source: PSPA/madxPSPA/doc/usrguide/match/match_xeq.html @ 430

Last change on this file since 430 was 430, checked in by touze, 11 years ago

import madx-5.01.00
File size: 4.5 KB
Line 
1<head>
2<title>the mad program</title>
3<!-- Changed by: Chris ISELIN, 27-Jan-1997 -->
4<!-- Changed by: Oliver Bruning, 20-Jun-2002 -->
5</head>
6
7<body bgcolor="#ffffff">
8
9<center>
10EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
11<IMG SRC="http://cern.ch/madx/icons/mx7_25.gif" align=right>
12<h2>Matching Methods</h2>
13</center>
14<p>
15MADX currently supports four different matching algorithms:
16<p>
17<ul>
18<li>
19<h2><a name=lmdif>LMDIF: Fast Gradient Minimisation</a></h2>
20The LMDIF command minimises the sum of squares of the constraint
21functions using their numerical derivatives:
22<pre>
23LMDIF,CALLS=integer,TOLERANCE=real;
24</pre>
25It is the fastest minimisation method available in MAD.
26The command has two attributes:
27<ul>
28<li>CALLS:
29The maximum number of calls to the penalty function (default: 1000).
30<li>TOLERANCE:
31The desired tolerance for the minimum (default: 10**(-6)).
32</ul>
33Example:
34<pre>
35LMDIF,CALLS=2000,TOLERANCE=1.0E-8;
36</pre>
37<li>
38<h2><a name=migrad>MIGRAD: Gradient Minimisation</a></h2>
39The MIGRAD command minimises the penalty
40function using the numerical derivatives of the sum of squares:
41<pre>
42MIGRAD,CALLS=integer,TOLERANCE=real,STRATEGY=1;
43</pre>
44The command has three attributes:
45<ul>
46<li>CALLS:
47The maximum number of calls to the penalty function (default: 1000).
48<li>TOLERANCE:
49The desired tolerance for the minimum (default: 10**(-6)).
50<li>STRATEGY:
51A code for the strategy to be used (default: 1).
52Details are given in <a href="bibliography.html#minuit">[James]</a>.
53</ul>
54Example:
55<pre>
56MIGRAD,CALLS=2000,TOLERANCE=1.0E-8;
57</pre>
58<li>
59<h2><a name=simplex>SIMPLEX: Simplex Minimisation</a></h2>
60The SIMPLEX command minimises the penalty
61function by the simplex method:
62<pre>
63SIMPLEX,CALLS=integer,TOLERANCE=real;
64</pre>
65Details are given in <a href="bibliography.html#minuit">[James]</a>.
66The command has two attributes:
67<ul>
68<li>CALLS:
69The maximum number of calls to the penalty function (default: 1000).
70<li>TOLERANCE:
71The desired tolerance for the minimum (default: 10**(-6)).
72</ul>
73Example:
74<pre>
75SIMPLEX,CALLS=2000,TOLERANCE=1.0E-8;
76</pre>
77<li>
78<h2><a name=jacobian>JACOBIAN: Newton Minimisation</a></h2>
79The JACOBIAN command minimises the penalty
80function calculating the Jacobian and solving the linear problem. A QR or LQ  decomposition is performed when the system is over or under-determined. Before starting the matching routine two optional transformations (COOL and RANDOM) are performed.
81
82
83
84
85<pre>
86JACOBIAN,CALLS=integer,TOLERANCE=real,REPEAT=integer,STRATEGY=integer,COOL=real,BALANCE=real, random=real;
87</pre>
88The command has the attributes:
89<ul>
90<li>CALLS:
91The maximum number of calls to the penalty function (default: 30).
92<li>TOLERANCE:
93The desired tolerance for the minimum (default: 10**(-6)).
94<li>REPEAT:
95The number of call of the JACOBIAN routine (default: 1).
96<li>BISEC:
97Selects the maximum number of iteratation used to
98determin the step length which reduces the penalty function during the main
99iteration. A large number (i.e. 6) reduce the probability to diverge from the
100solution, but increase the one for being trapped in a local minum.
101<li>STRATEGY:
102A code for the strategy to be used (default: 3). If STRATEGY=1 the routine resets the values of the variables which exceeds the limits. If STRATEGY=2 the routine print the Jacobian and exit without matching. If STRATEGY=3 the routine  disables the variables which exceeds the limits keeping however the number of variables greater or equal to the number of the constraints.
103<li>COOL, BALANCE:
104The factors which specify the following transformation:<pre>
105  if "balance" >=0
106     newval=(1-cool)*oldval+cool*( (1-balance)*maxval+balance*minval )
107  else
108     newval=(1-cool)*oldval+cool* optval
109</pre>
110where <tt>newval</tt> is the new value after the transformation, <tt>oldval</tt> is the previous value, <tt>maxval, minval, optval</tt> are the maximum value, minimum value, optimal value of the variable specified in the <a href="match_vary.html">VARY</a> command.
111<li>RANDOM:
112The factors which specify the following transformation:<pre>
113   newval= (1+ random * rand() ) * oldval
114</pre>
115where <tt>newval</tt> is the new value after the transformation, <tt>oldval</tt> is the previous value, <tt>rand()</tt> is a stochastic variable with a uniform (-0.5,0.5) distribution.
116</ul>
117Example:
118<pre>
119JACOBIAN,CALLS=20,TOLERANCE=1.0E-8,STRATEGY=3,COOL=0.1,BALANCE=0.5,RANDOM=0.01;
120</pre>
121</ul>
122<hr>
123
124<address>
125<a href="http://bruening.home.cern.ch/bruening/">Oliver Br&uuml;ning</a>,
126June, 2002.
127<a href="http://rdemaria.home.cern.ch/rdemaria/">Riccardo de Maria</a>, February, 2006.
128</address>
129
130</body>
Note: See TracBrowser for help on using the repository browser.