Difference between revisions of "cpp/algorithm/inner product"

Revision as of 13:38, 11 July 2018

Defined in header `<numeric>`
template< class InputIt1, class InputIt2, class T > T inner_product( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init );	(1)
template<class InputIt1, class InputIt2, class T, class BinaryOperation1, class BinaryOperation2> T inner_product( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init, BinaryOperation1 op1, BinaryOperation2 op2 );	(2)

Computes inner product (i.e. sum of products) or performs ordered map/reduce operation on the range [first1, last1) and the range beginning at first2.

1) Initializes the accumulator acc with the initial value init and then

modifies it with the expression acc = acc + first1 first2, then modifies again with the expression acc = acc + (first1+1) * *(first2+1), etc	(until C++20)
modifies it with the expression acc = std::move(acc) + first1 first2, then modifies again with the expression acc = std::move(acc) + (first1+1) * *(first2+1), etc	(since C++20)

until reaching last1. For built-in meaning of + and *, this computes inner product of the two ranges.

2) Initializes the accumulator acc with the initial value init and then

modifies it with the expression acc = op1(acc, op2(first1, first2)), then modifies again with the expression acc = op1(acc, op2((first1+1), (first2+1))), etc	(until C++20)
modifies it with the expression acc = op1(std::move(acc), op2(first1, first2)), then modifies again with the expression acc = op1(std::move(acc), op2((first1+1), (first2+1))), etc	(since C++20)

until reaching last1.

`op1` or `op2` must not have side effects.	(until C++11)
`op1` or `op2` must not invalidate any iterators, including the end iterators, or modify any elements of the range involved.	(since C++11)

first1, last1	-	the first range of elements
first2	-	the beginning of the second range of elements
init	-	initial value of the sum of the products
op1	-	binary operation function object that will be applied. This "sum" function takes a value returned by op2 and the current value of the accumulator and produces a new value to be stored in the accumulator. The signature of the function should be equivalent to the following: Ret fun(const Type1 &a, const Type2 &b); The signature does not need to have const &. The types Type1 and Type2 must be such that objects of types T and Type3 can be implicitly converted to Type1 and Type2 respectively. The type Ret must be such that an object of type T can be assigned a value of type Ret.
op2	-	binary operation function object that will be applied. This "product" function takes one value from each range and produces a new value. The signature of the function should be equivalent to the following: Ret fun(const Type1 &a, const Type2 &b); The signature does not need to have const &. The types Type1 and Type2 must be such that objects of types InputIt1 and InputIt2 can be dereferenced and then implicitly converted to Type1 and Type2 respectively. The type Ret must be such that an object of type Type3 can be assigned a value of type Ret.
Type requirements
- `InputIt1, InputIt2` must meet the requirements of LegacyInputIterator.
- `ForwardIt1, ForwardIt2` must meet the requirements of LegacyForwardIterator.
- `T` must meet the requirements of CopyAssignable and CopyConstructible.

Return value

The final value of acc as described above.

Possible implementation

First version

template<class InputIt1, class InputIt2, class T>
T inner_product(InputIt1 first1, InputIt1 last1,
                InputIt2 first2, T init)
{
    while (first1 != last1) {
         init = std::move(init) + *first1 * *first2; // std::move since C++20
         ++first1;
         ++first2;
    }
    return init;
}

Second version

template<class InputIt1, class InputIt2,
         class T,
         class BinaryOperation1, class BinaryOperation2>
T inner_product(InputIt1 first1, InputIt1 last1,
                InputIt2 first2, T init,
                BinaryOperation1 op1
                BinaryOperation2 op2)
{
    while (first1 != last1) {
         init = op1(std::move(init), op2(*first1, *first2)); // std::move since C++20
         ++first1;
         ++first2;
    }
    return init;
}

Notes

The parallelizable version of this algorithm, std::transform_reduce, requires op1 and op2 to be commutative and associative, but std::inner_product makes no such requirement, and always performs the operations in the order given.

Example

Run this code

#include <numeric>
#include <iostream>
#include <vector>
#include <functional>
int main()
{
    std::vector<int> a{0, 1, 2, 3, 4};
    std::vector<int> b{5, 4, 2, 3, 1};
 
    int r1 = std::inner_product(a.begin(), a.end(), b.begin(), 0);
    std::cout << "Inner product of a and b: " << r1 << '\n';
 
    int r2 = std::inner_product(a.begin(), a.end(), b.begin(), 0,
                                std::plus<>(), std::equal_to<>());
    std::cout << "Number of pairwise matches between a and b: " <<  r2 << '\n';
}

Output:

Inner product of a and b: 21
Number of pairwise matches between a and b: 2

Compiler support
Freestanding and hosted
Language
Standard library
Standard library headers
Named requirements
Feature test macros (C++20)
Language support library
Concepts library (C++20)
Metaprogramming library (C++11)
Diagnostics library
General utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Localizations library
Input/output library
Filesystem library (C++17)
Regular expressions library (C++11)
Concurrency support library (C++11)
Execution support library (C++26)
Technical specifications
Symbols index
External libraries

transform_reduce (C++17)	applies an invocable, then reduces out of order (function template) [edit]
accumulate	sums up or folds a range of elements (function template) [edit]
partial_sum	computes the partial sum of a range of elements (function template) [edit]

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Difference between revisions of "cpp/algorithm/inner product"

Revision as of 13:38, 11 July 2018

Contents

Parameters

Return value

Possible implementation

Notes

Example

See also

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@@ Line 6: / Line 6: @@
 template< class InputIt1, class InputIt2, class T >
 T inner_product( InputIt1 first1, InputIt1 last1,
-                  InputIt2 first2, T value );
+                  InputIt2 first2, T init );
 }}
 {{dcl | since= | num= 2 |1=
@@ Line 12: / Line 12: @@
           class BinaryOperation1, class BinaryOperation2>
 T inner_product( InputIt1 first1, InputIt1 last1,
-                  InputIt2 first2, T value,
+                  InputIt2 first2, T init,
                   BinaryOperation1 op1,
                   BinaryOperation2 op2 );
@@ Line 45: / Line 45: @@
 {{par | first1, last1 | the first range of elements}}
 {{par | first2 | the beginning of the second range of elements}}
-{{par | value | initial value of the sum of the products}}
+{{par | init | initial value of the sum of the products}}
 {{par op2 | op1 | This "sum" function takes a value returned by op2 and the current value of the accumulator and produces a new value to be stored in the accumulator. | t1=T | t2=Type3 | rt=T}}
 {{par op2 | op2 | This "product" function takes one value from each range and produces a new value. | p1=InputIt1 | p2=InputIt2 | rt=Type3}}
@@ Line 62: / Line 62: @@
 template<class InputIt1, class InputIt2, class T>
 T inner_product(InputIt1 first1, InputIt1 last1,
-                 InputIt2 first2, T value)
+                 InputIt2 first2, T init)
 {
      while (first1 != last1) {
-          value = std::move(value) + *first1 * *first2; // std::move since C++20
+          init = std::move(init) + *first1 * *first2; // std::move since C++20
           ++first1;
           ++first2;
      }
-     return value;
+     return init;
 }
   | 2=
@@ Line 76: / Line 76: @@
           class BinaryOperation1, class BinaryOperation2>
 T inner_product(InputIt1 first1, InputIt1 last1,
-                 InputIt2 first2, T value,
+                 InputIt2 first2, T init,
                  BinaryOperation1 op1
                  BinaryOperation2 op2)
 {
      while (first1 != last1) {
-          value = op1(std::move(value), op2(*first1, *first2)); // std::move since C++20
+          init = op1(std::move(init), op2(*first1, *first2)); // std::move since C++20
           ++first1;
           ++first2;
      }
-     return value;
+     return init;
 }
 }}