<?xml version="1.0" encoding="UTF-8"?>
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 * Scilab ( https://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) 2000 - INRIA - Carlos Klimann
 *
 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
 * This file is hereby licensed under the terms of the GNU GPL v2.0,
 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * This file was originally licensed under the terms of the CeCILL v2.1,
 * and continues to be available under such terms.
 * For more information, see the COPYING file which you should have received
 * along with this program.
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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="samplef">
    <refnamediv>
        <refname>samplef</refname>
        <refpurpose>sample values with replacement from a population
            with given frequencies.
        </refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>s = samplef(n,X,f,orient)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>n</term>
                <listitem>
                    <para>positive integer (size of sample)</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>X</term>
                <listitem>
                    <para>matrix. Population, samples are extracted from this matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>f</term>
                <listitem>
                    <para>
                        matrix of positive real values. Indicates the corresponding frequencies of the values in <literal>X</literal>.
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>orient</term>
                <listitem>
                    <para>
                        Optional parameter. Admissible values are <literal>{'*'}, 1, 2, 'r' </literal> or <literal>'c'</literal>. The orientation to sample rows or columns. See Description below.
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>s</term>
                <listitem>
                    <para>
                         vector or matrix containing the sampled values of <literal>X</literal> at frequencies <literal>f</literal>.
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            This function returns <literal>s</literal>, a  vector of length <literal>n</literal>.  It contains
            a  sample of  <literal>n</literal>  extractions, with  replacement, from  the
            vector  (or  matrix)  <literal>X</literal>,  each element  counted  with  the
            frequency given by the corresponding value in vector <literal>f</literal>.
        </para>
        <para>
            <literal>s=samplef(n,X,f)</literal> (or
            <literal>s=samplef(n,X,f,'*')</literal>)   returns  a
            vector <literal>s</literal> whose values are a random sample of n values from
            <literal>X</literal>,   each  value   with  a   probability  to   be  sampled
            proportional  to the corresponding  value of  <literal>f</literal>, extracted
            with replacement, from <literal>X</literal>.  <literal>f</literal> must have same length than <literal>X</literal>.
        </para>
        <para>
            <literal>s=samplef(n,X,f,'r')</literal>           (or,          equivalently,
            <literal>s=samplef(n,X,f,1)) </literal>   returns    a    matrix   of    type
            <literal>size(X,'r') * n</literal>.  It contains a random sample of <literal>n</literal> rows from
            <literal>X</literal>, each row with  a probability to be sampled proportional
            to   the  corresponding   value  of   <literal>f</literal>,   extracted  with
            replacement, from the  rows of <literal>X</literal>. The length  of <literal>f</literal> must be
            equal to the number of rows of <literal>X</literal>.
        </para>
        <para>
            <literal>s=samplef(n,X,f,'c')</literal>           (or,          equivalently,
            <literal>s=samplef(n,X,f,2))</literal>    returns    a    matrix   of    type
            <literal>n * size(X,'c')</literal>.  It  contains a random sample  of <literal>n</literal> columns
            from  <literal>X</literal>, each  column  with a  probability  to be  sampled
            proportional  to the corresponding  value of  <literal>f</literal>, extracted
            with replacement, from the columns  of <literal>X</literal>.  The length of <literal>f</literal>
            must be equal to the number of columns of <literal>X</literal>.
        </para>
    </refsection>
    <refsection>
        <title> Random number generator </title>
        <para>
             <literal>samplef</literal> is based on <link linkend="grand">grand</link> for generating the random samples. Use <literal>grand("setsd", seed)</literal> to change the seed for <literal>samplef</literal>.
        </para>
        <programlisting role="example"><![CDATA[
            seed = getdate("s");
            grand("setsd", seed); //sets the seed to current date

            seed = 0;
            grand("setsd", seed); //sets the seed to default value
            ]]>
        </programlisting>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
X = [3 7 9; 22 4 2];
f1 = [10 1 1 1 1 1];
f2 = [1 ; 15];
f3 = [10 1 1];
s=samplef(20, X, f1)      //the first value of matrix X will be chosen with frequency 10/15
s=samplef(20, X, f2, 'r') //the second row of matrix a will be chosen with frequency  15/16
s=samplef(20, X, f3, 'c') //the first column of matrix a will be chosen with frequency 10/12
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="sample">sample</link>
            </member>
            <member>
                <link linkend="samwr">samwr</link>
            </member>
            <member>
                <link linkend="grand">grand</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
