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<?xml version="1.0" encoding="UTF-8"?>
<refentry version="5.0-subset Scilab" xml:id="extraction" xml:lang="en"
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">
<info>
<pubdate>$LastChangedDate: 2008-03-26 08:50:39 +0000 (mer, 26 mar 2008)
$</pubdate>
</info>
<refnamediv>
<refname>extraction</refname>
<refpurpose>matrix and list entry extraction</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
x(i)
x(i,j)
x(i,j,k,..)
[...]=l(i)
[...]=l(k1)...(kn)(i) or [...]=l(list(k1,...,kn,i))
l(k1)...(kn)(i,j) or l(list(k1,...,kn,list(i,j))
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry>
<term>x</term>
<listitem>
<para>matrix of any possible types</para>
</listitem>
</varlistentry>
<varlistentry>
<term>l</term>
<listitem>
<para>list variable</para>
</listitem>
</varlistentry>
<varlistentry>
<term>i,j, k</term>
<listitem>
<para>indices</para>
</listitem>
</varlistentry>
<varlistentry>
<term>k1,...kn</term>
<listitem>
<para>indices</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<variablelist>
<varlistentry>
<term>MATRIX CASE</term>
<listitem>
<para><literal>i</literal>, <literal>j</literal>,
<literal>k</literal>,.. can be:</para>
<variablelist>
<varlistentry>
<term>a real scalar or a vector or a matrix with positive
elements.</term>
<listitem>
<itemizedlist>
<listitem>
<para><literal>r=x(i,j)</literal> builds the matrix
<literal>r</literal> such as
<literal>r(l,k)=x(int(i(l)),int(j(k)))</literal> for
<literal>l</literal> from 1 to
<literal>size(i,'*')</literal> and <literal>k</literal>
from 1 to <literal>size(j,'*')</literal>.</para>
<para><literal>i</literal> (<literal>j</literal>) Maximum
value must be less or equal to
<literal>size(x,1)</literal>
(<literal>size(x,2)</literal>).</para>
</listitem>
<listitem>
<para><literal>r=x(i)</literal> with <literal>x</literal>
a 1x1 matrix builds the matrix <literal>r</literal> such
as <literal>r(l,k)=x(int(i(l)),int(i(k)))</literal> for
<literal>l</literal> from 1 to
<literal>size(i,1)</literal> and <literal>k</literal> from
1 to <literal>size(i,2)</literal>.</para>
<para>Note that in this case index <literal>i</literal> is
valid only if all its entries are equal to one.</para>
</listitem>
<listitem>
<para><literal>r=x(i)</literal> with <literal>x</literal>
a row vector builds the row vector <literal>r</literal>
such as <literal>r(l)=x(int(i(l)))</literal> for
<literal>l</literal> from 1 to
<literal>size(i,'*')</literal><literal>i</literal> Maximum
value must be less or equal to
<literal>size(x,'*')</literal>.</para>
</listitem>
<listitem>
<para><literal>r=x(i)</literal> with <literal>x</literal>
a matrix with one or more columns builds the column vector
<literal>r</literal> such as <literal>r(l)</literal>
(<literal>l</literal> from 1 to
<literal>size(i,'*')</literal>) contains the
<literal>int(i(l))</literal> entry of the column vector
formed by the concatenation of the <literal>x</literal>'s
columns.</para>
<para><literal>i</literal> Maximum value must be less or
equal to <literal>size(x,'*')</literal>.</para>
</listitem>
</itemizedlist>
</listitem>
</varlistentry>
<varlistentry>
<term>the symbol <literal> : </literal></term>
<listitem>
<para><literal /> which stands for "all elements".</para>
<itemizedlist>
<listitem>
<para><literal>r=x(i,:)</literal> builds the matrix
<literal>r</literal> such as
<literal>r(l,k)=x(int(i(l)),k))</literal> for
<literal>l</literal> from 1 to
<literal>size(i,'*')</literal> and <literal>k</literal>
from 1 to <literal>size(x,2)</literal></para>
</listitem>
<listitem>
<para><literal>r=x(:,j)</literal> builds the matrix
<literal>r</literal> such as
<literal>r(l,k)=x(l,int(j(k)))</literal> for
<literal>l</literal> from 1 to
<literal>size(r,1)</literal> and <literal>k</literal> from
1 to <literal>size(j,'*')</literal>.</para>
</listitem>
<listitem>
<para><literal>r=x(:)</literal> builds the column vector
<literal>r</literal> formed by the column concatenations
of<literal> x</literal> columns. It is equivalent to
<literal>matrix(x,size(x,'*'),1)</literal>.</para>
</listitem>
</itemizedlist>
</listitem>
</varlistentry>
<varlistentry>
<term>a vector of boolean</term>
<listitem>
<para>If an index (<literal>i</literal> or
<literal>j</literal> ) is a vector of booleans it is
interpreted as <literal>find(i)</literal> or respectively
<literal>find(j)</literal></para>
</listitem>
</varlistentry>
<varlistentry>
<term>a polynomial</term>
<listitem>
<para>If an index (<literal>i</literal> or
<literal>j</literal> ) is a vector of polynomials or implicit
polynomial vector it is interpreted as
<literal>horner(i,m)</literal> or respectively
<literal>horner(j,n)</literal> where <literal>m</literal> and
<literal>n</literal> are associated <literal>x</literal>
dimensions. Even if this feature works for all polynomials, it
is recommended to use polynomials in <literal>$</literal> for
readability.</para>
</listitem>
</varlistentry>
</variablelist>
<para>For matrices with more than 2 dimensions (see:<link
linkend="hypermatrices">hypermatrices</link>) the dimensionality
is automatically reduced when right-most dimensions are equal to
1.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>LIST OR TLIST CASE</term>
<listitem>
<para>If they are present the <literal>ki</literal> give the path to
a sub-list entry of <literal>l</literal> data structure. They allow
a recursive extraction without intermediate copies. The
instructions</para>
<para>
<literal>[...]=l(k1)...(kn)(i)</literal>
</para>
<para>and</para>
<para>
<literal>[...]=l(list(k1,...,kn,i))</literal>
</para>
<para>are interpreted as:</para>
<para><literal>lk1 = l(k1)</literal> <literal> .. = .. </literal>
<literal>lkn = lkn-1(kn)</literal> <literal>[...] = lkn(i)</literal>
And the <literal>l(k1)...(kn)(i,j)</literal> and</para>
<para><literal>l(list(k1,...,kn,list(i,j))</literal> instructions
are interpreted as: <literal>lk1 = l(k1)</literal> <literal> .. = ..
</literal> <literal>lkn = lkn-1(kn)</literal> <literal>
lkn(i,j)</literal> <literal>i</literal> and <literal>j</literal>,
can be: When path points on more than one list component the
instruction must have as many left hand side arguments as selected
components. But if the extraction syntax is used within a function
input calling sequence each returned list component is added to the
function calling sequence.</para>
<para>Note that, <literal> l(list())</literal> is the same as
<literal> l</literal>.</para>
<variablelist>
<varlistentry>
<term>i and j may be :</term>
<listitem>
<variablelist>
<varlistentry>
<term>real scalar or vector or matrix with positive
elements.</term>
<listitem>
<para><literal>[r1,...rn]=l(i)</literal> extracts the
<literal>i(k)</literal> elements from the list l and store
them in <literal>rk</literal> variables for
<literal>k</literal> from 1 to
<literal>size(i,'*')</literal></para>
</listitem>
</varlistentry>
<varlistentry>
<term>the symbol <literal> : </literal></term>
<listitem>
<para>which stands for "all elements".</para>
</listitem>
</varlistentry>
<varlistentry>
<term>a vector of booleans.</term>
<listitem>
<para>If <literal>i</literal> is a vector of booleans it is
interpreted as <literal>find(i)</literal>.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>a polynomial.</term>
<listitem>
<para>If <literal>i</literal> is a vector of polynomials or
implicit polynomial vector it is interpreted as
<literal>horner(i,m)</literal> where
<literal>m=size(l)</literal>. Even if this feature works for
all polynomials, it is recommended to use polynomials in
<literal>$</literal> for readability.</para>
</listitem>
</varlistentry>
</variablelist>
</listitem>
</varlistentry>
<varlistentry>
<term>k1,..kn may be :</term>
<listitem>
<variablelist>
<varlistentry>
<term>real positive scalar,</term>
<listitem>
<para></para>
</listitem>
</varlistentry>
<varlistentry>
<term>a polynomial,</term>
<listitem>
<para>interpreted as <literal>horner(ki,m)</literal> where
<literal>m</literal> is the corresponding sub-list
size.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>a character string</term>
<listitem>
<para>associated with a sub-list entry name.</para>
</listitem>
</varlistentry>
</variablelist>
</listitem>
</varlistentry>
</variablelist>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Remarks</title>
<para>For soft coded matrix types such as rational functions and state
space linear systems, <literal>x(i)</literal> syntax may not be used for
vector element extraction due to confusion with list element extraction.
<literal>x(1,j)</literal> or <literal>x(i,1)</literal> syntax must be
used.</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
// MATRIX CASE
a=[1 2 3;4 5 6]
a(1,2)
a([1 1],2)
a(:,1)
a(:,3:-1:1)
a(1)
a(6)
a(:)
a([%t %f %f %t])
a([%t %f],[2 3])
a(1:2,$-1)
a($:-1:1,2)
a($)
//
x='test'
x([1 1;1 1;1 1])
//
b=[1/%s,(%s+1)/(%s-1)]
b(1,1)
b(1,$)
b(2) // the numerator
// LIST OR TLIST CASE
l=list(1,'qwerw',%s)
l(1)
[a,b]=l([3 2])
l($)
x=tlist(l(2:3)) //form a tlist with the last 2 components of l
//
dts=list(1,tlist(['x';'a';'b'],10,[2 3]));
dts(2)('a')
dts(2)('b')(1,2)
[a,b]=dts(2)(['a','b'])
]]></programlisting>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member><link linkend="find">find</link></member>
<member><link linkend="horner">horner</link></member>
<member><link linkend="parents">parents</link></member>
</simplelist>
</refsection>
</refentry>
|
