cell

cell, a FORTRAN90 code which defines a cell array, a generalization of an array which can compactly store and retrieve vector or matrix data of varying size, such as the rows of a triangular matrix.

In MATLAB, a cell array is a structure which generalizes a matrix. It can be thought of as an object A, whose entries can be indexed by expressions such as A(I,J). In a matrix, each entry is a numeric scalar object. In a cell array, each entry A(I,J) is simply an object of unspecified type, dimension, and range.

In the simplified version of a cell array presented here, the cell array is a vector (one index) or matrix (two indices), each of whose entries is, in turn, a vector or a matrix of standard numeric type. We still allow the individual entries to have differing ranges. Thus, a lower triangular matrix can be thought of as a cell array A that stores the rows. Row 3 of the triangular matrix can be thought of as the third entry in A. To retrieve a particular number in row 3, we have to determine where the row is stored, and then where the desired item is stored in the row.

The vectors or matrices which are the entries of a particular cell array will all share a common numeric type, which we will designate as

• C4, 4 byte + 4 byte complex;
• C8, 8 byte + 8 byte double precision complex;
• I4, 4 byte integer;
• R4, 4 byte real;
• R8, 8 byte double precision real;

We use a simple code to describe the numeric type, indexing scheme, and entry type of a cell array. For example, an "R8CVM" would be a cell array of numeric type double precision real (R8), which is a single indexed vector (V) whose entries are matrices (M).

To see how cell arrays can be useful, we will concentrate on the idea of efficient storage. Thus, suppose we simply want to store rows 0 through 5 of Pascal's triangle. Since these quantities are integers, we could use numeric type I4. Since we want to refer to items by row, we only need a single index to access entries. Each entry is a row. This means the code for the cell array would be I4CVV.

We could think of this cell array as having the following structure:

```        A = { { 1 },
{ 1, 1 },
{ 1, 2, 1 },
{ 1, 3, 3, 1 },
{ 1, 4, 6, 4, 1 },
{ 1, 5, 10, 10, 5, 1 } }
```
We can imagine that the cell array A is simply a vector of length 6, and that the A(3), for example, is the vector {1,2,1}. On the other hand, in this case it is very tempting to also consider the array notation A(3,2), which now must be carefully interpreted, since the 3 is a cell array index (3rd row) which is easy to know is only allowed to extend from 1 to 6, while the 2 is a row index (item 2 of the current row) whose validity is hard to know unless we know the legal extent of that row.

Especially when we contemplate more complicated structures, it might be better to replace the notation A(3,2) by A(3)(2), meaning third entry of A, second item in that entry. In this way, we can immediately understand that B(3,2)(4) means that B is a matrix of entries, each of which is a vector, while C(3)(2,4) means C is a vector whose entries are matrices.

To create a cell array, the user must provide information about the dimension (1 for "V" and 2 for "M") of the cell array, and the range of each entry (length of V entries or rows*columns for M entries). This is used to determine the total size needed for the cell array, and the offsets needed to quickly access individual items in the entries.

Cell arrays of type **CVV are most commonly useful, given how often triangular arrays and matrices occur, as well as lists, each of whose entries is in turn a list of varying length.

Cell arrays of types I4CVV and R8CVV are implemented in this code.

Languages:

cell is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

INDEX, a FORTRAN90 code which converts a multidimensional vector index to a one-dimensional vector index; it can handle zero and one based indexing schemes, as well as column major and row major conventions.

SUBPAK, a FORTRAN90 code which contains many utility routines;

VEC_IO, a FORTRAN90 code which reads and writes vectors of fixed size, to and from a disk file, in any order;

Source Code:

Last revised on 06 June 2020.