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<H2>inner_product()</H2>
<P><B>Library:</B>&nbsp;&nbsp;<A HREF="2-10.html">Numerics</A></P>

<PRE><HR><B><I>Function</I></B><HR></PRE>

<UL>
<LI><A HREF="#sec1">Local Index</A></LI>
<LI><A HREF="#sec2">Summary</A></LI>
<LI><A HREF="#sec3">Synopsis</A></LI>
<LI><A HREF="#sec4">Description</A></LI>
<LI><A HREF="#sec5">Complexity</A></LI>
<LI><A HREF="#sec6">Example</A></LI>
<LI><A HREF="#sec7">Standards Conformance</A></LI>
</UL>
<A NAME="sec1"><H3>Local Index</H3></A>
No Entries
<A NAME="sec2"><H3>Summary</H3></A>
<P>A generalized numeric operation that computes the inner product <SAMP>A X B</SAMP> of two ranges <SAMP>A</SAMP> and <SAMP>B</SAMP></P>
<A NAME="sec3"><H3>Synopsis</H3></A>

<PRE>#include &lt;numeric&gt;

namespace std {
  template &lt;class InputIterator1, class InputIterator2,
            class T&gt;
  T inner_product(InputIterator1 start1, 
                  InputIterator1 finish1,
                  InputIterator2 start2, T init);
  
  template &lt;class InputIterator1, class InputIterator2,
            class T,
            class BinaryOperation1,
            class BinaryOperation2&gt;
  T inner_product(InputIterator1 start1, 
                  InputIterator1 finish1,
                  InputIterator2 start2, T init,
                  BinaryOperation1 binary_op1,
                  BinaryOperation2 binary_op2);
}
</PRE>
<A NAME="sec4"><H3>Description</H3></A>
<P>There are two versions of <SAMP>inner_product()</SAMP>. 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 initializes <SAMP>acc</SAMP> with <SAMP>init</SAMP> and then modifies it with:</P>
<P><SAMP>acc = acc + ((*i1) * (*i2))</SAMP></P>
<P>for every iterator <SAMP>i1</SAMP> in the range <SAMP>[start1, finish1)</SAMP> and iterator <SAMP>i2</SAMP> in the range <SAMP>[start2, start2 + (finish1 - start1))</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:</P>
<P><SAMP>acc  =  binary_op1(acc, binary_op2(*i1,  *i2))</SAMP></P>
<P>for every iterator <SAMP>i1</SAMP> in the range <SAMP>[start1, finish1)</SAMP> and iterator <SAMP>i2</SAMP> in the range <SAMP>[start2, start2 + (finish1  - start1))</SAMP>.</P>
<A NAME="sec5"><H3>Complexity</H3></A>
<P>The <SAMP>inner_product()</SAMP> algorithm computes exactly <SAMP>(finish1 - start1)</SAMP> applications of either:</P>
<P><SAMP>acc + (*i1) * (*i2)</SAMP></P>
<P> or </P>
<P><SAMP>binary_op1(acc, binary_op2(*i1, *i2)).</SAMP></P>
<A NAME="sec6"><H3>Example</H3></A>

<UL><PRE>//
//  inr_prod.cpp
//

#include &lt;algorithm&gt;     // for copy
#include &lt;numeric&gt;       // for inner_product
#include &lt;iostream&gt;      // for cout, endl
#include &lt;list&gt;          // for list
#include &lt;vector&gt;        // for vector
#include &lt;functional&gt;    // for plus, minus


int main ()
{
    typedef std::list&lt;int, std::allocator&lt;int&gt; &gt;   List;
    typedef std::vector&lt;int, std::allocator&lt;int&gt; &gt; Vector;
    typedef std::ostream_iterator&lt;int, char, 
                          std::char_traits&lt;char&gt; &gt; os_iter;

    // Initialize a list and a vector using arrays of ints.
    int a1[] = { 6, -3, -2 };
    int a2[] = { -2, -3, -2 };

    List   l (a1, a1 + sizeof a1 / sizeof *a1);
    Vector v (a2, a2 + sizeof a2 / sizeof *a2);

    // Calculate the inner product of the two sets of values.
    List::value_type prod = std::inner_product (l.begin (), 
                                      l.end (), v.begin (), 0);

    // Calculate a wacky inner product using the same values.
    List::value_type wacky =
        std::inner_product (l.begin (), l.end (), v.begin (), 
                            0, std::plus&lt;List::value_type&gt;(),
                            std::minus&lt;List::value_type&gt;());
    // Print the output.
    std::cout &lt;&lt; "For the sets of numbers: { ";
    std::copy (v.begin (), v.end (), os_iter (std::cout, " "));

    std::cout &lt;&lt; "} and { ";
    std::copy (l.begin (), l.end (), os_iter (std::cout, " "));

    std::cout &lt;&lt; "}\nThe inner product is: " &lt;&lt; prod
              &lt;&lt; "\nThe wacky result is:  " &lt;&lt; wacky
              &lt;&lt; std::endl;

    return 0;
}


Program Output:
For the sets of numbers: { -2 -3 -2 } and { 6 -3 -2 }
The inner product is: 1
The wacky result is:  8
</PRE></UL>
<UL><PRE></PRE></UL>
<A NAME="sec7"><H3>Standards Conformance</H3></A>
<P><I>ISO/IEC 14882:1998 -- International Standard for Information Systems -- Programming Language C++, Section 26.4.2</I></P>

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