Matrix scalar product - c++

Question

I have a task to calculate a scalar product
s=(B*(r+q+r), A*A*p)
As I understand, I need to calculate 2 vectors: first - B*(r+q+r), second - AAp, and then calculate a scalar product.
#include <iostream>
#include <vector>
using namespace std;
using matrix = vector<vector<double>>;
matrix add(matrix A, matrix B) {
matrix C;
C.resize(A.size());
for (int i = 0; i< A.size(); i++) {
C[i].resize(B.size());
for (int j = 0; j < B.size(); j++) {
C[i][j] = A[i][j] + B[i][j];
}
}
return C;
}
matrix multiple(matrix A, matrix B)
{
matrix C;
C.reserve(100);
C.resize(B.size());
for (int i = 0; i < A.size(); i++) {
C[i].resize(B.size());
for (int j = 0; j < B.size(); j++) {
for (int k = 0; k < B.size(); k++)
C[i][j] += A[i][k] * B[k][j];
}
}
return C;
}
void main() {
matrix A = { {1,2,3}, {1,2,1}, {3,2,0} };
matrix B = { {4,1,2},{0,4,3},{1,1,1} };
matrix r = { {-0.7f, 1.3, 0.2} };
matrix q = { { -1.6f, 0.8, 1.1} };
matrix p = { {0.1, 1.7, -1.5} };
matrix r_q = add(r, q);
for (int i = 0; i < r_q.size(); i++) {
for (int j = 0; j < r_q.size(); j++) {
cout << r_q[i][j] << "\t";
}
cout << "\n";
}
matrix a_a = multiple(A, A);
matrix a_a_p = multiple(a_a,p);
getchar();
}
Problems:
add method work not correct, it put in result only one number - sum of the first items.
Multipling matrix with the same dimensions (A*A) work correct. Multipling matrix with the different dimensions (a_a * p) - return error "vector subscript out of range".
Thanks for any advice.

Answer 1

The OP chose to implement both matrices and vectors using a std::vector<std::vector<double>>.
This may not be a good design choice in general, but also in particular, to be consistent to the mathematical meaning of all the involved operations, all the vectors should be considered (and declared as well) as "column" matrices (or Nx1 matrices):
matrix r = { {-0.7}, {1.3}, {0.2} };
matrix q = { {-1.6}, {0.8}, {1.1} };
matrix p = { {0.1}, {1.7}, {-1.5} };
Then, in the functions that perform the calculations, special attention should be paid to the correct sizes of rows and columns to avoid out of bounds accesses.
matrix add(matrix const &A, matrix const &B)
{
if (A.size() != B.size() || A.size() == 0)
throw std::runtime_error("number of rows mismatch");
size_t columns = A[0].size();
matrix C(A.size(), std::vector<double>(columns, 0.0));
for (size_t i = 0; i < A.size(); i++)
{
if ( A[i].size() != columns || B[i].size() != columns )
throw std::runtime_error("number of columns mismatch");
for (size_t j = 0; j < columns; j++)
{
C[i][j] = A[i][j] + B[i][j];
}
}
return C;
}
matrix multiple(matrix const &A, matrix const &B)
{
if ( A.size() == 0 || B.size() == 0 || B[0].size() == 0)
throw std::runtime_error("size mismatch");
size_t columns = B[0].size();
matrix C(A.size(), std::vector<double>(columns, 0.0));
for (size_t i = 0; i < A.size(); i++)
{
if ( A[i].size() != B.size() || B[i].size() != columns )
throw std::runtime_error("inner size mismatch");
for (size_t j = 0; j < columns; j++)
{
for (size_t k = 0; k < B.size(); k++)
C[i][j] += A[i][k] * B[k][j];
}
}
return C;
}
The compiler should have also warned the OP about the incorrect use of void main instead of int main and about the comparisons between signed and unsigned integer expressions (I used size_t instead of int).
From a mathematical point of view, it's worth noting that to solve OP problem, that is to calculate the scalar product s = (B(r+q+r), AAp), the operations really needed (to be implemented) are the sum of vectors, the product of a matrix by a vector (easier and more efficient then matrix multiplication) and the dot product of two vectors:
t = r + q + r
b = Bt
u = Ap
a = Au
s = (b, a)