overloading operator for linear algebra - c++

Question

I want to implement the Euler method in two dimensions and I don´t want to use any library (for practice).
Therefore I want to use my own linear algebra with overloaded functions.
The two first overloads seem to work but there´s still a problem with the multiplication matrix * vector i.e a (2x2)*(2x1).
class vector{
public:
double a;
double b;
vector::vector();
vector::vector(double a, double b){
this->a = a;
this->b = b;
};
vector operator+(vector &a);
vector operator*(double factor);
vector operator*(matrix &B);
};
class matrix{
public:
double a1;
double a2;
double b1;
double b2;
matrix::matrix();
matrix::matrix(double a1, double a2, double b1, double b2) {
this->a1 = a1;
this->a2 = a2;
this->b1 = b1;
this->b2 = b2;
};
};
vector vector::operator+(vector& v){
return vector(this->a+v.a,this->b+v.b);
};
vector vector::operator*(double factor){
return vector(this->a*factor, this->b*factor);
};
vector vector::operator*(matrix& B){
vector newv(this->a*B.a1 + B.a2*b, this->a*B.a1 + B.b2*b);
return newv;
};
Errors when I compile it:
'vector vector::operator *(matrix &)' : overloaded member function not found in 'vector'
unable to resolve function overload

Answer 1

Since you're a bit short on details, I must fill in the gap with guesses. My guess is that you try to support something like the following:
matrix m;
vector v, w;
// fill m and v with values
w = m*v;
I'm also guessing that your matrix has the following form:
( a1 a2 )
( b1 b2 )
You now have two options: Either implement matrix-vector multiplication in the class matrix, or implement it as a free function.
If you want to put if in the matrix class, you'd change the code as follows (note that there are many more things for the code that should be changed, but those are unrelated to the question):
class vector
{
// omit the operator* for matrix, otherwise unchanged
};
class matrix
{
// all that's already in the class
vector operator*(vector const& v) const;
};
vector matrix::operator*(vector const& v) const
{
return vector(a1*v.a + a2*v.b, b1*v.a + b2*v.b);
}
// the rest of your code
If you want to make it a free function (I personally would do it that way, but I'm sure that opinion is not universally held), you'd write
class vector
{
// omit the operator* for matrix, otherwise unchanged
};
class matrix
{
// completely unchanged
};
vector operator*(matrix const& m, vector const& v)
{
return vector(m.a1*v.a + m.a2*v.b, m.b1*v.a + m.b2*v.b);
}
// the rest of your code

Answer 2

I would prefer a BLAS library as an implementation in long term against reinvent the wheel again for basic matrix operations. Additionally some of the BLAS libraries are multithreaded and/or GPU based; they are widely used and tested.
In terms of design I would introduce functions what could be easily implemented by BLAS against operators:
C = α * A + β * B
C = α * A * B + β *C
So as a header:
...
bool blasAdd(const double alfa_, const Matrix& A_, const double beta_, const Matrix& B_, Matrix& C_);
bool blasMultiply(const double alfa_, const Matrix& A_, const Matrix& B_, const double beta_, Matrix& C_);
...
In this way your code automatically could be optimized for BLAS.
My favorite BLAS implementation is Intel MKL, but there are also many free BLAS implementations in the market (e.g.: boost BLAS).