USU Math 4610
Routine Name: Vector Addition and Subtraction
Author: Philip Nelson
Language: C++. The code can be compiled using the GNU C++ compiler (gcc). A make file is included to compile an example program
For example,
make
will produce an executable ./vectorOps.out that can be executed.
Description/Purpose: This routine overloads the + and - operators in c++ allowing two vectors to be added and subtracted with the following syntax, a + b and a - b.
Input: The operator requires two operands, a and b, where a, b are std::vector<T>
@tparam T Type of the elements in the first vector
@tparam U Type of the elements in the second vector
@tparam R Type of the elements in the result vector
@param a The first vector
@param b The second vector
Output: A vector with the result of vector addition or subtraction with the two vector operands.
Usage/Example:
int main()
{
std::vector<double> a = {-1.1, 2.3, 3.5};
std::vector<double> b = {4.2, 5.4, 6.6};
std::cout << "a\t" << a << '\n';
std::cout << "b\t" << b << '\n';
std::cout << "a + b\t" << a + b << '\n';
std::cout << "a - b\t" << a - b << '\n';
}
Output from the lines above
a [ 1.1 2.3 3.5 ]
b [ 4.2 5.4 6.6 ]
a + b [ 5.3 7.7 10.1 ]
a - b [ -3.1 -3.1 -3.1 ]
explanation of output:
The first two lines display two vectors a and b.
The third line is the result of a + b and the fourth line is the result of a - b.
Implementation/Code: The following is the code for vector addition and subtraction
For code re-usability, the implementation takes advantage of the c++ preprocessor to generate the actual addition and subtraction code. The difference between adding and subtracting vectors is simply the difference between using the plus operator or the minus operator. Hence, vector_add_subtract defines the generic form of the operation with the operator replaced with a variable. This way vector_add_subtract(+) vector_add_subtract(-) can fill in the operator and the preprocessor will generate the code, no branching structure or duplicate code required.
#define vector_add_subtract(op) \
template <typename T, typename U, typename R = decltype(T() op U())> \
std::vector<R> operator op(std::vector<T> const& a, std::vector<U> const& b) \
{ \
// check the sizes are equal \
if (a.size() != b.size()) \
{ \
std::cerr << "ERROR: bad size in vector addition\n"; \
exit(EXIT_FAILURE); \
} \
\
// initalize it result vector \
std::vector<R> result(a.size()); \
\
// add or subtract the vectors elementwise \
for (auto i = 0u; i < a.size(); ++i) \
{ \
result[i] = a[i] op b[i]; \
} \
\
// return the result \
return result; \
}
// Call the macro with addition and subtraction operator
vector_add_subtract(+) vector_add_subtract(-)
Last Modified: October 2018