings ([a,b] := a <= x <= b, (a,b) := a < x < b):

   .. list-table::
      :header-rows: 0

      * - "mt"
        - Verwendet den Mersenne-Twister Generator (default). "mt" ist das gleiche wie "mt:real1".
      * - "mt:real1"
        - generates a random number on [0,1]-real-interval.
      * - "mt:real2"
        - generates a random number on [0,1)-real-interval.
      * - "mt:real3"
        - generates a random number on (0,1)-real-interval.
      * - "mt:int31"
        - generates a random number on [0,0x7fffffff]-interval.
      * - "mt:int32"
        - generates a random number on [0,0xffffffff]-interval.
      * - "mt:res53"
        - generates a random number on [0,1) with 53-bit resolution.
      * - "ranlib"
        - generates a random number on (0,1)-real-interval.

.. us.example

**Beispiel**

::

   * srand("test")
       1.0000
   * rand(3, 3)
   *   0.5536     0.7214     0.6267
       0.0735     0.9892     0.8892
       0.4024     0.0891     0.5894

Mit der folgenden Funktion nach der Box-Muller-Methode können normalverteilte 
(Gauß-Verteilung) Zufallszahlen erzeugt werden:

::

   def randn(nRows, nColumn)
   {
       return sqrt( -2.0 * log(1.0 - rand(nRows, nColumn))) .* cos(2 * PI * rand(nRows, nColumn));
   }

Die Zahlen von 1 bis 10 in zufälliger Reihenfolge::

   sorti(rand(1,10))
    6.0000     1.0000    10.0000     7.0000     2.0000     8.0000     9.0000     5.0000     3.0000     4.0000 

.. highlightlang:: none

::

      A C-program for MT19937, with initialization improved 2002/1/26.
      Coded by Takuji Nishimura and Makoto Matsumoto.

      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.

.. us.history

**History**

.. list-table::
   :header-rows: 1

   * - Version
     - Beschreibung
   * - 5.14.0
     - Neuer Parameter *ssGenerator*

.. seealso::
   :ref:`uberblick-mathematik`,
   :ref:`srand`

:sub:`id-1224554`