Implementations of come collider physics observables. Some observables require the FastJet Python interface to be importable; if it's not, no warnings or errors will be issued, the observables will simply not be included in this module.

### D2

Ratio of EFPs (specifically, energy correlation functions) designed to tag two prong signals. In graphs, the formula is:

For additional information, see the original paper.

```
energyflow.D2(measure='hadr', beta=2, strassen=False, reg=0., kappa=1, normed=None, coords=None, check_input=True)
```

Since a `D2`

defines and holds a `Measure`

instance, all `Measure`

keywords are accepted.

**Arguments**

**measure**: {`'hadr'`

,`'hadrdot'`

,`'hadrefm'`

,`'ee'`

,`'eeefm'`

}- The choice of measure. See Measures for additional info.

**beta**:*float*- The parameter $\beta$ appearing in the measure. Must be greater than zero.

**strassen**:*bool*- Whether to use matrix multiplication to speed up the evaluation. Not recommended when $\beta=2$ since EFMs are faster.

**reg**:*float*- A regularizing value to be added to the denominator in the event that it is zero. Should typically be something less than 1e-30.

**kappa**: {*float*,`'pf'`

}- If a number, the energy weighting parameter $\kappa$. If
`'pf'`

, use $\kappa=v-1$ where $v$ is the valency of the vertex.

- If a number, the energy weighting parameter $\kappa$. If
**normed**:*bool*- Controls normalization of the energies in the measure.

**coords**: {`'ptyphim'`

,`'epxpypz'`

,`None`

}- Controls which coordinates are assumed for the input. See Measures for additional info.

**check_input**:*bool*- Whether to check the type of the input each time or assume the first input type.

#### compute

```
compute(event=None, zs=None, thetas=None, nhats=None)
```

Computes the value of the observable on a single event.

**Arguments**

**event**: 2-d array_like or`fastjet.PseudoJet`

- The event as an array of particles in the coordinates specified
by
`coords`

.

- The event as an array of particles in the coordinates specified
by
**zs**: 1-d array_like- If present,
`thetas`

must also be present, and`zs`

is used in place of the energies of an event.

- If present,
**thetas**: 2-d array_like- If present,
`zs`

must also be present, and`thetas`

is used in place of the pairwise angles of an event.

- If present,
**nhats**: 2-d array like- If present,
`zs`

must also be present, and`nhats`

is used in place of the scaled particle momenta. Only applicable when EFMs are being used.

- If present,

**Returns**

*float*- The observable value.

#### batch_compute

```
batch_compute(events, n_jobs=None)
```

Computes the value of the observable on several events.

**Arguments**

**events**: array_like or`fastjet.PseudoJet`

- The events as an array of arrays of particles in coordinates
matching those anticipated by
`coords`

.

- The events as an array of arrays of particles in coordinates
matching those anticipated by
**n_jobs**:*int*or`None`

- The number of worker processes to use. A value of
`None`

will use as many processes as there are CPUs on the machine.

- The number of worker processes to use. A value of

**Returns**

*1-d numpy.ndarray*- A vector of the observable values for each event.

##### efpset

```
efpset
```

`EFPSet`

held by the object to compute fundamental EFP values.

### C2

Ratio of Energy Correlation Functions designed to tag two prong signals. In graphs, the formula is:

For additional information, see the original paper.

```
energyflow.C2(measure='hadr', beta=2, strassen=False, reg=0., kappa=1, normed=None, coords=None, check_input=True)
```

Since a `C2`

defines and holds a `Measure`

instance, all `Measure`

keywords are accepted.

**Arguments**

**measure**: {`'hadr'`

,`'hadrdot'`

,`'hadrefm'`

,`'ee'`

,`'eeefm'`

}- The choice of measure. See Measures for additional info.

**beta**:*float*- The parameter $\beta$ appearing in the measure. Must be greater than zero.

**strassen**:*bool*- Whether to use matrix multiplication to speed up the evaluation. Not recommended when $\beta=2$ since EFMs are faster.

**reg**:*float*- A regularizing value to be added to the denominator in the event that it is zero. Should typically be something less than 1e-30.

**kappa**: {*float*,`'pf'`

}- If a number, the energy weighting parameter $\kappa$. If
`'pf'`

, use $\kappa=v-1$ where $v$ is the valency of the vertex.

- If a number, the energy weighting parameter $\kappa$. If
**normed**:*bool*- Controls normalization of the energies in the measure.

**coords**: {`'ptyphim'`

,`'epxpypz'`

,`None`

}- Controls which coordinates are assumed for the input. See Measures for additional info.

**check_input**:*bool*- Whether to check the type of the input each time or assume the first input type.

#### compute

```
compute(event=None, zs=None, thetas=None, nhats=None)
```

Computes the value of the observable on a single event.

**Arguments**

**event**: 2-d array_like or`fastjet.PseudoJet`

- The event as an array of particles in the coordinates specified
by
`coords`

.

- The event as an array of particles in the coordinates specified
by
**zs**: 1-d array_like- If present,
`thetas`

must also be present, and`zs`

is used in place of the energies of an event.

- If present,
**thetas**: 2-d array_like- If present,
`zs`

must also be present, and`thetas`

is used in place of the pairwise angles of an event.

- If present,
**nhats**: 2-d array like- If present,
`zs`

must also be present, and`nhats`

is used in place of the scaled particle momenta. Only applicable when EFMs are being used.

- If present,

**Returns**

*float*- The observable value.

#### batch_compute

```
batch_compute(events, n_jobs=None)
```

Computes the value of the observable on several events.

**Arguments**

**events**: array_like or`fastjet.PseudoJet`

- The events as an array of arrays of particles in coordinates
matching those anticipated by
`coords`

.

- The events as an array of arrays of particles in coordinates
matching those anticipated by
**n_jobs**:*int*or`None`

- The number of worker processes to use. A value of
`None`

will use as many processes as there are CPUs on the machine.

- The number of worker processes to use. A value of

**Returns**

*1-d numpy.ndarray*- A vector of the observable values for each event.

##### efpset

```
efpset
```

`EFPSet`

held by the object to compute fundamental EFP values.

### C3

Ratio of Energy Correlation Functions designed to tag three prong signals. In graphs, the formula is:

For additional information, see the original paper.

```
energyflow.C3(measure='hadr', beta=2, reg=0., kappa=1, normed=None, coords=None, check_input=True)
```

Since a `D2`

defines and holds a `Measure`

instance, all `Measure`

keywords are accepted.

**Arguments**

**measure**: {`'hadr'`

,`'hadrdot'`

,`'hadrefm'`

,`'ee'`

,`'eeefm'`

}- The choice of measure. See Measures for additional info.

**beta**:*float*- The parameter $\beta$ appearing in the measure. Must be greater than zero.

**reg**:*float*- A regularizing value to be added to the denominator in the event that it is zero. Should typically be something less than 1e-30.

**kappa**: {*float*,`'pf'`

}- If a number, the energy weighting parameter $\kappa$. If
`'pf'`

, use $\kappa=v-1$ where $v$ is the valency of the vertex.

- If a number, the energy weighting parameter $\kappa$. If
**normed**:*bool*- Controls normalization of the energies in the measure.

**coords**: {`'ptyphim'`

,`'epxpypz'`

,`None`

}- Controls which coordinates are assumed for the input. See Measures for additional info.

**check_input**:*bool*- Whether to check the type of the input each time or assume the first input type.

#### compute

```
compute(event=None, zs=None, thetas=None, nhats=None)
```

Computes the value of the observable on a single event.

**Arguments**

**event**: 2-d array_like or`fastjet.PseudoJet`

- The event as an array of particles in the coordinates specified
by
`coords`

.

- The event as an array of particles in the coordinates specified
by
**zs**: 1-d array_like- If present,
`thetas`

must also be present, and`zs`

is used in place of the energies of an event.

- If present,
**thetas**: 2-d array_like- If present,
`zs`

must also be present, and`thetas`

is used in place of the pairwise angles of an event.

- If present,
**nhats**: 2-d array like- If present,
`zs`

must also be present, and`nhats`

is used in place of the scaled particle momenta. Only applicable when EFMs are being used.

- If present,

**Returns**

*float*- The observable value.

#### batch_compute

```
batch_compute(events, n_jobs=None)
```

Computes the value of the observable on several events.

**Arguments**

**events**: array_like or`fastjet.PseudoJet`

- The events as an array of arrays of particles in coordinates
matching those anticipated by
`coords`

.

- The events as an array of arrays of particles in coordinates
matching those anticipated by
**n_jobs**:*int*or`None`

- The number of worker processes to use. A value of
`None`

will use as many processes as there are CPUs on the machine.

- The number of worker processes to use. A value of

**Returns**

*1-d numpy.ndarray*- A vector of the observable values for each event.

##### efpset

```
efpset
```

`EFPSet`

held by the object to compute fundamental EFP values.

### image_activity

```
energyflow.image_activity(ptyphis, f=0.95, R=1.0, npix=33, center=None, axis=None)
```

Image activity, also known as $N_f$, is the minimum number of pixels in an image that contain a fraction $f$ of the total pT.

**Arguments**

**ptyphis**:*2d numpy.ndarray*- Array of particles in hadronic coordinates; the mass is optional since it is not used in the computation of this observable.

**f**:*float*- The fraction $f$ of total pT that is to be contained by the pixels.

**R**:*float*- Half of the length of one side of the square space to tile with pixels when forming the image. For a conical jet, this should typically be the jet radius.

**npix**:*int*- The number of pixels along one dimension of the image, such that the
image has shape
`(npix,npix)`

.

- The number of pixels along one dimension of the image, such that the
image has shape
**center**:*str*or`None`

- If not
`None`

, the centering scheme to use to center the particles prior to calculating the image activity. See the option of the same name for`center_ptyphims`

.

- If not
**axis**:*numpy.ndarray*or`None`

- If not
`None`

, the`[y,phi]`

values to use for centering. If`None`

, the center of the image will be at`(0,0)`

.

- If not

**Returns**

*int*- The image activity defined for the specified image paramters.

### zg

```
energyflow.zg(ptyphims, zcut=0.1, beta=0, R=1.0, algorithm='ca')
```

Groomed momentum fraction of a jet, as calculated on an array of particles in hadronic coordinates. First, the particles are converted to FastJet PseudoJets and clustered according to the specified algorithm. Second, the jet is groomed according to the specified SoftDrop parameters and the momentum fraction of the surviving pair of Pseudojets is computed. See the SoftDrop paper for a complete description of SoftDrop.

**Arguments**

**ptyphims**:*numpy.ndarray*- An array of particles in hadronic coordinates that will be clustered into a single jet and groomed.

**zcut**:*float*- The $z_{\rm cut}$ parameter of SoftDrop. Should be between
`0`

and`1`

.

- The $z_{\rm cut}$ parameter of SoftDrop. Should be between
**beta**:*int*or*float*- The $\beta$ parameter of SoftDrop.

**R**:*float*- The jet radius to use for the grooming. Only relevant if
`beta!=0`

.

- The jet radius to use for the grooming. Only relevant if
**algorithm**: {'kt', 'ca', 'antikt'}- The jet algorithm to use when clustering the particles. Same as
the argument of the same name of
`cluster`

.

- The jet algorithm to use when clustering the particles. Same as
the argument of the same name of

**Returns**

*float*- The groomed momentum fraction of the given jet.

### zg_from_pj

```
energyflow.zg_from_pj(pseudojet, zcut=0.1, beta=0, R=1.0)
```

Groomed momentum fraction $z_g$, as calculated on an ungroomed (but already clustered) FastJet PseudoJet object. First, the jet is groomed according to the specified SoftDrop parameters and then the momentum fraction of the surviving pair of Pseudojets is computed. See the SoftDrop paper for a complete description of SoftDrop. This version of $z_g$ is provided in addition to the above function so that a jet does not need to be reclustered if multiple grooming parameters are to be used.

**Arguments**

**pseudojet**:*fastjet.PseudoJet*- A FastJet PseudoJet that has been obtained from a suitable clustering (typically Cambridge/Aachen for SoftDrop).

**zcut**:*float*- The $z_{\rm cut}$ parameter of SoftDrop. Should be between
`0`

and`1`

.

- The $z_{\rm cut}$ parameter of SoftDrop. Should be between
**beta**:*int*or*float*- The $\beta$ parameter of SoftDrop.

**R**:*float*- The jet radius to use for the grooming. Only relevant if
`beta!=0`

.

- The jet radius to use for the grooming. Only relevant if

**Returns**

*float*- The groomed momentum fraction of the given jet.