# Fingerprinting¶

## Ashlock Fingerprints¶

In [Ashlock2008], [Ashlock2009] a methodology for obtaining visual
representation of a strategy’s behaviour is described. The basic method is to
play the strategy against a probe strategy with varying noise parameters.
These noise parameters are implemented through the `JossAnnTransformer`

.
The Joss-Ann of a strategy is a new strategy which has a probability `x`

of cooperating, a probability `y`

of defecting, and otherwise uses the
response appropriate to the original strategy. We can then plot the expected
score of the strategy against `x`

and `y`

and obtain a heat plot
over the unit square. When `x + y >= 1`

the `JossAnn`

is created
with parameters `(1-y, 1-x)`

and plays against the Dual of the probe
instead. A full definition and explanation is given in
[Ashlock2008], [Ashlock2009].

Here is how to create a fingerprint of `WinStayLoseShift`

using
`TitForTat`

as a probe:

```
>>> import axelrod as axl
>>> axl.seed(0) # Fingerprinting is a random process
>>> strategy = axl.WinStayLoseShift
>>> probe = axl.TitForTat
>>> af = axl.AshlockFingerprint(strategy, probe)
>>> data = af.fingerprint(turns=10, repetitions=2, step=0.2)
>>> data
{...
>>> data[(0, 0)]
3.0
```

The `fingerprint`

method returns a dictionary mapping coordinates of the
form `(x, y)`

to the mean score for the corresponding interactions.
We can then plot the above to get:

```
>>> p = af.plot()
>>> p.show()
```

In reality we would need much more detail to make this plot useful.

Running the above with the following parameters:

```
>>> af.fingerprint(turns=50, repetitions=2, step=0.01)
```

We get the plot:

We are also able to specify a matplotlib colour map, interpolation and can remove the colorbar and axis labels:

```
>>> p = af.plot(cmap='PuOr', interpolation='bicubic', colorbar=False, labels=False)
>>> p.show()
```

Note that it is also possible to pass a player instance to be fingerprinted and/or as a probe. This allows for the fingerprinting of parametrized strategies:

```
>>> axl.seed(0)
>>> player = axl.Random(p=.1)
>>> probe = axl.GTFT(p=.9)
>>> af = axl.AshlockFingerprint(player, probe)
>>> data = af.fingerprint(turns=10, repetitions=2, step=0.2)
>>> data
{...
>>> data[(0, 0)]
4.4...
```

## Transitive Fingerprint¶

Another implemented fingerprint is the transitive fingerprint. The transitive fingerprint represents the cooperation rate of a strategy against a set of opponents over a number of turns.

By default the set of opponents consists of `50`

Random players that
cooperate with increasing probability. This is how to obtain the transitive
fingerprint for `TitForTat`

:

```
>>> axl.seed(0)
>>> player = axl.TitForTat()
>>> tf = axl.TransitiveFingerprint(player)
>>> data = tf.fingerprint(turns=40)
```

The data produced is a `numpy`

array showing the cooperation rate against
a given opponent (row) in a given turn (column):

```
>>> data.shape
(50, 40)
```

It is also possible to visualise the fingerprint:

```
>>> p = tf.plot()
>>> p.show()
```

It is also possible to fingerprint against a given set of opponents:

```
>>> axl.seed(1)
>>> opponents = [s() for s in axl.demo_strategies]
>>> tf = axl.TransitiveFingerprint(player, opponents=opponents)
>>> data = tf.fingerprint(turns=5, repetitions=10)
```

The name of the opponents can be displayed in the plot:

```
>>> p = tf.plot(display_names=True)
>>> p.show()
```