How to define a [ ][ ] operator for a matrixclass in Qt?

Question

I am working on my own matrix class in Qt. I know there is a QGenericMatrix class template, but I need to set the size at runtime, which is not possible with this one. Apart from that I see this as a nice project to revive my linear algebra knowledge by implementing this.

However, I have already been able to define the * operator (multiplication) as follows:

MyMatrix.h

public:
   MyMatrix(int rows, int cols, double initValues=0.0);        // constructor to create NxM matrix with N=col, M=rows

   MyMatrix& operator*(double value);                           // multiply matrix with a double 
private:
    int rows;
    int cols;
    double **mat;
    void initMatrix(int rows=1, int cols=1);        // initialise the matrix, if no rows,cols are given it creates a "1x1 matrix"

MyMatrix.cpp

// constructor
MyMatrix::MyMatrix(int rows, int cols, double initValues)
{
    initMatrix(rows, cols);
    for (int i = 0; i < this->rows; ++i) {
        for (int j = 0; j < this->cols; ++j) {
            this->mat[i][j] = initValues;
        }
    }
}
// multiply each element in matrix by value
MyMatrix& MyMatrix::operator*(double value) {
    for (int i = 0; i < this->rows; ++i) {
        for (int j = 0; j < this->cols; ++j) {
            this->mat[i][j] = this->mat[i][j] * value;
        }
    }
    return *this;
}
// initialise all matrix cells
void MyMatrix::initMatrix(int rows, int cols)
{
    this->rows = rows;                          // assign argument to member variable rows
    this->cols = cols;                          // assign argument to member variable cols

    this->mat = new double*[this->rows];        // initialise mat with list of doubles ptrs with length rows
    for (int i = 0; i < this->rows; ++i) {      // iterate over each row-element
        this->mat[i] = new double[this->cols];  // initialise each rows-element with list of doubles with length cols
    }
}

main.cpp

    int rows = 2;
    int cols = 3;
    MyMatrix mat1(rows, cols, 1.0);             // creates matrix with all elements 1.0

    mat1 = mat1 * 3.0;

Note I extracted only the relevant parts, the class has grown already, so I guess posting the all three files completely would be more confusing.

So far so good. The above seems to do what it should.

---

Now, I want to be able to directly access each element in the matrix. Similar to how one can access elements in a QVector, like so:

Read an element:

   double temp = mat1[2][2]               // read the element in row=2, column=2

Write to an element:

   double temp = 17;
   mat1[2][2] = temp              // set value of element in row=2, column=2 to given double temp (here 17).

But I do not know how to define this [][] operator. I tried the following definition analog to the multiplication with a double, and because I need to give the row and column. I thought I try:

MyMatrix.h

   MyMatrix& operator[int c][int r](double value);    // write
   MyMatrix& operator[int c][int r]();                // read

The implementation to overwrite/read the element in row r and column c which I have in mind should look like this:

MyMatrix.cpp

// write to element
MyMatrix& MyMatrix::operator[int r][int c](double value) {
    this->mat[r][c] = value;
    return *this;
}
// read to element
double& MyMatrix::operator[int r][int c]() {
    return this->mat[r][c];
}

---

But that does not do the Trick.

Btw: Even before compiling QtCreator says:

/path/MyMatrixClass/mymatrix.cpp:60: error: expected ']'
/path/MyMatrixClass/mymatrix.cpp:60: to match this '['
/path/MyMatrixClass/mymatrix.cpp:60: error: expected '(' for function-style cast or type construction
/path/MyMatrixClass/mymatrix.cpp:61: error: use of undeclared identifier 'r'
/path/MyMatrixClass/mymatrix.cpp:61: error: use of undeclared identifier 'c'

I tried already searching a for these errors, but so far I could not find anything giving me a clue to what I want to achieve.

So, perhaps someone can give me a link on where to look for an example or some advice on how I can achieve what I want.

---

PS: Later I also want to be able to extract a certain row, or certain column, but I guess (=hope) that should be straight forward once I know how to handle the [][] operator the right way.

This is the first time I am really defining my own operators for a class. And I think I got the general idea from the * operator. (I have also + and - operators already working). However, until now I used Qt mostly for GUI building, simple data handling with QVectors, plotting spectra and alike. So, I guess I am just missing some basic Qt/c++ syntax.

Answer 1

You can have the matrix use the operator() with as many parameters as you like. Squared brackets won't work.

double const& operator()(size_t rowIndex, size_t colIndex) const;
double& operator()(size_t rowIndex, size_t colIndex);

Then, you can use your matrix class like this

Matrix M(n, n);
for (size_t i = 0; i < n; ++i) {
    M(i, i) = 1.0;
}
return M;

Answer 2

There is no [][] operator. If you use the [] on two-diminsional array, you will get another pointer. Finally, you apply [] operator a second time on pointer returned from the first [] operator. Can use this little hack below. But this wont solve your problems on the long run:

#include <iostream>
#include <vector>
class Matrix
{
    int rows, cols;
    double**data;
public: 
    Matrix(int rows, int cols, double init)
        :rows(rows),cols(cols),data(new double*[rows])
    {
        for (int i = 0; i < this->rows; ++i) {
            data[i] = new double[cols];
            for (int j = 0; j < this->cols; ++j) {
                this->data[i][j] = init;
            }
        }
    }

    const double *operator[](int row)const
    {
        return data[row];
    }

    const double& operator[](const std::pair<int,int>& key)const
    {
        return data[key.first][key.second];
    }

    double& operator[](const std::pair<int, int>& key)
    {
        // validate the key
        return data[key.first][key.second];
    }

    double *operator[](int row)
    {
        return data[row];
    }
};

int main()
{
    Matrix m(3, 4, 0);

    m[2][1] = 3;

    std::cout << m[std::make_pair(2, 1)];
    // C++17 also allows:
    // std::cout << m[{2, 1}];
    std::cin.get();

}

Outputs: 3

I added a std::pair approach, m[{2, 1}] looks like syntax suggar. I cannot recommend the pointer solution. You dont have to reinvent the wheel neither. Take a look at newmath 11: http://www.robertnz.net/nm11.htm

Answer 3

So, since the QVector class is already quite powerful, and I assume it shall later more easy to deal with vector operations on my matrix class, I did now the following

My matrix class now the following content:

MyMatrix.h

Public:
    MyMatrix(int rows, int cols, double initValues=0.0);   // constructor 
    QVector<double> operator[](int idx);

Private:
    QVector<QVector<double>> *mat;

My implementation of the operator is then as follows:

MyMatrix.cpp

// constructor
MyMatrix::MyMatrix(int rows, int cols, double initValues)
{
    QVector<double> tmpRow(cols, initValues);
    this->mat = new QVector<QVector<double>>(rows, tmpRow);
}

// operator definition
QVector<double> MyMatrix::operator[](int idx) {
    QVector<double> temp = this->mat[0][idx];
    return temp;
}

I dont really understand though why the [0] is needed. Because mat is a QVector< QVector < double >>, so the first should give a QVector< double >, but for some reason it behaves not as I would expect, i.e. this->mat[idx] should return the QVector< double >.

Anyway, with the above I can now use it like this:

main.cpp

    qDebug() << mat1[0];           // prints the QVector in row=0    
    qDebug() << mat1[1];           // prints the QVector in row=1
    qDebug() << mat1[1][1];        // prints element in row=1 and column=1
    qDebug() << mat1[1][2];        // prints element in row=1 and column=2  

This then prints:

QVector(1, 1, 1)
QVector(1, 1, 1)
1
1

So that is not yet really finished, but I think I am now heading in the right direction.

Btw, @PaulMcKenzie shared a link saying that () is better than []. I implemented the operator for () and []. Both worked, just with the exception, that the syntax is with () slightly different; the usage is then:

main.cpp

    qDebug() << mat1(0);           // prints the QVector in row=0    
    qDebug() << mat1(1)[1];        // prints element in row=1 and column=1

Which looks odd. So I think in my case the [] looks better, and I can directly use the QVector as normal with the [].

I will look into this in more detail tomorrow to see if I can now achieve what I want. Either way, so far thank for all the input. Any comment is greatly appreciated.