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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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	<H2>inner_product()</H2>
	<P><B>Library:</B>  <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 <numeric>

	namespace std {
	template <class InputIterator1, class InputIterator2,
	class T>
	T inner_product(InputIterator1 start1,
	InputIterator1 finish1,
	InputIterator2 start2, T init);

	template <class InputIterator1, class InputIterator2,
	class T,
	class BinaryOperation1,
	class BinaryOperation2>
	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 <algorithm> // for copy
	#include <numeric> // for inner_product
	#include <iostream> // for cout, endl
	#include <list> // for list
	#include <vector> // for vector
	#include <functional> // for plus, minus



	int main ()
	{
	typedef std::list<int, std::allocator<int> > List;
	typedef std::vector<int, std::allocator<int> > Vector;
	typedef std::ostream_iterator<int, char,
	std::char_traits<char> > 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<List::value_type>(),
	std::minus<List::value_type>());
	// Print the output.
	std::cout << "For the sets of numbers: { ";
	std::copy (v.begin (), v.end (), os_iter (std::cout, " "));

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

	std::cout << "}\nThe inner product is: " << prod
	<< "\nThe wacky result is: " << wacky
	<< 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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