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<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) 2008 - INRIA
 * Copyright (C) 2016 - Samuel GOUGEON
 *
 * 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.
 *
 -->
<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="linspace" xml:lang="en">
    <refnamediv>
        <refname>linspace</refname>
        <refpurpose>generates linearly spaced numbers between 2 reached bounds</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>
            row = linspace(x1, x2)
            row = linspace(x1, x2, n)
            Matrix = linspace(Col1, Col2)
            Matrix = linspace(Col1, Col2, n)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>x1, x2</term>
                <listitem>
                    <para>
                        Real or complex scalars:
                        Bounds between which values must be generated.
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Col1, Col2</term>
                <listitem>
                    <para>
                        Column vectors of same heights of real or complex numbers.
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>n</term>
                <listitem>
                    <para>
                        integer number of requested values or columns.
                        Default value: 100
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>row</term>
                <listitem>
                    <para>
                        row vector of <literal>n</literal> numbers.
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Matrix</term>
                <listitem>
                    <para>
                        Matrix with <literal>n</literal> columns of numbers.
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>linspace(x1, x2)</literal>
            generates a row vector of <literal>n</literal> equally spaced
            values ranging exactly from <literal>x1</literal> to <literal>x2</literal>.
        </para>
        <note>
            <para>
                The syntax <literal>y1:y2</literal> or <literal>y1:step:y2</literal>
                like <literal>1:0.1:%pi</literal> does the same but fixes the
                starting bound <literal>y1</literal> and
                <emphasis role="bold">the step</emphasis>. The <literal>y2</literal>
                is used as stopping bound to not be overstepped. The last value
                actually generated may not reach it.
                <literal>y2</literal> is then not included in the result.
            </para>
            <para>
                Instead of fixing the step to a given value, <literal>linspace</literal>
                fixes the final bound <literal>x2</literal> to be exactly
                <emphasis role="bold">reached</emphasis>, and computes the step
                accordingly.
            </para>
        </note>
        <para>
            If <literal>x1</literal> or <literal>x2</literal> are complex numbers,
            then <literal>linspace(x1,x2)</literal> interpolates separately the real and
            the imaginary parts of <literal>x1</literal> and <literal>x2</literal>.
        </para>
        <para>
            If some column vectors <literal>Col1</literal> and <literal>Col2</literal>
            are provided, <literal>linspace</literal> works in a row-wise way:
            the resulting <literal>Matrix</literal> has the same number of rows,
            and <literal>n</literal> columns. We get
            <literal>Matrix(i,:) = linspace(Col1(i), Col2(i), n)</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
linspace(1, %pi, 0)         // n = 0
linspace(1, 2, 10)          // x2 > x1 : increasing values
linspace(2, 1, 10)          // x2 < x1 : decreasing values
linspace(1+%i, 2-2*%i, 5)      // with complex numbers
linspace([1:4]', [5:8]', 10)   // with input columns
 ]]></programlisting>
        <screen><![CDATA[--> linspace(1, %pi, 0)    // n = 0
 ans  =
    []

--> linspace(1, 2, 10)    // x2 > x1 : increasing values

 ans  =
   1.   1.111   1.222   1.333   1.444   1.556   1.667   1.778   1.889   2.


--> linspace(2, 1, 10)    // x2 < x1 : decreasing values

 ans  =
   2.   1.889   1.778   1.667   1.556   1.444   1.333   1.222   1.111   1.


--> linspace(1+%i, 2-2*%i, 5)      // with complex numbers

 ans  =
   1. +i     1.25 +0.25i   1.5 -0.5i   1.75 -1.25i   2. -2.i


--> linspace([1:4]', [5:8]', 10)   // with input columns

 ans  =
   1.   1.444   1.889   2.333   2.778   3.222   3.667   4.111   4.556   5.
   2.   2.444   2.889   3.333   3.778   4.222   4.667   5.111   5.556   6.
   3.   3.444   3.889   4.333   4.778   5.222   5.667   6.111   6.556   7.
   4.   4.444   4.889   5.333   5.778   6.222   6.667   7.111   7.556   8.
]]></screen>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="colon">colon</link>
            </member>
            <member>
                <link linkend="logspace">logspace</link>
            </member>
            <member>
                <link linkend="grand">grand</link>
            </member>
        </simplelist>
    </refsection>
    <refsection>
        <title>History</title>
        <revhistory>
            <revision>
                <revnumber>5.4.0</revnumber>
                <revremark>
                    <itemizedlist>
                        <listitem>Column vectors can now be provided.
                        </listitem>
                        <listitem>The third input argument (n) must be an integer value.
                        </listitem>
                    </itemizedlist>
                </revremark>
            </revision>
            <revision>
                <revnumber>6.0</revnumber>
                <revremark>
                    <itemizedlist>
                        <listitem>linspace(a, b, n&lt;=0) now returns [] instead of b.
                        </listitem>
                        <listitem>bounds are now checked against %inf or %nan values.
                        </listitem>
                    </itemizedlist>
                </revremark>
            </revision>
        </revhistory>
    </refsection>
</refentry>