# 7.2. Extractors and Comparators¶

## 7.2.1. Available Extractors¶

Extractor

Name

Default sigma

Unit

angle

Angle

2.0

°

average_distance

Average distance

0.05

Å

bandgap

BandGap

0.002

Ha

bandstructure

BandStructure

0.002

Ha

bulkmodulus

Bulk modulus

0.001

hartree/bohr³

cell_angles

Cell angles

2.0

°

cell_lengths

Cell lengths

0.05

Å

cell_volume

Cell volume

50.0

Å³

charges

Charges

0.1

au

dihedral

Dihedral

2.0

°

distance

Distance

0.05

Å

distance_vector

Distance vector

0.05

Å

energy

Energy

0.002

Ha

forces

Forces

0.003

Ha/bohr

hessian

Hessian

1.0

Ha/bohr²

pes

PES

0.002

Ha

pes_compared

PES compared

0.002

Ha

pesscan_angle

PESScan angle

2.0

°

pesscan_dihedral

PESScan dihedral

2.0

°

pesscan_distance

PESScan distance

0.05

bohr

rmsd

RMSD

0.1

Å

shearmodulus

Shear modulus

0.001

Ha/bohr³

stresstensor

Stress tensor

0.0001

au

stresstensor_1d

Stress tensor 1D

0.0001

hartree/bohr

stresstensor_2d

Stress tensor 2D

0.0001

hartree/bohr²

stresstensor_3d

Stress tensor 3D

0.0001

hartree/bohr³

stresstensor_diagonal_2d

Stress tensor diagonal 2D

0.0001

hartree/bohr²

stresstensor_diagonal_3d

Stress tensor diagonal 3D

0.0001

hartree/bohr³

stresstensor_offdiagonal_2d

Stress tensor off-diagonal 2D

0.0001

hartree/bohr²

stresstensor_offdiagonal_3d

Stress tensor off-diagonal 3D

0.0001

hartree/bohr³

vibfreq

Vibrational frequencies

5.0

cm⁻¹

youngmodulus

Young modulus

0.001

hartree/bohr³

### 7.2.1.1. Angle¶

Extractor: angle

extract(amsresult, atom1: int, atom2: int, atom3: int, mic: bool = True)float

Extract the angle between three atoms (atom2 is the central atom). Atom indexing starts with 0.

mic: whether to use the minimum image convention for periodic systems.

Unit:

deg

Sigma:

2.0

### 7.2.1.2. Average distance¶

Extractor: average_distance

extract(amsresults, atomList: list)float

Extract the average interatomic distance between multiple atom pairs, defined by their indices [p1a1, p1a2, p2a1, p2a2, …], atom indexes zero based

Unit:

angstrom

Sigma:

0.05

### 7.2.1.3. BandGap¶

Extractor: bandgap

extract(amsresult)float

Extract the energy of the system.

Unit:

hartree

Sigma:

2e-3

### 7.2.1.4. BandStructure¶

Extractor: bandstructure

extract(amsresult, bands: Optional[List[int]] = None, relative_to='min', only_high_symmetry_points=False, spin='up')float

Extracts the band structure. The energies are returned relative to the lowest energy.

bands: list of int

Band indices starting with 0. If None are given, all bands are used. Note that the number of bands may be different between reference engine and parametrized engine, so you should always explicitly specify the bands.

relative_to: str

“min”, “prev”, “prev_intra” (equivalent to “prev”), “prev_inter”, “absolute”, or a 2-tuple with zero-based indices of the value to use as reference

only_high_symmetry_points: bool

If True, only the energies at the high-symmetry points (the first coordinate along each edge) is used.

spin: str

If “up” (or if no spin-down bands are calculated) then use the spin-up bands. Otherwise, use the spin-down bands. For non-spinpolarized calculations, set spin=”up”.

Returns: 2D numpy array with shape (nEnergies, nBands). Each column corresponds to a different band.

Unit:

hartree

Sigma:

2.0e-3

### 7.2.1.5. Bulk modulus¶

Extractor: bulkmodulus

extract(amsresult)float

Extract the bulk modulus.

Unit:

hartree/bohr^3

Sigma:

### 7.2.1.6. Cell angles¶

Extractor: cell_angles

extract(amsresults, index=None)Union[float, numpy.ndarray]

Returns all or one angle between lattice vectors

index =
0: alpha for 3D system, gamma for 2D system (degrees)
1: beta for 3D system (degrees)
2: gamma for 3D system (degrees)
None: all of the above

Unit:

degree

Sigma:

2.0

Compared value type:

np.ndarray if index is None else float

### 7.2.1.7. Cell lengths¶

Extractor: cell_lengths

extract(amsresults, index=None)Union[float, numpy.ndarray]

Returns the lengths of all or one lattice vector.

index =
0: a (angstrom)
1: b (angstrom)
2: c (angstrom)
None: all of the above

Unit:

angstrom

Sigma:

0.05

Compared value type:

np.ndarray if index is None else float

### 7.2.1.8. Cell volume¶

Extractor: cell_volume

extract(amsresults)float

Returns the cell volume. System must be periodic in 3D.

Unit:

angstrom^3

Sigma:
Compared value type:

float

### 7.2.1.9. Charges¶

Extractor: charges

extract(amsresult, atomindex: Optional[int] = None)Union[numpy.ndarray, float]

Extract the atomic charges.
Charges at one specific atom can be requested with atomindex (atom indexing starts with 0).

Unit:

au

Sigma:

0.1

### 7.2.1.10. Dihedral¶

Extractor: dihedral

extract(amsresults, atom1: int, atom2: int, atom3: int, atom4: int, mic: bool = True)float

Extract the dihedral angle as defined by the four atom ids (atom indexing starts with 0), i.e. the angle between the planes formed by atom1-atom2-atom3 and atom2-atom3-atom4.

mic: whether to use the minimum image convention for periodic systems.

Unit:

deg

Sigma:

2.0

### 7.2.1.11. Distance¶

Extractor: distance

extract(amsresults, atom1: int, atom2: int, mic: bool = True)float

Extract the interatomic distance between two atoms, defined by their indices atom1 and atom2 (atom indexing starts with 0).

If mic==True, the minimum image convention is used for periodic systems.

Unit:

angstrom

Sigma:

0.05

### 7.2.1.12. Distance vector¶

Extractor: distance_vector

extract(amsresults, atom1: int, atom2: int)numpy.ndarray

Extract the distance vector between two atoms atom2 - atom1, defined by their molecule indices (atom indexing starts with 0).

Unit:

angstrom

Sigma:

0.05

### 7.2.1.13. Energy¶

Extractor: energy

extract(amsresult)float

Extract the energy of the system.

Unit:

hartree

Sigma:

2e-3

### 7.2.1.14. Forces¶

Extractor: forces

extract(amsresult, atindex: Optional[int] = None, xyz: Optional[int] = None)Union[float, numpy.ndarray]

Extract the atomic forces of a system (array), or the specific component xyz at index atindex (float).

Unit:

hartree/bohr

Sigma:

0.01

Properties

atindexoptional, int

Atom index, starting with 0

xyzoptional, 0 <= int <= 2

x(0), y(1) or z(2) component to be extracted.

### 7.2.1.15. Hessian¶

Extractor: hessian

extract(amsresult)numpy.ndarray

Extract the Cartiesian Hessian matrix.

Unit:

Ha/bohr^2

Sigma:

Undefined (defaults to 1.0)

### 7.2.1.16. PES¶

Extractor: pes

extract(results, relative_to='min')numpy.ndarray

Extracts the results of a PES Scan.

If relative_to is an integer, energies relative to that index (starting with 0) will be returned.

If relative_to is a string and equal to “previous”, then the first element returned is 0 and every subsequent element is the difference to the previous one. Example: pes is [2,0,1,4] then pes(relative_to=”previous”) will become [0, -2, 1, 3]

If relative_to is a string and a valid attribute of a numpy array (e.g. ‘min’ or ‘max’), then the return value of that function will be subtracted.

If relative_to is None, the energies are returned unmodified.

Unit:

Ha

Sigma:

2e-3

Compared value type:

ndarray

### 7.2.1.17. PES compared¶

Extractor: pes_compared

extract(results)numpy.ndarray

Extracts and compares the results of a PES Scan. The return value r is calculated as

\begin{align}\begin{aligned}\mu = \frac{1}{N} \sum_i^N y_i - \hat{y}_i\\r = \sqrt{ \sum_i^N (\hat{y}_i - y_i + \mu)^2 }\end{aligned}\end{align}

where N is the number of points in the PES scan.

Unit:

au

Sigma:

2e-3

Compared value type:

float

### 7.2.1.18. PESScan angle¶

Extractor: pesscan_angle

extract(results, A: int, B: int, C: int)

Extract an array of angles A-B-C for all frames in a PES Scan (atom indexing starts with 0).

Unit:

deg

Sigma:

2.0

### 7.2.1.19. PESScan dihedral¶

Extractor: pesscan_dihedral

extract(results, A: int, B: int, C: int, D: int)numpy.ndarray

Extract an array of dihedral angles A-B-C-D for all frames in a PES Scan (atom indexing starts with 0).

Unit:

deg

Sigma:

2.0

### 7.2.1.20. PESScan distance¶

Extractor: pesscan_distance

extract(results, A: int, B: int)numpy.ndarray

Extract an array of distances between two atoms for all frames in a PES Scan (atom indexing starts with 0).

Unit:

bohr

Sigma:

0.05

### 7.2.1.21. RMSD¶

Extractor: rmsd

extract(amsresult, ignore_hydrogen=False)

Uses the Kabsch algorithm to align and calculate the root-mean-square deviation of the atomic positions given two systems. Assumes all elements and their order is the same in both systems. When providing an external reference value, the object must be a 2d numpy array of the shape (Natoms, 3) (each element should store the atomic coordinates). Ignores hydrogen atoms if ignore_hydrogen is set to True.

Unit:

angstrom

Sigma:

0.1

### 7.2.1.22. Shear modulus¶

Extractor: shearmodulus

extract(amsresult)float

Extract the shear modulus.

Unit:

hartree/bohr^3

Sigma:

### 7.2.1.23. Stress tensor¶

Extractor: stresstensor

extract(amsresult)numpy.ndarray

Extracts the stress tensor

Unit:

au. For 3D systems this mean hartree/bohr^3, for 2D systems hartree/bohr^2 and for 1D systems hartree/bohr.

Sigma:

1e-4

### 7.2.1.24. Stress tensor 1D¶

Extractor: stresstensor_1d

extract(amsresult)numpy.ndarray

Extracts the stress tensor for a 1D system (1 element).

Unit:

hartree/bohr.

Sigma:

1e-4

### 7.2.1.25. Stress tensor 2D¶

Extractor: stresstensor_2d

extract(amsresult)numpy.ndarray

Extracts the stress tensor for a 2D system (4 elements).

Unit:

hartree/bohr^2.

Sigma:

1e-4

### 7.2.1.26. Stress tensor 3D¶

Extractor: stresstensor_3d

extract(amsresult)numpy.ndarray

Extracts the stress tensor for a 3D system (9 elements).

Unit:

hartree/bohr^3.

Sigma:

1e-4

### 7.2.1.27. Stress tensor diagonal 2D¶

Extractor: stresstensor_diagonal_2d

extract(amsresult)numpy.ndarray

Extracts the diagonal elements of the stress tensor for a 2D system (2 elements).

Unit:

hartree/bohr^2.

Sigma:

1e-4

### 7.2.1.28. Stress tensor diagonal 3D¶

Extractor: stresstensor_diagonal_3d

extract(amsresult)numpy.ndarray

Extracts the diagonal elements of the stress tensor for a 3D system (3 elements).

Unit:

hartree/bohr^3.

Sigma:

1e-4

### 7.2.1.29. Stress tensor off-diagonal 2D¶

Extractor: stresstensor_offdiagonal_2d

extract(amsresult)numpy.ndarray

Extracts the off-diagonal element of the stress tensor for a 2D system (1 element).

Unit:

hartree/bohr^2.

Sigma:

1e-4

### 7.2.1.30. Stress tensor off-diagonal 3D¶

Extractor: stresstensor_offdiagonal_3d

extract(amsresult)numpy.ndarray

Extracts the off-diagonal elements of the stress tensor for a 3D system (3 elements).

Unit:

hartree/bohr^3.

Sigma:

1e-4

### 7.2.1.31. Vibrational frequencies¶

Extractor: vibfreq

extract(results)numpy.ndarray

Extracts the vibrational frequencies.

Unit:

1/cm

Sigma:

5.0

### 7.2.1.32. Young modulus¶

Extractor: youngmodulus

extract(amsresult)float

Extract the Young’s modulus.

Unit:

hartree/bohr^3

Sigma:

## 7.2.2. Custom Extractors¶

The DataSet section described how an arbitrary linear combination of properties extracted from jobs $$P(J)$$ can be added to a Data Set for fitting. In this chapter, we are going to describe what happens when entries are added and evaluated by the Data Set and how the user can extend the number of properties that can be fitted with ParAMS.

We have briefly described the extractors in the Data Set: They are a collection of Python code snippets available to the DataSet instance which define how to extract an individual property $$P$$ from a job. The extractors available to each DataSet can be checked with the extractors attribute:

>>> ds = DataSet()
>>> ds.extractors
{'angles', 'vibfreq', 'charges', 'distance', 'stresstensor', 'energy', 'forces', 'hessian', 'dihedral'}


Any expression passed to the DataSet.add_entry() method can be constructed from the available extractors, for example "angles('myJob1')".

The design of the Data Set allows for an easy extension of the extractors to suit personal needs beyond what is already provided in the package. Users are encouraged to define additional extractors whenever a new property becomes relevant for the fitting process. In the following example, we will add the functionality to extract and evaluate elastic tensors to the Data Set:

>>> 'elastictensor' in ds.extractors
False


Start by creating an elastictensor.py in an empty directory of your choice with the following contents:

from numpy import ndarray, asarray

sigma = 1e-2
def extract(amsresults) -> ndarray:
return asarray(amsresults.get_engine_results('ElasticTensor'))


This is a minimal and complete definition of our extractor. The code snippet can be saved under any accessible path and used by providing DataSet with the corresponding directory. The base file name will be used as the extractor’s name (make sure not include extractors with the same names). Here, we have saved the above under path/to/extractors/:

>>> ds = DataSet(more_extractors='path/to/extractors/')
>>> 'elastictensor' ds.extractors
True


Because the Data Set natively works with plams.AMSResults, we were able to take a shortcut in the creation of our extractor: All we needed to do in this case is wrap a PLAMS method around the extract() function. Note that in addition to the function definition, we also provided a sigma variable. This serves as a default value when a related entry is added with through DataSet.add_entry() and should roughly be in the same order of magnitude as the “accepted accuracy” for this property. ParAMS will evaluate all entries according to $$(w/\sigma)(y-\hat{y})$$, where $$w$$ is the weight. Providing a sigma is not mandatory but highly recommended, any extractor without a sigma will set it’s value to 1.

Important

• An extractor stored as basename.py will be available through the basename string at runtime

• For every extractor, the extract() function returns the property value from a job

• ParAMS expects the first argument passed to any extract() function to be a plams.AMSResults instance (see PLAMS documentation)

• It is recommended to define a sigma:float variable, which should be in the same order of magnitude as the prediction accuracy for this property

However, because the definition of extract() is completely up to the user, it can be made to read and process data from any other source as well. Assuming that a property is stored in a text file, an extractor that is independent of plams.AMSResults could look like this:

def extract(_, filepath):
# AMSResults instance: _ is ignored.
with open(filepath) as f:


## 7.2.3. Supported Data Structures¶

The above definition of our elastic tensor extractor returns a numpy array to the DataSet instance when evaluated, however, in theory extractors can return an arbitrary data structure which calls for additional processing to make all results consistent. Internally, each time DataSet.evaluate() is called, reference and predicted results are reduced to one weighted vector of residuals $$(\boldsymbol{w}/\boldsymbol{\sigma})(\boldsymbol{y} - \boldsymbol{\hat{y}})$$, which is then passed to a loss function and evaluated. This implies that any two return values of the same extractor support subtraction and multiplication (which is why we convert the the elastic tensor to a numpy array before returning). For anything that does not, a custom compare() function has to be implemented alongside extract().

## 7.2.4. Custom Comparators¶

There might be cases where an extractor either returns a data type that does not support mathematical operations or the quality of a reference and predicted value can not be measured by a simple subtraction $$y - \hat{y}$$. In such cases it is necessary to define an additional compare() in the extractor:

# dictextractor.py
from typing import Dict

sigma = 0.1
def extract(amsresults) -> Dict:
return amsresults.some_dict_property()

def compare(y:Dict, yhat:Dict, au_to_ref:float) -> float:
y    = list(y.values())
yhat = list(yhat.values())

# Unit conversion must be handled by the custom comparator:
yhat = [i*au_to_ref for i in yhat]

for i,ihat  in zip(y, yhat):
...
return ...


A custom comparator defined in such a way will automatically be used in combination with the extractor.

Important

• Whenever the extract() function returns a data type that does not support mathematical operations, a compare() function must be additionally defined.

• compare() always follows the signature compare(y:Any, yhat:Any, au_to_ref:float) -> Union[ndarray,float,int]

• Note that compare() should handle possible unit conversions by applying the equivalent of yhat = au_to_ref*yhat