In order to understand the magclass format it is helpful to know the basic data structures in R:

A matrix is a 2D table (columns and rows) with values in it which all belong to the same variable type (e.g. all numeric or all characters). It can have dimnames giving each row and each column a name.

```
<- matrix(1:9, 3, 3, dimnames = list(c("AFR", "CPA", "EUR"),
a paste0("y", 2000:2002)))
a#> y2000 y2001 y2002
#> AFR 1 4 7
#> CPA 2 5 8
#> EUR 3 6 9
```

It is very handy for mathematical operations such as matrix multiplications and so on, but quite limited due to its restriction to 2 dimenions and only one allowed variable type for all entries.

An array is the extension of a matrix to more than two dimensions. A 2D array is identical to a matrix. As the matrix also the array is a very efficient structure for mathematical operations.

```
<- array(1:18, dim = c(3, 3, 2),
b dimnames = list(paste0("y", 2000:2002),
c("AFR", "CPA", "EUR"),
c("IndexA", "IndexB")))
b#> , , IndexA
#>
#> AFR CPA EUR
#> y2000 1 4 7
#> y2001 2 5 8
#> y2002 3 6 9
#>
#> , , IndexB
#>
#> AFR CPA EUR
#> y2000 10 13 16
#> y2001 11 14 17
#> y2002 12 15 18
```

A dataframe is similar in its structure to a matrix but has quite different advantages and disadvantages. As the matrix also the data frame is only two dimensional. The major difference between matrices and dataframes is that dataframes allow for different variable types per column. That means that one column can contain characters describing the data whereas another column can contain the values itself. Having this extension it is much easier to store higher dimensional data in it, as you can always use a structure in which each column except the last represent one dimension and the last dimension contains the data itself. The higher flexibility means that you can store the same data in very different ways, making it often hard to predict how the data frame will look like.

```
library(magclass)
as.data.frame(b)
#> AFR.IndexA CPA.IndexA EUR.IndexA AFR.IndexB CPA.IndexB EUR.IndexB
#> y2000 1 4 7 10 13 16
#> y2001 2 5 8 11 14 17
#> y2002 3 6 9 12 15 18
as.data.frame(as.magpie(b))
#> Cell Region Year Data1 Value
#> 1 NA AFR 2000 IndexA 1
#> 2 NA CPA 2000 IndexA 4
#> 3 NA EUR 2000 IndexA 7
#> 4 NA AFR 2001 IndexA 2
#> 5 NA CPA 2001 IndexA 5
#> 6 NA EUR 2001 IndexA 8
#> 7 NA AFR 2002 IndexA 3
#> 8 NA CPA 2002 IndexA 6
#> 9 NA EUR 2002 IndexA 9
#> 10 NA AFR 2000 IndexB 10
#> 11 NA CPA 2000 IndexB 13
#> 12 NA EUR 2000 IndexB 16
#> 13 NA AFR 2001 IndexB 11
#> 14 NA CPA 2001 IndexB 14
#> 15 NA EUR 2001 IndexB 17
#> 16 NA AFR 2002 IndexB 12
#> 17 NA CPA 2002 IndexB 15
#> 18 NA EUR 2002 IndexB 18
```

In the first example the array is directly transformed to a data frame whereas in the second example the matrix is transformed first to a magclass object and then to a data frame. Both data frames still contain the same data but in a different representation.

The main idea behind the magclass object was to have a data class for which it is always quite clear how the data is organized. Having this knowledge independent of the data itself allows to write more generic functions which can treat various kinds of data sets without knowing anything about it in advance.

The magclass data class is a child class of an array, meaning that it is based on most of its features. Contrary to an array the magpie object is always three dimensional, containing spatial information in the first dimension, temporal information in the second dimension and everything else in the third dimension.

```
as.magpie(b)
#> An object of class "magpie"
#> , , NA = IndexA
#>
#> NA
#> fake y2000 y2001 y2002
#> AFR 1 2 3
#> CPA 4 5 6
#> EUR 7 8 9
#>
#> , , NA = IndexB
#>
#> NA
#> fake y2000 y2001 y2002
#> AFR 10 11 12
#> CPA 13 14 15
#> EUR 16 17 18
```

However, that limitation to a 3D-structure does not mean that you are limited to data which only has 3 dimensions. Also data with more than one so-called “data dimension” (a dimension which is neither temporal nor spatial) can be handled:

```
<- array(1:6, c(3, 2), list(c("bla", "blub", "ble"),
ar c("up", "down")))
<- as.magpie(ar)
a head(a)
#> An object of class "magpie"
#> , , NA = bla.up
#>
#> NA
#> fake [,1]
#> GLO 1
#>
#> , , NA = blub.up
#>
#> NA
#> fake [,1]
#> GLO 2
getItems(a, dim = 3)
#> [1] "bla.up" "blub.up" "ble.up" "bla.down" "blub.down" "ble.down"
getItems(a[, , "up"], dim = 3)
#> [1] "bla.up" "blub.up" "ble.up"
getItems(a[, , "up", drop = TRUE], dim = 3)
#> [1] "bla" "blub" "ble"
getItems(a, dim = 3, split = TRUE)
#> $V1
#> [1] "bla" "blub" "ble"
#>
#> $V2
#> [1] "up" "down"
```

If an array has three dimensions and you take in one dimension exactly one element the array will be reduced to an 2D object, whereas the magclass object will always remain as 3D object. In addition to that a lot of checks will be executed when you do calculations with magclass objects that should prevent you from doing unwanted things such as accidentally sum up the wrong numbers if your objects are ordered differently:

```
<- as.magpie(b)
c # change order of spatial components
<- c[3:1, , ]
d
# correct summation based on dimension names:
+ d
c #> An object of class "magpie"
#> , , data = IndexA
#>
#> year
#> fake y2000 y2001 y2002
#> AFR 2 4 6
#> CPA 8 10 12
#> EUR 14 16 18
#>
#> , , data = IndexB
#>
#> year
#> fake y2000 y2001 y2002
#> AFR 20 22 24
#> CPA 26 28 30
#> EUR 32 34 36
# wrong summation (dimension names ignored):
as.array(c) + as.array(d)
#> , , NA = IndexA
#>
#> NA
#> fake y2000 y2001 y2002
#> AFR 8 10 12
#> CPA 8 10 12
#> EUR 8 10 12
#>
#> , , NA = IndexB
#>
#> NA
#> fake y2000 y2001 y2002
#> AFR 26 28 30
#> CPA 26 28 30
#> EUR 26 28 30
```

This additional comfort and safety is bought with performance meaning that if you are doing calculations which are very resource consuming you might want to convert your magclass object to an array, do your calculations (for which you then have to be very careful) and convert it back to a magclass object.

Magclass can be a good choice if you work with tempo-spatial data and want to establish a data standard for exchange between different R functions. If everybody is writing functions based on magclass objects all these functions will be directly compatible to each other. Having this compatibility your work will directly profit from the work of others, e.g. you are able to use plotting routines for your purposes even though they were developed for a completely different data source. Your code will be highly modular so that you can easily adapt it to modified requirements (e.g. exchanging a data read function by an API to a database). Having everybody working with the same functions can also lower the number of bugs in your code as each part of the code will be tested by several people and bugs will be found easier and fixed faster.

But why use magclass objects as this standard class for all functions and not something else as for instance data frames?

The main argument is that magclass objects are more standardized than the default data classes in R. It is always clear that the first dimension contains the spatial information, the second dimension contains temporal information and the third dimension contains the data. This makes it easier to develop generic plots because it is clear how the data has to be accessed.