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internals.rst

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ReverseDiffSource internals

All the core of the functions in the package ( differentiation, removal of neutral statements, factorization of identical calls) rely on 2 structures:

  1. The ExNode composite type that represents either:
    • a single operation (a function call)
    • an external reference (a variable that can be a parameter for derivation or a reference to a variable outside the scope of the expression)
    • a constant
ExNodes have parents which are typically the arguments of the function. Collectively they make a DAG but with several additions :
  • the order of arguments (parent nodes) is significant ( a ^ b is not the same as b ^ a)
  • there needs to be additionnal ordering information as statements not related sometimes need to execute in a specific order, this information is in the precedence field.
2. The ExGraph composite type that stores
  • ExNodes in a vector (in the order of execution),
  • information on how to map ExNodes to variable names (used and set),
  • and optionnaly information on how to map nodes to 'outer' nodes. This last mapping is necessary when the ExGraph is embedded in another parent graph ( for example the inner scope of for loops is represented as a subgraph).

Showing the code graph

Starting from an expression, it is possible to have a dump of the nodes composing its equivalent graph with the (unexported) tograph() call:

ex = quote
    a = 1 + x
    2 * exp(-a)
end


g = ReverseDiffSource.tograph(ex)

node | symbol     | ext ? | type       | parents  | precedence | main  | value         | 
---- | ---------- | ----- | ---------- | -------- | ---------- | ----- | ------------- | 
1    |            |       | [constant] |          |            | 1     | (Float64) NaN | 
2    | x >>       |       | [external] |          |            | :x    | (Float64) NaN | 
3    | a <<       |       | [call]     | 11, 1, 2 |            | :call | (Float64) NaN | 
4    |            |       | [constant] |          |            | 2     | (Float64) NaN | 
5    |            |       | [call]     | 8, 3     |            | :call | (Float64) NaN | 
6    |            |       | [call]     | 10, 5    |            | :call | (Float64) NaN | 
7    | nothing << |       | [call]     | 9, 4, 6  |            | :call | (Float64) NaN | 
8    |            |       | [constant] |          |            | -     | (Float64) NaN | 
9    |            |       | [constant] |          |            | *     | (Float64) NaN | 
10   |            |       | [constant] |          |            | exp   | (Float64) NaN | 
11   |            |       | [constant] |          |            | +     | (Float64) NaN |

Additionnaly, the plot() function (also unexported) will generate a GrapViz compatible graph description :

using GraphViz

Graph( ReverseDiffSource.plot( g ))

Should produce :

image