systems 0.0.1

# Systems

`systems` is a set of tools for describing, running and visualizing
[systems diagrams](https://lethain.com/systems-thinking/). You start
by writing a file describing your system:

Start(10) > Middle @ 2
Middle > End @ 1

and then are able to evaluate your system (use `--csv` for an
importable format):

cat tmp.txt | systems-run -r 3

Start Middle End
0 10 0 0
1 8 2 0
2 6 3 1
3 4 4 2

You can also export your system into [Graphviz](https://www.graphviz.org/):

cat tmp.txt | python viz.py

// Parsed
digraph {
0 [label=Start]
1 [label=Middle]
2 [label=End]
0 -> 1
1 -> 2
}

From there you could push that output through Graphviz's
`dot` renderer to generate a diagram:

cat tmp.txt | systems-viz | dot -Tpng -o tmp.png
open tmp.png

If you're trying to render the diagram into a Jupyterhub notebook,
take a [look at the Graphviz docs on rendering in Jupyterhub](https://graphviz.readthedocs.io/en/stable/manual.html#jupyter-notebooks),
and look at the `systems.viz.as_dot` function which takes a model
and return a `Digraph` object that you can call `_repr_svg_()` against
to render.

## Installation

To install via PyPi:

pip install systems

To install for local development:

git clone https://github.com/lethain/systems.git
cd systems
python3 -m venv ./env
source ./env/bin/activate
python setup.py develop

Run tests via:

python3 -m unittest tests/test_*.py

Please open an Github issue if you run into any problems!

## Using the command line tools

Run a model in a file:

cat tmp.txt | systems-run -r 3

Visualize a model into `dot` for Graphviz:

cat examples/hiring.txt | systems-viz | dot

## Example: Hiring Funnel

Let's say you wanted to describe your hiring funnel and retention
for a rapidly growing company, you could do so via:

[PossibleRecruiters] > Recruiters(10, 15) @ 1
[Candidates] > PhoneScreens @ Recruiters * 3
PhoneScreens > Onsites @ 0.5
Onsites > Offers @ 0.5
Offers > Hires @ 0.5
Hires > Employees @ 1.0
Employees > Departures @ 0.1, leak
Departures > [Departed] @ 1.0

Note that you're able to refer to the value of `Recruiters` when specifying
the size of the flow between `Candidates` and `PhoneScreens`. This allows you
to build feedback loops and such!

Then you could run the simulation for 10 rounds:

cat examples/links.txt | systems-run -r10

Recruiters PhoneScreens Onsites Offers Hires Employees Departures
0 10 0 0 0 0 0 0
1 11 30 0 0 0 0 0
2 12 33 15 0 0 0 0
3 13 36 16 7 0 0 0
4 14 39 18 8 3 0 0
5 15 42 19 9 4 3 0
6 15 45 21 9 4 7 0
7 15 45 22 10 4 11 0
8 15 45 22 11 5 14 1
9 15 45 22 11 5 18 1
10 15 45 22 11 5 22 1

You can also get the output as CSV:

cat examples/links.txt | systems-run -r10 --csv

Which you could... load into a spreadsheet or something to graph!

## Specifying stocks

By default stocks start with a value of zero. For example,
this would have both `a` and `b` would initialize at zero,
and have no maximum limit:

a > b @ 1

You can also initialize stocks with an infinite value, which
is typically done for stocks at the beginning and end of a model:

[a] > b @ 5
b > [c] @ 3

In the above, `a` and `c` would be infinite, and `b` would start
with a value of zero. However, you can also specify arbitrary
values:

a(10) > b(3) @ 5
b > c(12) @ 1
c > a

In this example, `a` is initialized at 10, `b` at 3, and `c` at 12.
Note that you only need to set the value at first reference. It is legal
to initialize a value at a later definition of a stock, e.g. this is fine:

a(1) > b @ 5
b(2) > c @ 3
c(3) > a @ 1

However, this is only legal when previous initializes specify no value,
an error will be thrown if you attempt to reinitialize a stock at a different
value, e.g. this is illegal:

a(1) > b(2) @ 1
b(3) > a @ 1

You can't initialize `b` twice with different values!

You are also able to specify maximum values for each stock by adding
a second parameter. You're not able to specify a maximum without specifying
an initial value, but you can simple use zero for the initial value to
achieve equivalent behavior:

a(10) > b(0, 5) @ 1

In the above, `a` has no maximum value, but
`b` will only have a capacity of 5.

## Flows

Each line specifies two nodes and the link between them. Links are described
following the `@` character. The most common type of flow is a `rate`, which
is a fixed transfer of values in one stock to another.

For example, moving two units per round between `a` and `b`:

# these are equivalent
a > b @ 2
a > b @ 2, leak

Up to two units will be transfered from `a` to `b` each round.

Another common kind of flow is the `conversion` flow, which takes
the entire contents of the source stock and multiplies that value
against the conversion rate, adding the result to the next flow.

# these are equivalent
a(10) > b @ 0.5
a(10) > b @ 0.5, conversion


The above would multiple `0.5` against `10` and move `5` units to `b`,
with the other `5` units being lost to the conversion rate (e.g. disappearing).
A common example of a conversion rate would be the offer acceptance rate
in a [hiring funnel](https://lethain.com/hiring-funnel/).

The third kind of flow is the `leak`, which combines properties of the
`rate` and `conversion` flows. It moves a fixed percentage of the source
flow into the destination flow, while leaving the remainder intact.

a(10) > b @ 0.2, leak

Considering the difference between the `conversion` and `leak`, if the above
were a `conversion`, then the value of `a` after one round would be `0`, but if it's
a `leak`, then the value would be `8`.

The final and most advanced kind of flow is the `formula` which can use the
value of other stocks along with basic arithmetic to represent arbitrarily
complex relationships (this is a riff on the "link" concept in most system dynamic
software):

[a] > b @ e * 2
b > c @ e
[d] > e @ 1

In this example, the rate between `a` and `b` is dictated by the value of
the `e` stock.

## Error messages

The parser will do its best to give you a useful error message.
For example, if you're missing delimiters:

cat examples/no_delim.txt | systems-run
line 1 is missing delimiter '>': "[a] < b @ 25"

At worst, it will give you the line number and line that is
creating an issue:

cat examples/invalid_flow.txt | systems-run
line 1 could not be parsed: "a > b @ 0..2"