USU Math 4610
Routine Name: Matrix 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 ./matrixOpts.out that can be executed.
Description/Purpose: This routine overloads the + and - operators in c++ allowing two matrices to be added or 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<std::vector<T>>
@tparam T Type of the elements in the first matrix
@tparam U Type of the elements in the second matrix
@tparam R Type of the elements in the result matrix
@param a The first matrix
@param b The second matrix
Output: A matrix with the result of matrix addition or subtraction with the two matrix operands.
Usage/Example:
int main()
{
Matrix<int> m1 = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
std::cout << m1 + m1 << std::endl;
std::cout << m1 - m1 << std::endl;
}
Output from the lines above
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |
| 2 4 6 |
| 8 10 12 |
| 14 16 18 |
| 0 0 0 |
| 0 0 0 |
| 0 0 0 |
explanation of output:
The matrix is m1.
The second matrix is the result of m1 + m1.
The third matrix is the result of m1 - m1.
Implementation/Code: The following is the code for Matrix 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 matrices is simply the difference between using the plus operator or the minus operator. Hence, matrix_add_subtract defines the generic form of the operation with the operator replaced with a variable. This way matrix_add_subtract(+) matrix_add_subtract(-) can fill in the operator and the preprocessor will generate the code, no branching structure or duplicate code required.
#define matrix_add_subtract(op) \
template <typename T, typename U, typename R = decltype(T() + U())> \
Matrix<R> operator op(Matrix<T> const& a, Matrix<U> const& b) \
{ \
// check sizes are compatible \
if (a.size() != b.size() || a[1].size() != b[0].size()) \
{ \
std::cerr << "ERROR: bad size in matrix_add_subtract\n"; \
exit(EXIT_FAILURE); \
} \
\
// initalize the result matrix \
Matrix<R> result(a.size()); \
\
// for every row in a \
for (auto i = 0u; i < a.size(); ++i) \
{ \
// initalize the next row of the result \
result[i].reserve(a[i].size()); \
\
// for every column of a \
for (auto j = 0u; j < a[i].size(); ++j) \
{ \
// push the ij'th elements of a and b added or subtracted \
result[i].push_back(a[i][j] op b[i][j]); \
} \
} \
\
// return the result matrix \
return result; \
}
// call the macro with the addition and subtraction operator
matrix_add_subtract(+) matrix_add_subtract(-)
Last Modified: October 2018