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<H2>inner_product</H2>
<HR><PRE>     Generalized Numeric Operation</PRE><HR>
<A NAME="Summary"><H3>Summary</H3></A>
<P>Computes the inner product <SAMP>A X B</SAMP> of two ranges <SAMP>A</SAMP> and <SAMP>B</SAMP>.</P>
<H3>Contents</H3>
<UL>
<A HREF="#Synopsis"><LI>Synopsis</LI></A>
<A HREF="#Description"><LI>Description</LI></A>
<A HREF="#Complexity"><LI>Complexity</LI></A>
<A HREF="#Example"><LI>Example</LI></A>
<A HREF="#Warnings"><LI>Warnings</LI></A>
</UL>
<A NAME="Synopsis"><H3>Synopsis</H3></A>
<PRE>#include &#60;numeric>
template &#60;class InputIterator1, class InputIterator2,</PRE>
<PRE>          class T>
T <B>inner_product</B> (InputIterator1 first1, InputIterator1 last1,
                 InputIterator2 first2, T init);</PRE><PRE>template &#60;class InputIterator1, class InputIterator2,
          class T,
          class BinaryOperation1,
          class BinaryOperation2>
T <B>inner_product</B> (InputIterator1 first1, InputIterator1 last1,
                 InputIterator2 first2, T init,
                 BinaryOperation1 binary_op1,
                 BinaryOperation2 binary_op2);
</PRE>
<A NAME="Description"><H3>Description</H3></A>
<P>There are two versions of <B><I>inner_product</B></I>.  The first computes an inner product using the default multiplication and addition operators, while the second allows you to specify binary operations to use in place of the default operations. </P>
<P>The first version of the function computes its result by initializing the accumulator <SAMP>acc</SAMP> with the initial value <SAMP>init</SAMP> and then modifying it with:</P>
<PRE> acc = acc + ((*i1) * (*i2))</PRE>
<PRE></PRE><P>for every iterator <SAMP>i1</SAMP> in the range <SAMP>[first1, last1)</SAMP> and iterator <SAMP>i2</SAMP> in the range <SAMP>[first2, first2 + (last1 - first1))</SAMP>.  The algorithm returns <SAMP>acc</SAMP>.</P>
<P>The second version of the function initializes <SAMP>acc</SAMP> with <SAMP>init</SAMP>, then computes the result:</P>
<PRE>acc  =  binary_op1(acc, binary_op2(*i1,  *i2))</PRE>
<PRE></PRE><P>for every iterator <SAMP>i1</SAMP> in the range <SAMP>[first1, last1)</SAMP> and iterator <SAMP>i2</SAMP> in the range <SAMP>[first2, first2 + (last1  - first1))</SAMP>.</P>
<A NAME="Complexity"><H3>Complexity</H3></A>
<P>The <B><I>inner_product</B></I> algorithm computes exactly <SAMP>(last1 - first1)</SAMP> applications of either:</P>
<PRE>acc + (*i1) * (*i2)</PRE>
<P> or </P>
<PRE>binary_op1(acc, binary_op2(*i1, *i2)).</PRE>
<A NAME="Example"><H3>Example</H3></A>
<PRE>//
// inr_prod.cpp
//
 #include &#60;numeric>       //For inner_product
 #include &#60;list>          //For list
 #include &#60;vector>        //For vectors
 #include &#60;functional>    //For plus and minus
 #include &#60;iostream.h></PRE>
<PRE> int main()
 {
   //Initialize a list and an int using arrays of ints
   int a1[3] = {6, -3, -2};
   int a2[3] = {-2, -3, -2};</PRE>
<PRE>   list&#60;int>   l(a1, a1+3);
   vector&#60;int> v(a2, a2+3);</PRE>
<PRE>   //Calculate the inner product of the two sets of values
   int inner_prod =
        <B>inner_product</B>(l.begin(), l.end(), v.begin(), 0);</PRE>
<PRE>   //Calculate a wacky inner product using the same values
   int wacky = 
         <B>inner_product</B>(l.begin(), l.end(), v.begin(), 0,
                       plus&#60;int>(), minus&#60;int>());</PRE>
<PRE>   //Print the output
   cout &#60;&#60; "For the two sets of numbers: " &#60;&#60; endl 
        &#60;&#60; "     ";
   copy(v.begin(),v.end(),ostream_iterator&#60;int>(cout," "));
   cout &#60;&#60; endl &#60;&#60; " and  ";
   copy(l.begin(),l.end(),ostream_iterator&#60;int>(cout," "));</PRE>
<PRE>   cout &#60;&#60; "," &#60;&#60; endl &#60;&#60; endl;
   cout &#60;&#60; "The inner product is: " &#60;&#60; inner_prod &#60;&#60; endl;
   cout &#60;&#60; "The wacky result is: " &#60;&#60; wacky &#60;&#60; endl;</PRE>
<PRE>   return 0;
 }</PRE>
<PRE>Output :
For the two sets of numbers:
     -2 -3 -2
 and  6 -3 -2 ,
The inner product is: 1
The wacky result is: 8
</PRE>
<A NAME="Warnings"><H3>Warnings</H3></A>
<P>If your compiler does not support default template parameters, then you need to always supply the <SAMP>Allocator</SAMP> template argument.  For instance, you'll have to write :</P>
<P><SAMP>list&#60;int, allocator> </SAMP>and <SAMP>vector&#60;int, allocator></SAMP></P>
<P>instead of </P>
<P><SAMP>list&#60;int> </SAMP>and<SAMP> vector&#60;int></SAMP></P>
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