Template-Based Helper Classes: An application to Multidimensional Arrays

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Introduction

Multidimensional arrays provide a simple reshaping matrix structures. It could be created and initialized as a vector, and read as 3D matrix. However, subscripting is not that easy. Subscripting operators should reduce dimension of entire multi-array. The problem becomes harder when adding region-of-interest scripting facility. Region-of-interest scripting facility allows selecting separate rows, columns, and plates in different orders. More complexities may be added to support reference indexing. A typical solution is helper classes. Boost library has implemented a helper class to multi_array for reference indexing and named as multi_array_ref. Matrix Template Library (MTL) provided helper classes to the matrix. Two helper classes were developed to emulate row set and column set. Communication between helper classes is made via copy constructors. More helper classes are needed for every new structure. This yields to more tightly coupled classes as many programmers tend to use friend classes.

Problem Statement and Basic Idea

We need more encapsulation of helper classes with original interfacing class. This could be accomplished by adding more template arguments. Classes with different template arguments lead to separate classes. However, it makes the whole class more cohesive and prevent user from using helper classes in a wrong way. In my master thesis I needed a flexible multidimensional array with the following specs.

1. array-like subscripting operators[].
2. matlab-like region of interests subscripting facility.
3. reference-like array to allow editing a set of selected entries.

1. Array-like subscripting operators[]

This piece of code declaresa a new initialized 3D multi-dimensional array.

tensor<double, 3, 1, false> itns3(dblbegin
5, 7, 3, 1, 2,
4, 7, 2, 1, 2,
1, 8, 9, 3, 6, 
1, 3, 5, 7, 8,

1, 7, 3, 8, 2,
1, 7, 3, 8, 2,
1, 7, 3, 8, 2,
1, 7, 3, 8, 2,

5, 7, 3, 1, 2,
4, 7, 2, 1, 2,
1, 8, 9, 3, 6,
1, 3, 5, 7, 8
clend, sizebegin 3, 4, 5 clend);

Where dblbegin, sizebegin, and clend are defined as follows:

#define dblbegin clbegin(double)
#define sizebegin clbegin(_sizetype)
#define clend )

and clbegin macro is defined as:

#define clbegin(T) (commalist<T>(),

Actually cl-prefix stands for comma-list. commalist<T> template class was developed to allow comma-concatenation. I guess comma-concatenation is simpler on gnu-C++.

Now the container itns3 has three dimensions [3, 4, 5] which is 3-plates, 4-rows each, and 5-cols for each row. Now consider using subscripting operator getting first plate, how many dimensions shall this array hold? Yup, tensor with two dims. That is why the subscripting is defined as follows:

tensor<T, N-1, D, true> operator[](const _sizetype& i);
const tensor<T, N-1, D, false> operator[](const _sizetype& i) const;

Other implemetations for multi-arrays makes use of helper classes named subset, rows, cols, rowset, colset, ...


Now moving to second facility;

2. Matlab-like region-of-interests subscripting facility

Region of interest (roi) lets you to select first and third rows for all columns. Consider the following:

tensor<double, 2> itns2(dblbegin 
5, 7, 3, 1, 2,
4, 7, 2, 1, 2,
1, 8, 9, 3, 6,
1, 3, 5, 7, 8
clend, sizebegin 4, 5 clend);

Now consider selecting all rows and cols numbered [0, 4, 2, 3]

itns2[all][select(0, 4, 2, 3, -1)]=3.0;

where select, and all are defined as follows:

#define all ixrange()
#define select rangelist<_indextype>

and ixrange() is defined as follows:

typedef range<_indextype> ixrange;

This means subscripting operator should return tensor and not tensor as discussed earlier.

This means that we need a new helper class presenting the new dimension we iterate on. In simple words, we first select two rows, and the new subscripting shall select three cols. That is why we need the D template parameter! And roi-subscripting operator should be declared as follows:

const tensor<T, N, D+1, false> operator[](const tensor<_indextype, 1> idx) const;
tensor<T, N, D+1, true> operator[](const tensor<_indextype, 1> idx);

Other implemetations make use of friend helper classes, and usually named as rowset and colset.

Lets move to next requirement:

3. Reference-like array to allow editing a set of selected entries

Reference containers capture addresses of selected entries and allow you to modify them. This was usually implemented with helper classes named reference_container, array<smart_ptr<T> >, or ref_array.
A tensor has one of two states if const subscripting operators should return a copy of entries, if not, a reference to entries should be returned. One more boolean template argument is added describing the entire tensor as a reference or not.

Class and Operator Headers

Consider the following class header:

// tensor<typename, # dims, dim to iterate on, being ref or not>

template<class T, _sizetype N=1, _sizetype D=1, _booltype REF=false>
class tensor : public io

const tensor<T, N-1, 1, false> operator[](const _sizetype& i) const

and this returns a lowerdimensioned referenced tensor:

tensor<T, N-1, 1, true> operator[](const _sizetype& i)

Now consider the region-of-interest subscripting operator. It should return a matrix of chosen rows, and next subscripting operator should iterate on the next dimension.

const tensor<T, N, D+1> operator[](const tensor<_indextype, 1> idx) const 

and this is a referenced copy too.

tensor<T, N, D+1, true> operator[](const tensor<_indextype, 1> idx) 

Thank You

Thanks a lot for your time. I just want to clarify that this is a testing version; I hope you enjoy this.