Efficient coding with memory management - c++

Question

I've switched recently from matlab to c++ in order to run simulations faster, however it still runs slow. I'm pretty positive that there is much to improve in terms of memory usage.
Consider the following code, it shows an example of two array/vector declaration, that I use in a simulation.
One with known fixed length (array01) and another with unknown length (array02) that changes during the run.
The question here is what is the best/proper/efficient way of declaring variables ( for both array types) in terms of memory usage and performance.
# include <iostream>
# include <vector>
# include <ctime>
# include <algorithm>
using namespace std;
const int n = 1000;
const int m= 100000;
int main()
{
srand((unsigned)time(NULL));
vector <double> array02;
vector <vector<double>> Array01(n,m);
for (unsigned int i=0; i<n; i++)
{
for (unsigned int j=0; j<m;j++)
{
array02.clear();
rr = rand() % 10;
for (unsigned int l = 0 ; l<rr <l++)
{
array02.pushback(l);
}
// perform some calculation with array01 and array02
}
}
}

Answer 1

You should consider defining your own Matrix class with a void resize(unsigned width, unsigned height) member function, and a double get(unsigned i, unsigned j) inlined member function and/or a double& at(unsigned i, unsigned j) inlined member function (both giving Mi,j element). The matrix internal data could be a one-dimensional array or vector of doubles. Using a vector of vectors (all of the same size) is not the best (or fastest) way to represent a matrix.
class Matrix {
std::vector<double> data;
unsigned width, height;
public:
Matrix() : data(), width(0), height(0) {};
~Matrix() = default;
/// etc..., see rule of five
void resize(unsigned w, unsigned h) {
data.resize(w*h);
width = w; height = h;
}
double get(unsigned i, unsigned j) const {
assert(i<width && j<height);
return data[i*width+j];
}
double& at(unsigned i, unsigned j) {
assert(i<width && j<height);
return data[i*width+j];
}
}; // end class Matrix
Read also about the rule of five.
You could also try scilab (it is free software). It is similar to Matlab and might have different performances. Don't forget to use a recent version.
BTW, there are tons of existing C++ numerical libraries dealing with matrices. Consider using one of them. If performance is of paramount importance, don't forget to ask your compiler to optimize your code after you have debugged it.
Assuming you are on Linux (which I recommend for numerical computations; it is significant that most supercomputers run Linux), compile using g++ -std=c++11 -Wall -Wextra -g during the debugging phase, then use g++ -std=c++11 -Wall -Wextra -mtune=native -O3 during benchmarking. Don't forget to profile, and remember that premature optimization is evil (you first need to make your program correct).
You might even spend weeks, or months and perhaps many years, of work to use techniques like OpenMP, OpenCL, MPI, pthreads or std::thread for parallelization (which is a difficult subject you'll need years to master).
If your matrix is big, and/or have additional properties (is sparse, triangular, symmetric, etc...) there are many mathematical and computer science knowledge to master to improve the performance. You can make a PhD on that, and spend your entire life on the subject. So go to your University library to read some books on numerical analysis and linear algebra.
For random numbers C++11 gives you <random>; BTW use C++11 or C++14, not some earlier version of C++.
Read also http://floating-point-gui.de/ and a good book about C++ programming.
PS. I don't claim any particular expertise on numerical computation. I prefer much symbolic computation.

Answer 2

First of all don't try to reinvent the wheel :) Try to use some heavily optimized numerical library, for example
Intel MKL (Fastest and most used math library for Intel and compatible processors)
LAPACK++ (library for high performance linear algebra)
Boost (not only numerical, but solves almost any problem)
Second: If you need a matrix for a very simple program, use vector[i + width * j] notation. It's faster because you save an extra memory allocation.
Your example doesn't event compile. I tried to rewrite it a little:
#include <vector>
#include <ctime>
int main()
{
const int rowCount = 1000;
const int columnCount = 1000;
srand(time(nullptr));
// Declare matrix
std::vector<double> matrix;
// Preallocate elemts (faster insertion later)
matrix.reserve(rowCount * columnCount);
// Insert elements
for (size_t i = 0; i < rowCount * columnCount; ++i) {
matrix.push_back(rand() % 10);
}
// perform some calculation with matrix
// For example this is a matrix element at matrix[1, 3]:
double element_1_3 = matrix[3 + 1 * rowCount];
return EXIT_SUCCESS;
}
Now the speed depends on rand() (which is slow).

Answer 3

As people said:
Prefer a 1d array instead of 2d array for matrices.
Don't reinvent the wheel, use existing library: I think that Eigen library is the best suite for you, judging from your code. It also have very, very optimized code generated since it use C++ template static calculation when ever possible.