← Back to branch summary

~ubuntu-branches/ubuntu/raring/scilab/raring-proposed

« back to all changes in this revision

Viewing changes to modules/signal_processing/help/en_US/corr.xml

  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

Show diffs side-by-side

added added

removed removed

Lines of Context:
modules/signal_processing/help/en_US/corr.xml
1
 
<?xml version="1.0" encoding="UTF-8"?>
2
 
<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="corr">
3
 
  <refnamediv>
4
 
    <refname>corr</refname>
5
 
    <refpurpose> correlation, covariance</refpurpose>
6
 
  </refnamediv>
7
 
  <refsynopsisdiv>
8
 
    <title>Calling Sequence</title>
9
 
    <synopsis>[cov,Mean]=corr(x,[y],nlags)
10
 
      [cov,Mean]=corr('fft',xmacro,[ymacro],n,sect)
11
 
      
12
 
      [w,xu]=corr('updt',x1,[y1],w0)
13
 
      [w,xu]=corr('updt',x2,[y2],w,xu)
14
 
      ...
15
 
      [wk]=corr('updt',xk,[yk],w,xu)
16
 
    </synopsis>
17
 
  </refsynopsisdiv>
18
 
  <refsection>
19
 
    <title>Arguments</title>
20
 
    <variablelist>
21
 
      <varlistentry>
22
 
        <term>x</term>
23
 
        <listitem>
24
 
          <para>a real vector</para>
25
 
        </listitem>
26
 
      </varlistentry>
27
 
      <varlistentry>
28
 
        <term>y</term>
29
 
        <listitem>
30
 
          <para>a real vector, default value x.</para>
31
 
        </listitem>
32
 
      </varlistentry>
33
 
      <varlistentry>
34
 
        <term>nlags</term>
35
 
        <listitem>
36
 
          <para>integer, number of correlation coefficients desired.</para>
37
 
        </listitem>
38
 
      </varlistentry>
39
 
      <varlistentry>
40
 
        <term>xmacro</term>
41
 
        <listitem>
42
 
          <para>a scilab external (see below).</para>
43
 
        </listitem>
44
 
      </varlistentry>
45
 
      <varlistentry>
46
 
        <term>ymacro</term>
47
 
        <listitem>
48
 
          <para>a scilab external (see below), default value xmacro</para>
49
 
        </listitem>
50
 
      </varlistentry>
51
 
      <varlistentry>
52
 
        <term>n</term>
53
 
        <listitem>
54
 
          <para>an integer, total size of the sequence (see below).</para>
55
 
        </listitem>
56
 
      </varlistentry>
57
 
      <varlistentry>
58
 
        <term>sect</term>
59
 
        <listitem>
60
 
          <para>size of sections of the sequence (see below).</para>
61
 
        </listitem>
62
 
      </varlistentry>
63
 
      <varlistentry>
64
 
        <term>xi</term>
65
 
        <listitem>
66
 
          <para>a real vector</para>
67
 
        </listitem>
68
 
      </varlistentry>
69
 
      <varlistentry>
70
 
        <term>yi</term>
71
 
        <listitem>
72
 
          <para>a real vector,default value xi.</para>
73
 
        </listitem>
74
 
      </varlistentry>
75
 
      <varlistentry>
76
 
        <term>cov</term>
77
 
        <listitem>
78
 
          <para>real vector, the correlation coefficients</para>
79
 
        </listitem>
80
 
      </varlistentry>
81
 
      <varlistentry>
82
 
        <term>Mean</term>
83
 
        <listitem>
84
 
          <para>real number or vector,  the mean of x and if given y</para>
85
 
        </listitem>
86
 
      </varlistentry>
87
 
    </variablelist>
88
 
  </refsection>
89
 
  <refsection>
90
 
    <title>Description</title>
91
 
    <para>
92
 
      Computes
93
 
    </para>
94
 
    <programlisting role=""><![CDATA[ 
95
 
         n - m 
96
 
         ====
97
 
         \                                       1
98
 
cov(m) =  >   (x(k) - xmean) (y(m+k) - ymean) * ---
99
 
         /                                       n
100
 
         ====
101
 
         k = 1
102
 
 ]]></programlisting>
103
 
    <para>
104
 
      for   m=0,..,<literal>nlag-1</literal> and two vectors <literal>x=[x(1),..,x(n)]</literal>
105
 
      <literal>y=[y(1),..,y(n)]</literal>
106
 
    </para>
107
 
    <para>
108
 
      Note that if x and y sequences are differents corr(x,y,...) is
109
 
      different with corr(y,x,...)
110
 
    </para>
111
 
    <variablelist>
112
 
      <varlistentry>
113
 
        <term>Short sequences</term>
114
 
        <listitem>
115
 
          <para>
116
 
            <literal>[cov,Mean]=corr(x,[y],nlags)</literal> returns the first nlags
117
 
            correlation coefficients and Mean = <literal>mean(x)</literal>
118
 
            (mean of <literal>[x,y]</literal> if <literal>y</literal> is an argument).
119
 
            The sequence <literal>x</literal> (resp. <literal>y</literal>) is assumed real, and <literal>x</literal> 
120
 
            and <literal>y</literal> are of same dimension n.
121
 
          </para>
122
 
        </listitem>
123
 
      </varlistentry>
124
 
      <varlistentry>
125
 
        <term>Long sequences</term>
126
 
        <listitem>
127
 
          <para>
128
 
            <literal>[cov,Mean]=corr('fft',xmacro,[ymacro],n,sect)</literal> Here <literal>xmacro</literal> is either
129
 
          </para>
130
 
          <itemizedlist>
131
 
            <listitem>
132
 
              <para> 
133
 
                a function of type <literal>[xx]=xmacro(sect,istart)</literal> which
134
 
                returns a vector <literal>xx</literal> of dimension
135
 
                <literal>nsect</literal> containing the part of the sequence with
136
 
                indices from <literal>istart</literal> to
137
 
                <literal>istart+sect-1</literal>.
138
 
              </para>
139
 
            </listitem>
140
 
            <listitem>
141
 
              <para>
142
 
                a fortran subroutine or C procedure which performs the same
143
 
                calculation. (See the source code of <literal>dgetx</literal> for an
144
 
                example). <literal>n</literal> = total size of the
145
 
                sequence. <literal>sect</literal> = size of sections of the
146
 
                sequence. <literal>sect</literal> must be a power of
147
 
                2. <literal>cov</literal> has dimension
148
 
                <literal>sect</literal>. Calculation is performed by FFT.
149
 
              </para>
150
 
            </listitem>
151
 
          </itemizedlist>
152
 
        </listitem>
153
 
      </varlistentry>
154
 
      <varlistentry>
155
 
        <term>Updating method</term>
156
 
        <listitem>
157
 
          <programlisting role=""><![CDATA[ 
158
 
[w,xu]=corr('updt',x1,[y1],w0)
159
 
[w,xu]=corr('updt',x2,[y2],w,xu)
160
 
 ...
161
 
wk=corr('updt',xk,[yk],w,xu)
162
 
 ]]></programlisting>
163
 
          <para>
164
 
            With this calling sequence the calculation is updated at each
165
 
            call to <literal>corr</literal>.
166
 
          </para>
167
 
          <programlisting role=""><![CDATA[ 
168
 
w0 = 0*ones(1,2*nlags);
169
 
nlags = power of 2.
170
 
 ]]></programlisting>
171
 
          <para>
172
 
            <literal>x1,x2,...</literal> are parts of <literal>x</literal> such that
173
 
            <literal>x=[x1,x2,...]</literal> and sizes of <literal>xi</literal> a power of
174
 
            2.  To get <literal>nlags</literal> coefficients a final fft must be
175
 
            performed <literal>c=fft(w,1)/n</literal>; <literal>cov=c(1nlags)</literal>
176
 
            (<literal>n</literal> is the size of <literal>x (y)</literal>).  Caution: this
177
 
            calling sequence assumes that <literal>xmean = ymean = 0</literal>.
178
 
          </para>
179
 
        </listitem>
180
 
      </varlistentry>
181
 
    </variablelist>
182
 
  </refsection>
183
 
  <refsection>
184
 
    <title>Examples</title>
185
 
    <programlisting role="example"><![CDATA[ 
186
 
x=%pi/10:%pi/10:102.4*%pi;
187
 
rand('seed');rand('normal');
188
 
y=[.8*sin(x)+.8*sin(2*x)+rand(x);.8*sin(x)+.8*sin(1.99*x)+rand(x)];
189
 
c=[];
190
 
for j=1:2,for k=1:2,c=[c;corr(y(k,:),y(j,:),64)];end;end;
191
 
c=matrix(c,2,128);cov=[];
192
 
for j=1:64,cov=[cov;c(:,(j-1)*2+1:2*j)];end;
193
 
rand('unif')
194
 
 
195
 
rand('normal');x=rand(1,256);y=-x;
196
 
deff('[z]=xx(inc,is)','z=x(is:is+inc-1)');
197
 
deff('[z]=yy(inc,is)','z=y(is:is+inc-1)');
198
 
[c,mxy]=corr(x,y,32);
199
 
x=x-mxy(1)*ones(x);y=y-mxy(2)*ones(y);  //centring
200
 
c1=corr(x,y,32);c2=corr(x,32);
201
 
norm(c1+c2,1)
202
 
[c3,m3]=corr('fft',xx,yy,256,32);
203
 
norm(c1-c3,1)
204
 
[c4,m4]=corr('fft',xx,256,32);
205
 
norm(m3,1),norm(m4,1)
206
 
norm(c3-c1,1),norm(c4-c2,1)
207
 
x1=x(1:128);x2=x(129:256);
208
 
y1=y(1:128);y2=y(129:256);
209
 
w0=0*ones(1:64);   //32 coeffs
210
 
[w1,xu]=corr('u',x1,y1,w0);w2=corr('u',x2,y2,w1,xu);
211
 
zz=real(fft(w2,1))/256;c5=zz(1:32);
212
 
norm(c5-c1,1)
213
 
[w1,xu]=corr('u',x1,w0);w2=corr('u',x2,w1,xu);
214
 
zz=real(fft(w2,1))/256;c6=zz(1:32);
215
 
norm(c6-c2,1)
216
 
rand('unif')
217
 
 
218
 
// test for Fortran or C external 
219
 
//
220
 
deff('[y]=xmacro(sec,ist)','y=sin(ist:(ist+sec-1))');
221
 
x=xmacro(100,1);
222
 
[cc1,mm1]=corr(x,2^3);
223
 
[cc,mm]=corr('fft',xmacro,100,2^3);
224
 
[cc2,mm2]=corr('fft','corexx',100,2^3);
225
 
[max(abs(cc-cc1)),max(abs(mm-mm1)),max(abs(cc-cc2)),max(abs(mm-mm2))]
226
 
 
227
 
deff('[y]=ymacro(sec,ist)','y=cos(ist:(ist+sec-1))');
228
 
y=ymacro(100,1);
229
 
[cc1,mm1]=corr(x,y,2^3);
230
 
[cc,mm]=corr('fft',xmacro,ymacro,100,2^3);
231
 
[cc2,mm2]=corr('fft','corexx','corexy',100,2^3);
232
 
[max(abs(cc-cc1)),max(abs(mm-mm1)),max(abs(cc-cc2)),max(abs(mm-mm2))]
233
 
 ]]></programlisting>
234
 
  </refsection>
235
 
  <refsection role="see also">
236
 
    <title>See Also</title>
237
 
    <simplelist type="inline">
238
 
      <member>
239
 
        <link linkend="fft">fft</link>
240
 
      </member>
241
 
    </simplelist>
242
 
  </refsection>
243
 
</refentry>