如何使用在主 function (c++) 中创建的 object 定义 function？

Question

I'm trying to write a program that will give me the cross-validation bandwidth for a kernel estimator in c++ (there are around 20,000 data points so Matlab is way too slow). I'm doing this by using a secant algorithm on the derivative of the objective of the leave-one-out estimator. My problem is that this function takes as arguments the data, which is pulled in the main function from a csv file.

One of the arguments of the secant algorithm is a function that takes a double and returns a double, but the function I've written for the objective's derivative has to take a whole host of other crap that mathematically we'd consider parameters (things like the data, the choice of kernel function, etc.).

I need to be able to write a function that uses the function defining the objective, puts in the data that the main function pulls from the file, and takes as its only input a double variable. Is there a way of doing this?

double cvobjective(double data[], int n, double (*k)(double), double (*kd)(double), double h)
{
    double cvob = 0;
    double xi;
    double xj;
    for(int i = 0; i < n; ++i)
    {
        xi = data[i];
        double sumki = 0;
        double sumkdi = 0;
        for(int j = 0; j < n; ++j) //find sum of k((xj-xi)/h) and k'((xj-xi)/h)*(xj-xi)
        {
            xj = data[j];
            sumki = sumki + k((xj-xi)/h);
            sumkdi = sumkdi + kd((xj-xi)/h)*(xj-xi);
        }
        sumki = sumki-k(0);//gets rid of the terms where i=j
        sumkdi = sumkdi-kd(0);
        cvob = cvob - reciprocal(sumki)*(reciprocal(h)*sumki+reciprocal(pow(h,2))*sumkdi);
    }
    return cvob;
}

double secantmethod(double (*obj)(double), double init, double tolerance, int giveup)
{
    double x = init;
    double old = init+1;
    double newp;
    double fold = obj(old);
    double fnew;

    for(int i=0;i<giveup;++i)
    {
        fnew = obj(x);
        if(abs(fnew-fold)<tolerance)
        {
            cout << "Objective values get too close after " << i << " iterations." << endl;
            break;
        }
        newp = newp - (x-old)*reciprocal(fnew-fold)*fnew;
        old = x;
        x = newp;
        cout << "Estimate is currently: " << x << endl;
        fold = fnew;

        if(abs(fnew)<tolerance)
            break;
        if(i == giveup - 1)
            cout << "Secant algorithm did not converge." << endl;
    }
    return newp;
}

int main()
{
    const int N = 19107;
    double incomes[N];
    std::ifstream ifile("incomes.csv", std::ios::in);
    std::vector<double> scores;

    //check to see that the file was opened correctly:
    if (!ifile.is_open()) {
        std::cerr << "There was a problem opening the input file.\n";
        exit(1);//exit or do additional error checking
    }

    double num = 0.0;
    //keep storing values from the text file so long as data exists:
    while (ifile >> num) {
        scores.push_back(num);
    }

    //verify that the scores were stored correctly:
    for (int i = 0; i < scores.size(); ++i) {
        incomes[i]=scores[i];
    }

    double sv = silverman(incomes,N);
    double cvbandwidth = secantmethod(cvobj,sv,0.000001,100);
    cout << setprecision(10) << cvbandwidth << endl;
    return 0;
}

Obviously I've left out some of the code for the more peripheral functions that aren't important. I thought about if it would be possible to change the secantmethod algorithm so that it expected to take a function that had as its input all of the things that cvobjective has as inputs but it wasn't immediately clear to me how I'd do that.

Ideally I'd be able to create a function inside of main so that the incomes array was in the scope of that function, but either I don't understand lambdas properly or they aren't particularly suited to this purpose. Failing that, if there's a way for changing secantmethod in the way described above, that would also work.

EDIT: In the above cvobj isn't defined and currently serves as a placeholder. What I'd like it to be is something like

double cvobj(double h)
return cvobjective(incomes,N,normpdf,normpdfdiff,h);

but obviously when I try that, it complains that incomes and N aren't in the scope of the function.

Answer 1

So I think I found a workaround, which was to define the class

class kernelwdata
{
public:
    double observations[N];
    double cvobj(double h)
    {
        return cvobjective(observations,N,normpdf,normpdfdiff,h);
    }
};

and change secantmethod so that it takes kernelwdata as the input. Now the code shown before looks like

double cvobjective(double data[], int n, double (*k)(double), double (*kd)(double), double h)
{
    double cvob = 0;
    double xi;
    double xj;
    for(int i = 0; i < n; ++i)
    {
        xi = data[i];
        double sumki = 0;
        double sumkdi = 0;
        for(int j = 0; j < n; ++j) //find sum of k((xj-xi)/h) and k'((xj-xi)/h)*(xj-xi)
        {
            xj = data[j];
            if(j==i)
                xj=xi+1;
            sumki = sumki + k((xj-xi)/h);
            sumkdi = sumkdi + kd((xj-xi)/h)*(xj-xi);
        }
        sumki = sumki-k(1/h);//gets rid of the terms where i=j
        sumkdi = sumkdi-kd(1/h);
        cvob = cvob - reciprocal(sumki)*(reciprocal(h)*sumki+reciprocal(pow(h,2))*sumkdi);
    }
    return cvob;
}

class kernelwdata
{
public:
    double observations[N];
    double cvobj(double h)
    {
        return cvobjective(observations,N,normpdf,normpdfdiff,h);
    }
};

double secantmethod(kernelwdata obj, double init, double tolerance, int giveup)
{
    double x = init;
    double old = init+1;
    double newp;
    double fold = obj.cvobj(old);
    double fnew;

    for(int i=0;i<giveup;++i)
    {
        fnew = obj.cvobj(x);
        cout << "fold is " << fold << " and fnew is " << fnew << endl;
        if(abs(fnew-fold)<tolerance)
        {
            cout << "Objective values get too close after " << i << " iterations." << endl;
            break;
        }
        newp = newp - (x-old)*reciprocal(fnew-fold)*fnew;
        old = x;
        x = newp;
        cout << "Estimate is currently: " << x << endl;
        fold = fnew;

        if(abs(fnew)<tolerance)
            break;
        if(i == giveup - 1)
            cout << "Secant algorithm did not converge." << endl;
    }
    return newp;
}

double silverman(double data[], int n)
{
    double mean = 0;
    for(int counter = 0; counter < n; ++counter)
        mean = mean+data[counter]/n;
    double sigmahat = 0;
    for(int counter = 0; counter < n; ++counter)
    {
        sigmahat = sigmahat + pow(data[counter]-mean,2);
    }
    sigmahat = sigmahat/(n-1);
    sigmahat = sqrt(sigmahat);
    double m = (double) n;
    return sigmahat*pow(m,-0.2);
}

int main()
{
    kernelwdata incomes;
    std::ifstream ifile("incomestest.csv", std::ios::in);
    std::vector<double> scores;

    //check to see that the file was opened correctly:
    if (!ifile.is_open()) {
        std::cerr << "There was a problem opening the input file.\n";
        exit(1);//exit or do additional error checking
    }

    double num = 0.0;
    //keep storing values from the text file so long as data exists:
    while (ifile >> num) {
        scores.push_back(num);
    }

    //verify that the scores were stored correctly:
    for (int i = 0; i < scores.size(); ++i) {
        incomes.observations[i]=scores[i];
    }

    //double sv = silverman(incomes.observations,N);
    double cvbandwidth = secantmethod(incomes,10,0.000001,100);
    cout << "The cross-validation bandwidth is: " << setprecision(10) << cvbandwidth << endl;
    return 0;
}

and I'm now arguing with the output it's giving me (pretty sure a maths problem somewhere) rather than not being a thing I can compile yet.