C++ Advice on manipulating output Matrix data - c++

Question

I have the following code.
Essentially it is creating N random normal variables, and running through an equation M times for a simulation.
The output should be an NxM matrix of data, however the only way I could do the calculation has the output as MxN. ie each M run should be a column, not a row.
I have attempted in vain to follow some of the other suggestions that have been posted on previous similar topics.
Code:
#include <iostream>
#include <time.h>
#include <random>
int main()
{
double T = 1; // End time period for simulation
int N = 4; // Number of time steps
int M = 2; // Number of simulations
double x0 = 1.00; // Starting x value
double mu = 0.00; // mu(x,t) value
double sig = 1.00; // sigma(x,t) value
double dt = T/N;
double sqrt_dt = sqrt(dt);
double** SDE_X = new double*[M]; // SDE Matrix setup
// Random Number generation setup
double RAND_N;
srand ((unsigned int) time(NULL)); // Generator loop reset
std::default_random_engine generator (rand());
std::normal_distribution<double> distribution (0.0,1.0); // Mean = 0.0, Variance = 1.0 ie Normal
for (int i = 0; i < M; i++)
{
SDE_X[i] = new double[N];
for (int j=0; j < N; j++)
{
RAND_N = distribution(generator);
SDE_X[i][0] = x0;
SDE_X[i][j+1] = SDE_X[i][j] + mu * dt + sig * RAND_N * sqrt_dt; // The SDE we wish to plot the path for
std::cout << SDE_X[i][j] << " ";
}
std::cout << std::endl;
}
std::cout << std::endl;
std::cout << " The simulation is complete!!" << std::endl;
std::cout << std::endl;
system("pause");
return 0;
}

Answer 1

Well why can't you just create the transpose of your SDE_X matrix then? Isn't that what you want to get?

Answer 2

Keep in mind, that presentation has nothing to do with implementation. Whether to access columns or rows is your decision. So you want an implementation of it transposed. Then quick and dirty create your matrix first, and then create your number series. Change i and j, and N and M.
I said quick and dirty, because the program at all is bad:
why don't you just keep it simple and use a better data structure for your matrix? If you know the size: compile-time array or dynamic vectors at runtime? Maybe there are some nicer implementation for 2d array.
There is a bug I think: you create N doubles and access index 0 to N inclusive.
In every iteration you set index 0 to x0 what is also needless.
I would change your code a bit make more clear:
create your matrix at first
initialize the first value of the matrix
provide an algorithm function calculating a target cell taking the matrix and the parameters.
Go through each cell and invoke your function for that cell

Answer 3

Thank you all for your input. I was able to implement my code and have it displayed as needed.
I added a second for loop to rearrange the matrix rows and columns.
Please feel free to let me know if you think there is anyway I can improve it.
#include <iostream>
#include <time.h>
#include <random>
#include <vector>
int main()
{
double T = 1; // End time period for simulation
int N = 3; // Number of time steps
int M = 2; // Number of simulations
int X = 100; // Max number of matrix columns
int Y = 100; // Max number of matrix rows
double x0 = 1.00; // Starting x value
double mu = 0.00; // mu(x,t) value
double sig = 1.00; // sigma(x,t) value
double dt = T/N;
double sqrt_dt = sqrt(dt);
std::vector<std::vector<double>> SDE_X((M*N), std::vector<double>((M*N))); // SDE Matrix setup
// Random Number generation setup
double RAND_N;
srand ((unsigned int) time(NULL)); // Generator loop reset
std::default_random_engine generator (rand());
std::normal_distribution<double> distribution (0.0,1.0); // Mean = 0.0, Variance = 1.0 ie Normal
for (int i = 0; i <= M; i++)
{
SDE_X[i][0] = x0;
for (int j=0; j <= N; j++)
{
RAND_N = distribution(generator);
SDE_X[i][j+1] = SDE_X[i][j] + mu * dt + sig * RAND_N * sqrt_dt; // The SDE we wish to plot the path for
}
}
for (int j = 0; j <= N; j++)
{
for (int i = 0; i <=M; i++)
{
std::cout << SDE_X[i][j] << ", ";
}
std::cout << std::endl;
}
std::cout << std::endl;
std::cout << " The simulation is complete!!" << std::endl;
std::cout << std::endl;
system("pause");
return 0;
}