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| <TITLE>inner_product()</TITLE> |
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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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