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		<id>http://eclr.humanities.manchester.ac.uk/index.php?action=history&amp;feed=atom&amp;title=Numgrad_m</id>
		<title>Numgrad m - Revision history</title>
		<link rel="self" type="application/atom+xml" href="http://eclr.humanities.manchester.ac.uk/index.php?action=history&amp;feed=atom&amp;title=Numgrad_m"/>
		<link rel="alternate" type="text/html" href="http://eclr.humanities.manchester.ac.uk/index.php?title=Numgrad_m&amp;action=history"/>
		<updated>2026-04-25T06:35:15Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
		<generator>MediaWiki 1.30.1</generator>

	<entry>
		<id>http://eclr.humanities.manchester.ac.uk/index.php?title=Numgrad_m&amp;diff=4273&amp;oldid=prev</id>
		<title>Rb at 08:36, 8 February 2022</title>
		<link rel="alternate" type="text/html" href="http://eclr.humanities.manchester.ac.uk/index.php?title=Numgrad_m&amp;diff=4273&amp;oldid=prev"/>
				<updated>2022-02-08T08:36:47Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 08:36, 8 February 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Save the code below as numgrad.m in your working folder. This is required to make the GMM code work.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;source&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;source&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;%------------------------------------------------------------------------- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;%------------------------------------------------------------------------- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rb</name></author>	</entry>

	<entry>
		<id>http://eclr.humanities.manchester.ac.uk/index.php?title=Numgrad_m&amp;diff=4272&amp;oldid=prev</id>
		<title>Rb at 08:36, 8 February 2022</title>
		<link rel="alternate" type="text/html" href="http://eclr.humanities.manchester.ac.uk/index.php?title=Numgrad_m&amp;diff=4272&amp;oldid=prev"/>
				<updated>2022-02-08T08:36:06Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 08:36, 8 February 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l30&quot; &gt;Line 30:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 30:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;end&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;end&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\&lt;/del&gt;source&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;/&lt;/ins&gt;source&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rb</name></author>	</entry>

	<entry>
		<id>http://eclr.humanities.manchester.ac.uk/index.php?title=Numgrad_m&amp;diff=4271&amp;oldid=prev</id>
		<title>Rb: Created page with &quot;&lt;source&gt; %-------------------------------------------------------------------------  %   Computes numerical gradient at each observation %-------------------------------------...&quot;</title>
		<link rel="alternate" type="text/html" href="http://eclr.humanities.manchester.ac.uk/index.php?title=Numgrad_m&amp;diff=4271&amp;oldid=prev"/>
				<updated>2022-02-08T08:35:21Z</updated>
		
		<summary type="html">&lt;p&gt;Created page with &amp;quot;&amp;lt;source&amp;gt; %-------------------------------------------------------------------------  %   Computes numerical gradient at each observation %-------------------------------------...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;source&amp;gt;&lt;br /&gt;
%------------------------------------------------------------------------- &lt;br /&gt;
%   Computes numerical gradient at each observation&lt;br /&gt;
%-------------------------------------------------------------------------&lt;br /&gt;
function G = numgrad( f,x,varargin )&lt;br /&gt;
&lt;br /&gt;
    f0  = feval( f,x,varargin{:} );             % n by 1&lt;br /&gt;
    n   = length( f0 );&lt;br /&gt;
    k   = length( x );&lt;br /&gt;
    fdf = zeros( n,k );&lt;br /&gt;
 &lt;br /&gt;
    % Compute step size &lt;br /&gt;
    dx      = sqrt( eps )*( abs( x ) + eps );&lt;br /&gt;
    xh      = x + dx;&lt;br /&gt;
    dx      = xh - x;    &lt;br /&gt;
    ind     = dx &amp;lt; sqrt(eps);&lt;br /&gt;
    dx(ind) = sqrt(eps);&lt;br /&gt;
&lt;br /&gt;
    % Compute gradient&lt;br /&gt;
    xdx = bsxfun( @plus, diag( dx ), x );&lt;br /&gt;
    for i=1:k;&lt;br /&gt;
        &lt;br /&gt;
        fdf(:,i) = feval( f, xdx(:,i), varargin{:} );&lt;br /&gt;
    end&lt;br /&gt;
&lt;br /&gt;
    G0 = repmat( f0, 1, k );                        % n by k        &lt;br /&gt;
    G1 = repmat( dx&amp;#039;, n, 1 );&lt;br /&gt;
    G  = ( fdf-G0 )./G1;&lt;br /&gt;
&lt;br /&gt;
end&lt;br /&gt;
&lt;br /&gt;
&amp;lt;\source&amp;gt;&lt;/div&gt;</summary>
		<author><name>Rb</name></author>	</entry>

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