implementation of multi-dimensional array with an array or vector

问题

I want to implement multi-dimensional array using single array or vector, which can be accessed like usual multi-dimensional array(ex: a[1][2][3]). Where I am stuck at is how to implement [ ] operator. If the dimension of an array is 1, then a[1] should return the element which is located at index 1. But what if the dimension is more than one? In case of nested vector,say 3-dimensinal vector, vec[1] will return vector<vector<some type> >.

The reason why I am trying to implement my own multi-dimensional array is that I don't know the dimension of an array at compile time. The dimension really depends on some conditions. Actually maximum dimension of an array is 3, so I can define three different vectors, but I personally don't think this is the right choice.

回答1:

operator[] can only take a single argument.

The best solution is to use operator() instead.

If you absolutely want to use operator[] then you can let it return a proxy object, of a type specific to the dimension, on which operator[] can be applied again, and so on.

This is a Frequently Asked Question, and is answered in the C++ FAQ’s “How do I create a subscript operator for a Matrix class?” (the link is to main English version of the FAQ).

It's often a good idea to consult the FAQ before asking.

回答2:

You can make an array of vectors

#include<string>
#include<vetor>
using namespace std;
int main()
{
  vector<int> a;
  vector<vector<int> >b; // must have space > >
  vector< vector < vector<int> > > c;
  a.push_back(20);
  a.push_back(10);
  b.push_back(a);
  c.push_back(b);

  int x = c[0][0][0];
  int y = c[0][0][1];
  cout<< y << "  "<< x <<endl;
  return 0;
}

回答3:

The type of any expression must be known at compile-time. a[1][2][3] must have a particular type. It's not possible for the type to vary between int and vector<int> depending on a run-time input.

It is certainly posssible to have a[1][2][3] do something , but this will have to return an object of a given type whose properties you query at runtime to see what happened. (For example, an array with runtime dimension of 1; or throw an exception if too many dimensions are requested).

As others have noted, experience shows that it's less coding and also more effective at runtime to take all dimensions in a single call a(1, 2, 3). If you use operator[] then remembering that operators are function calls, what's going on is a.operator[](1).operator[](2).operator[](3), the extra function calls may make it harder for your compiler to optimize.

Another option is to have the parameters be passed in a container such as a vector, i.e. the user would call a( vec ); where vec is a vector containing the coordinates.

回答4:

Hi I wrote this multidimensional matrix library (its not full fledged) it supports basic operations like dotproduct and pointwise elements.

https://github.com/josephjaspers/BlackCat_Tensors

Tensor<float> tensor3 = {3, 4, 5};   -- generates a 3 dimensional tensor
tensor3[1] = 3;                      -- returns the second matrix and sets all the values to 3. 
tensor3[1][2];                       -- returns the second matrx and then then 3rd column of that matrix
tensor3({1,2,3},{2,2});              -- at index 1,2,3, returns a sub-matrix of dimensions 2x2

All of the accessor operators [] (int index) and ({initializer_list<int> index},{initializer_list<int> shape}) return seperate tensors but they all refer to the same internal array. Therefor you can modify the original tensor from these sub_tensors.

All the data is allocated on a single array. If you want to use dotproduct you need to link it to BLAS. Here's the header file, it details most of the methods. https://github.com/josephjaspers/BlackCat_Tensors/blob/master/BC_Headers/Tensor.h

In the comments you wanted to elaborate upon accessing using proxy objects

Matrix/Vector

template<typename T>
struct Vector {
 T* data; int sz; 

 Vector<T>(T* data, int size){ 
        this->data = data; 
        this->sz = size; 
 } 
 T& operator[] (int index) { return data[i]; }
}

template<typename T>
struct Matrix {
int row; int col;

 //insert constructor here

 Vector<T> operator[] (int index) {
     return Vector<T>(data[index * row], row); //use col for col-major
 }

}

//Recursive method

template class T
class Tensor {
int* shape;
T* data;

    Tensor<T>(int*shape, int order, T* data){
       this->shape = shape;
       this->order = order;
       this->data  = data; 
    }

    Tensor<T> operator [] (int index) {
      return Tensor(shape, order -1, &data[index * shape[order - 2]); // if the order = 2(tensor is a matrix) multiply the `data` index by given param * the number of rows --> ergo returns a column vector)
    }
}

来源：https://stackoverflow.com/questions/27456458/implementation-of-multi-dimensional-array-with-an-array-or-vector

标签

c++

arrays

vector

multidimensional-array