CODEWITHSUNDEEP
c++
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Reputation: 121

How to write code to calculate partial derivative of several variable function in C++?

I already wrote the code to calculate the derivative of a single variable function at a point by making a class called "Der". In class Der, I defined two private variables double f and double df and a print() function to print the values of f and df. Inside the class, I overloaded the operators +, -, *, /, ^ to calculate the derivative of the sum, difference, multiplication etc of functions. I can't show the whole code because it's very long but I will show some snippets to give an idea.

class Der{
private:
    double f;  // function value at x
    double df; // derivative of function at x
public:
    Der();
    Der(double);
    Der operator+(Der); // f + g
    Der operator-(Der); // f - g
    Der operator*(Der); // f * g
    Der operator/(Der); // f / g
       
    friend Der operator+(double, Der); //c+f
    friend Der operator-(double, Der); //c-f
    friend Der operator*(double, Der); //c*f
    friend Der operator/(double, Der); //c/f
    Der operator^(double); // f^c,  Where c is constant
   
    friend Der sin(Der);
    friend Der cos(Der);
    friend Der tan(Der);
    friend Der log(Der);
    friend Der exp(Der);
    
    void print();
};

Der :: Der(){}

Der :: Der(double x){
    this->f = x;
    this->df = 1;
}

Der Der :: operator+(Der g){
    Der h;
    h.f = this->f + g.f;
    h.df = this->df + g.df;
    return h;
}

Der sin(Der g){
    Der h;
    h.f = sin(g.f);
    h.df = cos(g.f)*g.df;
    return h;
}
void Der :: print(){
    cout<<"Derivative of function at a point : "<<df<<endl;
}

int main()
    {
        Der x(10), f;
        f = x^2+x^3;
        f.print();
    }

Now I want to use this derivative calculator to calculate the partial derivative of a several variable function and ultimately to calculate the gradient of that function. I have some vague ideas but I am not able to implement it in code. I am a beginner in C++ programming, so it would be helpful if you don't use too many advanced concepts.

I have added how Der is used. The program should take inputs of independent variables like x(2), y(4), z(5) and function like f(x,y,z)=x^2*y*z+log(x*y*z). Then, it will give the partial derivative of f w.r.t x, y, z at point (2, 4, 5) in the form of an array. But, I just need some idea on how to code the partial derivative calculator.

Upvotes: 0

Views: 1808

Answers (1)

Beta
Beta

Reputation: 99094

You seem to be very close to the solution, but struggling with the step to functions defined over multiple dimensions.

Instead of having one member variable df, you need several of them, one for each partial derivative. You could hard-code them:

double dfx, dfy, dfz;

or use a container:

double df[3];

I'll use hard-coding for now. (Containers are a vitally important topic, and a std::vector is better than an array in almost all respects, but one thing at a time.)

It would also be wise to rename the other variable from x to v, since it represents the value of the function at the point of interest, not the location of the point. (This is worth thinking about.)

The old constructor took one value and one derivative:

Der :: Der(double x){
    this->f = x;
    this->df = 1;
}

This can be better written using initializers:

Der :: Der(double nx): x(nx), df(1)
{}

which makes it easy to rewrite the constructor to take three partial derivatives:

Der :: Der(double nv, double dx, double dy, double dz): v(nv), dfx(dx), dfy(dy), dfz(dz)
{}

Now we can declare functions:

Der x(2, 1, 0, 0), y(4, 0, 1, 0), z(5, 0, 0, 1);

And the logic of the arithmetical operations is straightforward. For instance, the first partial of the product of two functions:

dfx = A.v * B.dfx + A.dfx * B.v;

(In fact, you could abstract the arithmetic out of your current class and use it for both old and new classes, but one thing at a time.)

Upvotes: 3

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