C++ Error Code C2784 could not deduce template argument for - c++

Question

I am very new to object oriented programming and C++. I have been working on a matrix class and squarematrix class and have been running into some problems that I can't seem to figure out. The error code I have been getting is:
C2784:
'matrix<T,m,k> operator *(matrix<T,m,n> &,matrix<T,n,k> &)': could not
deduce template argument for 'matrix<T,m,n> &' from
'std::vector<std::vector<double,std::allocator<_Ty>>,std::allocator<std::vector<_Ty,std::allocator<_Ty>>>>'
I am really unsure why, because I have had other parts of my code work. The error is reported in the line with "product.elements = product.elements * elements;"
//Source.cpp
#include"Squarematrix.h"
#include<iostream>
#include<vector>
using namespace std;
int main() {
vector<double> a = { 1, 2,4,5,6};
squarematrix<double,2> N;
N.assign(a);
cout << N << N.pow(2)<< endl;
return(0);
}
//Matrix.h
#ifndef _Matrix_
#define _Matrix_
#include <iostream>
#include <vector>
#include <math.h>
using namespace std;
template<class T, int m, int n>
class matrix {
public:
vector<vector<T>> elements;
int nrow;
int ncol;
matrix();
matrix(matrix<T, m, n>&);
};
template<class T, int m, int n>
matrix<T, m, n>::matrix() {
vector<T>temp(n, 0);
elements.assign(m, temp);
nrow = m; //m=0
ncol = n; //n=0
}
template<class T, int m, int n>
matrix<T, m, n>::matrix(matrix<T, m, n>& a) {
elements = a.elements;
nrow = m;
ncol = n;
}
template<class T, int m, int n, int k>
matrix<T, m, k> operator*(const matrix<T, m, n>& a, const matrix<T, n, k>& b) {
matrix<T, m, k> product;
for (int i = 0; i < m; i++) {
for (int j = 0; j < k; j++) {
for (int h = 0; h < n; h++)
product.elements[i][j] += a.elements[i][h] * b.elements[h][j];
}
}
return product;
}
template<class T, int m, int n>
ostream& operator<< (ostream& o, const matrix<T, m, n>& input) {
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j)
o << input.elements[i][j] << " ";
o << endl;
}
return o;
}
#endif _Matrix_
//Squarematrix.h
#ifndef _Squarematrix_
#define _Squarematrix_
#include "Matrix.h"
#include <iostream>
#include <vector>
using namespace std;
template<class T, int n>
class squarematrix : public matrix<T, n, n> {
public:
squarematrix();
squarematrix(squarematrix<T, n>&);
squarematrix<T, n> pow(int); //calculate A^k
};
template<class T, int n>
squarematrix<T, n>::squarematrix(){
vector<T>temp(n, 0);
elements.assign(n, temp);
nrow = n; //n=0
ncol = n; //n=0
}
template<class T, int n>
squarematrix<T, n>::squarematrix(squarematrix<T, n>& a){
elements = a.elements;
nrow = n;
ncol = n;
}
template<class T, int n>
squarematrix<T, n> squarematrix<T, n>::pow(int k){
squarematrix<T, n> product;
product.elements = elements;
for (int power = 2; power <= k; power++) {
product.elements = product.elements * elements;
}
return product;
}
#endif _Squarematrix_

Answer 1

You don't need nrow and ncol - they're template parameters and known at compile time.
But that's not the problem - you're multiplying std::vector where you should be multiplying squarematrix:
template<class T, int n>
squarematrix<T, n> squarematrix<T, n>::pow(int k){
squarematrix<T, n> product = unit_matrix<T, n>();
for (int power = 1; power <= k; power++) {
product = product * *this;
}
return product;
}
where I've used a fictitious function that creates a unit matrix.
Writing that function left as an exercise.

Answer 2

this code product.elements = product.elements * elements expresses that you want use two std::vector to multiply, but you don't support the operator * operation with two parameters whose type is std::vector.
In your code, you support a operator * operation with type matrix, so if you want use it, you should change the code product.elements = product.elements * elements to product.elements = (product * *this).elements
that will be OK.
so the code of the member function pow of class Squarematrix is:
template<class T, int n>
squarematrix<T, n> squarematrix<T, n>::pow(int k){
squarematrix<T, n> product;
product.elements = this->elements;
for (int power = 2; power <= k; power++) {
product.elements = (product * *this).elements;
}
return product;
}
at last , #endif is the end of some predefined and don't follow some macro, otherwise, the compiler will throw some warnings or errors.