# Bimap

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##### Bimap objects and the Bimap interface

What we usually call "annotation maps" are in fact Bimap objects. In the following sections we present the bimap concept and the Bimap interface as it is defined in AnnotationDbi.

Keywords
classes, interface
##### Display methods

In the code snippets below, x is a Bimap object.

show(x): Display minimal information about Bimap object x.
summary(x): Display a little bit more information about Bimap object x.

##### The bimap concept

  - 2 sets of objects: the left objects and the right objects.
All the objects have a name and this name is unique in
each set (i.e. in the left set and in the right set).
The names of the left (resp. right) objects are called the
left (resp. right) keys or the Lkeys (resp. the Rkeys).


- Any number of links (edges) between the left and right
objects. Note that the links can be tagged. In our model,
for a given bimap, either none or all the links are tagged.

In other words, a bimap is a bipartite graph. Here are some examples:
  1. bimap B1: 4 left objects (Lkeys): "a", "b", "c", "d"
3 objects on the right (Rkeys): "A", "B", "C" Links (edges):
"a" <--> "A"
"a" <--> "B"
"b" <--> "A"
"d" <--> "C" Note that:
- There can be any number of links starting from or ending
at a given object.
- The links in this example are untagged.

  2. bimap B2: 4 left objects (Lkeys): "a", "b", "c", "d"
3 objects on the right (Rkeys): "A", "B", "C" Tagged links (edges):
"a" <-"x"-> "A"
"a" <-"y"-> "B"
"b" <-"x"-> "A"
"d" <-"x"-> "C"
"d" <-"y"-> "C" Note that there are 2 links between objects "d" and "C":
1 with tag "x" and 1 with tag "y".


##### Flat representation of a bimap

The flat representation of a bimap is a data frame. For example, for B1, it is:

    left  right
a      A
a      B
b      A
d      C

If in addition the right objects have 1 multivalued attribute, for example, a numeric vector:
    A <-- c(1.2, 0.9)
B <-- character(0)
C <-- -1:1

then the flat representation of B1 becomes:
    left  right  Rattrib1
a      A       1.2
a      A       0.9
a      B        NA
b      A       1.2
b      A       0.9
d      C        -1
d      C         0
d      C         1

Note that now the number of rows is greater than the number of links!

##### AnnDbBimap and FlatBimap objects

An AnnDbBimap object is a bimap whose data are stored in a data base. A FlatBimap object is a bimap whose data (left keys, right keys and links) are stored in memory (in a data frame for the links). Conceptually, AnnDbBimap and FlatBimap objects are the same (only their internal representation differ) so it's natural to try to define a set of methods that make sense for both (so they can be manipulated in a similar way). This common interface is the Bimap interface. Note that both AnnDbBimap and FlatBimap objects have a read-only semantic: the user can subset them but cannot change their data.

##### The "flatten" generic

    flatten(x) converts AnnDbBimap object x into FlatBimap
object y with no loss of information

Note that a FlatBimap object can't be converted into an AnnDbBimap object (well, in theory maybe it could be, but for now the data bases we use to store the data of the AnnDbBimap objects are treated as read-only). This conversion from AnnDbBimap to FlatBimap is performed by the "flatten" generic function (with methods for AnnDbBimap objects only).

##### Property0

The "flatten" generic plays a very useful role when we need to understand or explain exactly what a given Bimap method f will do when applied to an AnnDbBimap object. It's generally easier to explain what it does on a FlatBimap object and then to just say "and it does the same thing on an AnnDbBimap object". This is exactly what Property0 says:

    for any AnnDbBimap object x, f(x) is expected to be
indentical to f(flatten(x))

Of course, this implies that the f method for AnnDbBimap objects return the same type of object than the f method for FlatBimap objects. In this sense, the "revmap" and "subset" Bimap methods are particular because they are expected to return an object of the same class as their argument x, so f(x) can't be identical to f(flatten(x)). For these methods, Property0 says:
    for any AnnDbBimap object x, flatten(f(x)) is expected to
be identical to f(flatten(x))

Note to the AnnotationDbi maintainers/developpers: the checkProperty0 function (AnnDbPkg-checker.R file) checks that Property0 is satisfied on all the AnnDbBimap objects defined in a given package (FIXME: checkProperty0 is currently broken).

##### The Bimap interface in AnnotationDbi

The full documentation for the methods of the Bimap interface is splitted into 4 man pages: Bimap-direction, Bimap-keys and Bimap-toTable.

##### Aliases
• Bimap
• Bimap
• class:Bimap
• Bimap-class
• AnnDbBimap
• class:AnnDbBimap
• AnnDbBimap-class
• GoAnnDbBimap
• class:GoAnnDbBimap
• GoAnnDbBimap-class
• Go3AnnDbBimap
• class:Go3AnnDbBimap
• Go3AnnDbBimap-class
• GOTermsAnnDbBimap
• class:GOTermsAnnDbBimap
• GOTermsAnnDbBimap-class
• AnnDbMap
• class:AnnDbMap
• AnnDbMap-class
• IpiAnnDbMap
• class:IpiAnnDbMap
• IpiAnnDbMap-class
• AgiAnnDbMap
• class:AgiAnnDbMap
• AgiAnnDbMap-class
• ProbeAnnDbBimap
• class:ProbeAnnDbBimap
• ProbeAnnDbBimap-class
• ProbeGo3AnnDbBimap
• class:ProbeGo3AnnDbBimap
• ProbeGo3AnnDbBimap-class
• ProbeAnnDbMap
• class:ProbeAnnDbMap
• ProbeAnnDbMap-class
• ProbeIpiAnnDbMap
• class:ProbeIpiAnnDbMap
• ProbeIpiAnnDbMap-class
• show,FlatBimap-method
• show,AnnDbBimap-method
• summary,Bimap-method
• summary,AnnDbBimap-method
##### Examples
  library(hgu95av2.db)
ls(2)
hgu95av2GO # calls the "show" method
summary(hgu95av2GO)
hgu95av2GO2PROBE # calls the "show" method
summary(hgu95av2GO2PROBE)

Documentation reproduced from package AnnotationDbi, version 1.34.4, License: Artistic-2.0

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