<?xml version="1.0" encoding="UTF-8"?>
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 * 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" xml:id="cumsum">
    <refnamediv>
        <refname>cumsum</refname>
        <refpurpose>cumulative sum of array elements</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>y=cumsum(x)
            y=cumsum(x,orientation)
            y=cumsum(x,outtype)
            y=cumsum(x,orientation,outtype)
        </synopsis>
    </refsynopsisdiv>

    <refsection role="parameters">
        <title>Arguments</title>
        <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>This argument can be</para>
                    <itemizedlist>
                        <listitem>
                            <para>
                                either a string with possible values <literal>"*"</literal>, <literal>"r"</literal>, <literal>"c"</literal> or <literal>"m"</literal>
                            </para>
                        </listitem>
                        <listitem>
                            <para>or 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>
    </refsection>

    <refsection role="description">
        <title>Description</title>
        <para>
            Returns the cumulative sum of array elements.
            For an array <term>x</term>, <literal>y=cumsum(x)</literal> a matrix <term>y</term> of the same size as <term>x</term>.
            The value <literal>y(i)</literal> is the sum of all elements of <literal>x(1:i)</literal> <emphasis role="italic">i.e.</emphasis>:
        </para>
        <para>
            <latex><![CDATA[ y(i) = \sum_{k=1}^i x(k)]]></latex>
        </para>
        <para>
            <literal>y=cumsum(x,orientation)</literal> returns in <term>y</term> the cumulative sum of <term>x</term> along the dimension given by <term>orientation</term>:
        </para>
        <itemizedlist>
            <listitem>
                <para>
                    if <term>orientation</term> is equal to 1 or "r" then:
                </para>
                <para>
                    <latex><![CDATA[ y(\mathbf{l},j) = \sum_{\mathbf{i}=1}^l x(\mathbf{i},j)]]></latex>
                </para>
                <para>or </para>
                <para>
                    <latex><![CDATA[ y(\mathbf{l},j,k,\ldots) = \sum_{\mathbf{i}=1}^l x(\mathbf{i},j,k,\ldots)]]></latex>
                </para>
            </listitem>
            <listitem>
                <para>
                    if <term>orientation</term> is equal to 2 or "c" then:
                </para>
                <para>
                    <latex><![CDATA[ y(i,\mathbf{l}) = \sum_{\mathbf{j}=1}^l x(i,{\mathbf{j})]]></latex>
                </para>
                <para> or </para>
                <para>
                    <latex><![CDATA[ y(i,\mathbf{l},k,\ldots) = \sum_{\mathbf{j}=1}^l x(i,\mathbf{j},k,\ldots)]]></latex>
                </para>
            </listitem>
            <listitem>
                <para>
                    if <term>orientation</term> is equal to n then:
                </para>
                <para>
                    <latex><![CDATA[ y(i_1,\ldots,i_{n-1},\mathbf{l},i_{n+1},\ldots) = \sum_{\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=cumsum(x,"*")</literal> is equivalent to <literal>y=cumsum(x)</literal>
                </para>
            </listitem>
            <listitem>
                <para>
                    <literal>y=cumsum(x,"m")</literal> is equivalent to <literal>y=cumsum(x,orientation)</literal> where <term>orientation</term> is the index of the first dimension of <term>x</term> that is greater than 1. This option is used for Matlab compatibility.
                </para>
            </listitem>
        </itemizedlist>
        <para/>
        <para>
            The <term>outtype</term> argument rules the way the summation 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 |),
                </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 role="examples">
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=[1,2;3,4];
cumsum(A)
cumsum(A,1)

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

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

B=[%t %t %f %f];
cumsum(B) //evaluation in float
cumsum(B,"native") //similar to or(B)
 ]]></programlisting>
    </refsection>

    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="sum">sum</link>
            </member>
            <member>
                <link linkend="cumprod">cumprod</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
