<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) 2010 - Serge Steer - INRIA
 *
 * 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:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="cumprod" xml:lang="en">
    <refnamediv>
        <refname>cumprod</refname>
        <refpurpose>cumulative product of array elements</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>
          y = cumprod(x)
          y = cumprod(x, orientation)
          y = cumprod(x, outtype)
          y = cumprod(x, orientation, outtype)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <para>
            <variablelist>
                <varlistentry>
                    <term>x</term>
                    <listitem>
                        <para>
                            an array of  reals, complex, booleans,  polynomials or
                            rational fractions.
                        </para>
                    </listitem>
                </varlistentry>
                <varlistentry>
                    <term>orientation</term>
                    <listitem>
                        <para>
                            it can be either
                        </para>
                        <itemizedlist>
                            <listitem>
                                <para>
                                    a string with possible values <literal>"*"</literal>, <literal>"r"</literal>,
                                    <literal>"c"</literal> or  <literal>"m"</literal>
                                </para>
                            </listitem>
                            <listitem>
                                <para>a number with positive integer value</para>
                            </listitem>
                        </itemizedlist>
                    </listitem>
                </varlistentry>
                <varlistentry>
                    <term>outtype</term>
                    <listitem>
                        <para>
                            a string with possible values <literal>"native"</literal> or <literal>"double"</literal>.
                        </para>
                    </listitem>
                </varlistentry>
                <varlistentry>
                    <term>y</term>
                    <listitem>
                        <para>scalar or array</para>
                    </listitem>
                </varlistentry>
            </variablelist>
        </para>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            For an array <literal>x</literal>,
            <literal>y=cumprod(x)</literal> returns in the scalar <literal>y</literal> the
            cumulative product of all the elements of <literal>x</literal>.
        </para>
        <para>
            <literal>y=cumprod(x,orientation)</literal> returns in
            <literal>y</literal> the cumulative product of <literal>x</literal> along the
            dimension given by <literal>orientation</literal>:
        </para>
        <itemizedlist>
            <listitem>
                <para>
                    if <literal>orientation</literal> is equal to 1 or "r" then:
                </para>
                <para>
                    <latex><![CDATA[ y(\mathbf{l},j) = \prod_{\mathbf{i}=1}^l x(\mathbf{i},j)]]></latex>
                </para>
                <para>or </para>
                <para>
                    <latex><![CDATA[ y(\mathbf{l},j,k,\ldots) = \prod_{\mathbf{i}=1}^l x(\mathbf{i},j,k,\ldots)]]></latex>
                </para>
            </listitem>
            <listitem>
                <para>
                    if <literal>orientation</literal> is equal to 2 or "c" then:
                </para>
                <para>
                    <latex><![CDATA[ y(i,\mathbf{l}) = \prod_{\mathbf{j}=1}^l x(i,{\mathbf{j})]]></latex>
                </para>
                <para> or </para>
                <para>
                    <latex><![CDATA[ y(i,\mathbf{l},k,\ldots) = \prod_{\mathbf{j}=1}^l x(i,\mathbf{j},k,\ldots)]]></latex>
                </para>
            </listitem>
            <listitem>
                <para>
                    if <literal>orientation</literal> is equal to n then:
                </para>
                <para>
                    <latex><![CDATA[ y(i_1,\ldots,i_{n-1},\mathbf{l},i_{n+1},\ldots) = \prod_{\mathbf{i_n}=1}^l x(i_1,\ldots,i_{n-1},\mathbf{i_n},i_{n+1},\ldots)]]></latex>
                </para>
            </listitem>
            <listitem>
                <para>
                    <literal>y=cumprod(x,"*")</literal> is equivalent to <literal>y=cumprod(x)</literal>
                </para>
            </listitem>
            <listitem>
                <para>
                    <literal>y=cumprod(x,"m")</literal> is equivalent to
                    <literal>y=cumprod(x,orientation)</literal> where
                    <literal>orientation</literal> is the index of the
                    first dimension of  <literal>x</literal> that is greater than 1. This option is used for
                    Matlab compatibility.
                </para>
            </listitem>
        </itemizedlist>
        <para/>
        <para>
            The <literal>outtype</literal>  argument rules the way the product is done:
        </para>
        <itemizedlist>
            <listitem>
                <para>For arrays of floats, of polynomials, of rational
                    fractions, the evaluation is always done using floating points
                    computations. The <literal>"double"</literal> or <literal>"native"</literal> options are equivalent.
                </para>
            </listitem>
            <listitem>
                <para>For arrays of integers,</para>
                <para>
                    if <literal>outtype="native"</literal> the evaluation is done using integer
                    computations (modulo 2^b, where b is the number of bits used),
                </para>
                <para>
                    if <literal>outtype="double"</literal> the evaluation is done using floating point
                    computations.
                </para>
                <para>
                    The default value is <literal>outtype="native"</literal>.
                </para>
            </listitem>
            <listitem>
                <para>For arrays of booleans,</para>
                <para>
                    if <literal>outtype="native"</literal> the evaluation is done using boolean
                    computations (* is replaced by &amp;),
                </para>
                <para>
                    if <literal>outtype="double"</literal> the evaluation is done using floating point
                    computations (%t values are replaced by 1 and %f values by 0).
                </para>
                <para>
                    The default value is <literal>outtype="double"</literal>.
                </para>
            </listitem>
        </itemizedlist>
      <note>This function applies, with identical rules to <link linkend="sparse">sparse matrices</link>
      </note>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=[1,2;3,4];
cumprod(A)
cumprod(A,1)

I=uint8([2 95 103;254 9 0])
cumprod(I) //native evaluation
cumprod(I,"double")
cumprod(I,2,"double")

s=poly(0,"s");
P=[s,%i+s;s^2,1];
cumprod(P),
cumprod(P,2)

B=[%t %t %f %f];
cumprod(B) //evaluation in float
cumprod(B,"native") //similar to and(B)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="prod">prod</link>
            </member>
            <member>
                <link linkend="cumsum">cumsum</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
