How to store a parametric matrix like a function in C++

Question

I have a matrix M, whose each element is dependent on a single variable t in a different quadratic form without the constant.

Just for example,

M[1,1] = 2t^2 + 4t
M[3,2] = t^2 - 5t
M[2,4] = -t^2 + 5t

The matrix is acquired after a series of calculation and each element, or say, the coefficients before t^2 and t, are figured out through a combination of a bunch of other functions.

I was wondering how I can store the matrix like a function M(t) so each time I can call the function to generate a matrix with different t.

Thanks!

UPDATE: The purpose is to get the smallest eigenvalue of the matrix given different t, so I was thinking I could generate a matrix each time and feed it to a eigenvalue solver to get the smallest eigenvalue for each t.

Write a function `double M(double t, int row, int col)`. Do *not* try to use square brackets to access the elements. — n. m. could be an AI, May 03 '16 at 13:53
@n.m. Could you be more specific? You mean I return an array of array via this function? — James LT, May 03 '16 at 13:56
Do you need to generate the matrix and store it, or can it be implied by the functions? — molbdnilo, May 03 '16 at 13:59
I believe the OP wants to return a matrix, something like Matrix m = parametricMatrix.createMatrix(5.345); IMHO, the parametric matrix and the explicit one should be model by two different objects (but it is difficult to judged without more context) — Alessandro Teruzzi, May 03 '16 at 13:59
No, you don't return or have any arrays. You return an individual matrix cell. — n. m. could be an AI, May 03 '16 at 14:11
No wait, I think I misunderstood the question. Please ignore my above comments. — n. m. could be an AI, May 03 '16 at 14:12
Voted to close as unclear (I can think of solutions for at least three different interpretations of this question). — Cheers and hth. - Alf, May 03 '16 at 14:14
"The matrix is acquired after a series of calculation and each element is figured out through a combination of a bunch of other functions" Do you mean that each element is a quadratic function of one variable and its coefficients are calculated by some process? — n. m. could be an AI, May 03 '16 at 14:15
You can write a function which stores the coefficients of the polys in two Matrix and calculates the returnig Matrix as: M(i,j) = t * (a(i,j) + t * b(i,j)) — Bob__, May 03 '16 at 14:16
It is unclear what you are asking, but maybe expression templates are what you are after https://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Expression-template — StoryTeller - Unslander Monica, May 03 '16 at 14:18
@n.m. Yes, the coefficients are calculated by other complex processes. — James LT, May 03 '16 at 15:45
@Bob__ That's a good idea, actually. Btw, do you mean t^2 before a? — James LT, May 03 '16 at 15:46
@James No, I mean t*(b + t * a) instead of a * t^2 + b * t. It's Horner's method (rule) to calculate polynomials. — Bob__, May 03 '16 at 15:54

score 1 · Answer 1 · answered May 03 '16 at 14:10

From my limited understanding, what you are after is a function at specific point, for this, I would use a std::function<double(double)> (i.e. function that takes one double and returns a double (the result.) I guess that's what you are after? And each location of the matrix can be initialized with a lambda - e.g

// Assume my dumb matrix is a 2d vector
vector<vector<function<double(double)>>> matrix;

matrix[1][1] = [](double t) { return /* formula for: 2t^2 + 4t */ ; }

etc.

score 0 · Answer 2 · answered May 03 '16 at 13:52

0

you should create a class name Matrix and this class has a constructor which has only one parameter t.

answered May 03 '16 at 13:52

0xFFFFFFFF

852
5
9

score 0 · Answer 3 · answered May 03 '16 at 14:05

// quadratic polynomial
class QuadPoly {
public:
    QuadPoly(double _c2, double _c1, double _c0) : c2(_c2), c1(_c1), c0(_c0) {}
    // ... other constructors, assignment
    double operator()(double t) const {return (c2*t+c1)*t+c0;}
    // ... maybe operator+ operator-, if necessary
private:
    double c0, c1, c2;
};

// numerical Matrix
template<class T> class Matrix {
public:
    // ... constructors, destructor, assignment
    const T& operator()(int row, int col) const;
    T& operator()(int row, int col);
    // ... anything else
    friend class QuadPolyMatrix;
private:
    int nRows, nCols;
    int nVals; // nRows*nCols
    double* pVals; // or maybe double**
};

// matrix of quadratic polynomials
class QuadPolyMatrix : public Matrix<QuadPoly> {
public:
    Matrix<double> operator() (double t) const;
};

score 0 · Answer 4 · answered May 03 '16 at 14:11

1. Functions hardcoded

If you really need a matrix object, you can make a class with t in constructor and function, which returns values.

class CMatrix {
public:
    CMatrix( double t_ ) : t( t_ ) {}

    double GetElement( int row, int col ) const {
        if( row == 3 && col == 2 ) {
            return t * t - t * 5;
        } else if( ) ...
    }

private:
    double t;
};

After that you can construct CMatrix mat( t );

And then get elements by mat.GetElement( 3, 2 );.

2. More versatile variant.

Make typedef of functions (they all have the same signature double f( double t )) and an array of pointers to functions. Then, you can make a SetFunction method, which sets a function in a given coordinate and GetElement calls function in given coordinate with parameter, which is stored in the field (like prev. example). But in this case you must set all needed functions before calling.

How to store a parametric matrix like a function in C++

4 Answers4