opal.analysis package¶

Notebooks¶

cyclotron

opal.analysis.FieldAnalysis module¶

class opal.analysis.FieldAnalysis.FieldAnalysis[source]¶

Bases: object

max(var, step=0)[source]¶

Get the maximum value of a variable.

Parameters

var (str) – variable name
step (int, optional) – time step

Returns

the maximum value of the given variable

Return type

numpy.float64

sum(var, step=0)[source]¶

Get the sum of the grid data of a variable.

Parameters

var (str) – variable name
step (int, optional) – time step

Returns

the sum of all grid values of the given variable

Return type

numpy.float64

total_charge(step=0)[source]¶

Get the total charge on the grid.

Parameters: step (int, optional) – time step
Returns: the total charge on the grid
Return type: numpy.float64

opal.analysis.H5Statistics module¶

class opal.analysis.H5Statistics.H5Statistics[source]¶

Bases: opal.analysis.Statistics.Statistics

_halo_2d_ellipsoidal_beam(q, p)[source]¶

Compute the 2D halo

Compute the 2D halo in horizontal, vertical or longitudinal direction according to

\[\begin{split}\begin{align} H_i & = \frac{\sqrt{3}}{2} \frac{\sqrt{A}}{B} - \frac{15}{7} \\ A & = {<}q^4{>}{<}p^4{>} + 3 {<}q^2p^2{>}^2 - 4 {<}qp^3{>} {<}q^3p{>} \\ B & = {<}q^2{>}{<}p^2{>} - {<}qp{>}^2 \end{align}\end{split}\]

with coordinate q and momentum p.

Parameters

q (array_like) – coordinate data
p (array_like) – momentum data

Returns

halo

Return type

float

References

https://journals.aps.org/prab/abstract/10.1103/PhysRevSTAB.5.124202

_select(data, attrval, val)[source]¶

Take a slice from the array

Parameters

data (array_like) – Container to extract data from
attrval (array_like) – Data to compare with in extraction value
val (int or float) – Value for extraction comparison

Returns

Slice of data

Return type

array_like

_selectBunch(data, bunch, step)[source]¶

Take a bunch slice from the array

Parameters

data (array_like) – The data where to extract
bunch (int) – Bunch to select
step (int) – Step in H5 file

Returns

Slice of data

Return type

array_like

find_beams(var, **kwargs)[source]¶

Compute the starting and end points of a beam via a histogram.

The purpose of this script is to distinguish bunches of a multi-bunch simulation.

Parameters

var (str) – The variable
step (int, optional) – Step in H5 file (default: 0)
bins (int, optional) – Number of bins for histogram (default: 0)
Wn (float, optional) – Critical frequency for lowpass filter (default: 0.15) (see https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.butter.html)

Returns

peaks (ndarray) – Indices of minima locations
hist (array) – The values of the corresponding numpy histogram.
bin_edges (array of dtype float) – Return the bin edges (length(hist)+1).

gaussian_kde(var, **kwargs)[source]¶

Representation of a kernel-density estimate using Gaussian kernels.

Parameters

var (str) – The variable
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

scipy kernel density estimator

Return type

scipy.stats.gaussian_kde

Notes

23. March 2018 https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html

halo_2d_ellipsoidal_beam(var, **kwargs)[source]¶

Compute the 2D halo for a ellipsoidal beam

Compute the 2D halo in horizontal, vertical or longitudinal direction according to

\[\begin{split}\begin{align} H_i & = \frac{\sqrt{3}} {2} \frac{\sqrt{A}} {B} - \frac{15}{7} \\ A & = {<}q^4{>}{<}p^4{>} + 3 {<}q^2p^2{>}^2 - 4 {<}qp^3{>} {<}q^3p{>} \\ B & = {<}q^2{>}{<}p^2{>} - {<}qp{>}^2 \end{align}\end{split}\]

with coordinate q and momentum p. Specify either the ‘step’ or ‘turn’ (probes only).

Parameters

var (str) – The direction ‘x’, ‘y’, ‘z’
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

halo

Return type

float

References

https://journals.aps.org/prab/abstract/10.1103/PhysRevSTAB.5.124202

halo_continuous_beam(var, **kwargs)[source]¶

Compute the halo for a continuous beam.

Compute the halo in horizontal or vertical direction according to

\[h_x = \frac{{<}x^4{>}} {{<}x^2{>}^2} - 2\]

Parameters

var (str) – The variable
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

halo

Return type

float

References

T. P. Wangler, Los Alamos National Laboratory, Los Alamos, NM 87545, K. R. Crandall, TechSource, Santa Fe, NM 87594-1057, BEAM HALO IN PROTON LINAC BEAMS, XX International Linac Conference, Monterey, California

halo_ellipsoidal_beam(var, **kwargs)[source]¶

Compute the halo for a ellipsoidal beam

Compute the halo in horizontal, vertical or longitudinal direction according to

\[h_x = \frac{{<}x^4{>}} {{<}x^2{>}^2} - \frac{15}{7}\]

Parameters

var (str) – The variable
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

halo

Return type

float

References

T. P. Wangler, Los Alamos National Laboratory, Los Alamos, NM 87545, K. R. Crandall, TechSource, Santa Fe, NM 87594-1057, BEAM HALO IN PROTON LINAC BEAMS, XX International Linac Conference, Monterey, California

histogram(var, bins, **kwargs)[source]¶

Compute a histogram of a dataset

Parameters

var (str) – The variable
bins (int or str) – Binning type or nr of bins (see https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.histogram.html)
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)
density (bool, optional) – Normalize such that integral over range is 1 (default: True).

Returns

numpy.histogram (array) – The values of the histogram. See density and weights for a description of the possible semantics.
bin_edges (array of dtype float) – Return the bin edges (length(hist)+1).

Notes

See https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.histogram.html

kurtosis(var, **kwargs)[source]¶

Compute the kurtosis (Fisher or Pearson) of a dataset.

Kurtosis is the fourth central moment divided by the square of the variance. Fisher’s definition is used, i.e. 3.0 is subtracted from the result to give 0.0 for a normal distribution.

Parameters

var (str) – The variable
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

kurtosis

Return type

float

Notes

23. March 2018 https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kurtosis.html

mean(var, **kwargs)[source]¶

Calculate the arithmetic mean.

Parameters

var (str) – The variable
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

arithmetic mean

Return type

float

moment(var, k, **kwargs)[source]¶

Calculate the k-th central moment.

Parameters

var (str) – The variable to compute k-th central moment
k (int) – The moment number, k = 1 is central mean
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

k-th central moment

Return type

float

Notes

https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.moment.html

projected_emittance(dim, **kwargs)[source]¶

Compute the projected emittance

It shifts the coordinates by their mean value such that the bunch is centered around zero.

\[\varepsilon = \sqrt{ {<}coords^2{>}{<}momenta^2{>} - {<}coords*momenta{>}^2 }\]

Parameters

dim (str) – the dimension ‘x’, ‘y’ or ‘z’
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

the projected emittance

Return type

float

radial_halo_2d_ellipsoidal_beam(azimuth, **kwargs)[source]¶

Compute the 2D radial halo for a ellipsoidal beam

Compute the 2D radial halo according to

\[\begin{split}\begin{align} H_i & = \frac{\sqrt{3}}{2} \frac{\sqrt{A}}{B} - \frac{15}{7} \\ A & = {<}r^4{>}{<}p^4{>} + 3 {<}r^2p^2{>}^2 - 4 {<}rp^3{>} {<}r^3p{>} \\ B & = {<}r^2{>}{<}p^2{>} - {<}rp{>}^2 \end{align}\end{split}\]

with radius r and radial momentum p.

Parameters

azimuth (float) – Azimuth for radial halo only (in degree)
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

halo

Return type

float

References

https://journals.aps.org/prab/abstract/10.1103/PhysRevSTAB.5.124202

radial_halo_ellipsoidal_beam(**kwargs)[source]¶

Compute the radial halo for a ellipsoidal beam

Compute the halo in radial direction according to

\[h_r = \frac{{<}r^4{>}} {{<}r^2{>}^2} - \frac{15}{7}\]

Parameters

bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

halo

Return type

float

References

T. P. Wangler, Los Alamos National Laboratory, Los Alamos, NM 87545, K. R. Crandall, TechSource, Santa Fe, NM 87594-1057, BEAM HALO IN PROTON LINAC BEAMS, XX International Linac Conference, Monterey, California

radial_moment(k, **kwargs)[source]¶

Calculate the k-th central radial moment.

Parameters

k (int) – The moment number, k = 1 is central mean
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

k-th central radial moment

Return type

float

Notes

https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.moment.html

radial_projected_emittance(azimuth, **kwargs)[source]¶

Compute the radial projected emittance

It shifts the coordinates by their mean value such that the bunch is centered around zero.

\[\varepsilon = \sqrt{ {<}r^2{>}{<}p_r^2{>} - {<}r*p_r{>}^2 }\]

Parameters

azimuth (float) – Azimuth angle (in degree)
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

the projected emittance

Return type

float

rotate(y, theta)[source]¶

Rotate the coordinates (x, y) by theta (degree)

Parameters

x (dask.array) – x-data
y (dask.array) – y-data
theta (float) – The angle in degree

Returns

rx (dask.array) – rotated coordinates x
ry (dask.array) – rotated coordinates y

Notes

\[\begin{split}\begin{align} R(\theta) & = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} \\ \begin{bmatrix} rx & ry \end{bmatrix} & = R(\theta) * \begin{bmatrix} x & y \end{bmatrix} \end{align}\end{split}\]

References

https://en.wikipedia.org/wiki/Rotation_matrix

selectData(var, **kwargs)[source]¶

Select subset of data

Given a H5 dataset, select a subset using the attributes step (or turn) and bunch.

Parameters

var (str) – Variable name
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

Data array

Return type

array_like

skew(var, **kwargs)[source]¶

Calculate the skewness.

Parameters

var (str) – The variable
bunch (int, optional) – Bunch to select (default: -1, which means all particles)
step (int, optional) – Step in H5 file (default: 0)
turn (int, optional) – Turn of dataset (default: None, which implies no specific turn selection) (probe H5 files only)

Returns

skewness

Return type

float

Notes

23. March 2018 https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skew.html

opal.analysis.OptimizerAnalysis module¶

class opal.analysis.OptimizerAnalysis.OptimizerAnalysis[source]¶

Bases: object

find(function, opt=0)[source]¶

Find the individual according to the given function in the Pareto file.

Parameters

function (callable) – A function that takes all objectives of 2 individuals as values of 2 lists as argument and returns the better individual. The objectives are considered alphabetically ordered
opt (int, optional) – Number of Pareto file

Returns

The ID of best individual that fulfills the custom function.

Return type

int

find_minimum(exclude=[], constraints={})[source]¶

Find the invidual with minimum sum of all objectives over all generations.

It is possible to exclude some objectives with the list exclude.

It is possible to give constraints on objectives as a dictionary, e.g. { “DPEAK_1_16”: 4.0 } means only individuals that have a “DPEAK_1_16” objective with a value <= 4.

Parameters

exclude (list, optional) – Objectives that should be excluded
constraints (dict, optional) – Constraints on objectives

Returns

float – Sum of objectives
int – Generation
int – Individual ID

print_individual(ind, gen=1, opt=0, pareto=False)[source]¶

Print the values of the design variables and objectives of an individual.

If pareto = True, gen is not considered.

Parameters

ind (int) – Individual identity number
gen (int, optional) – Generation, default: 1
opt (int, optional) – Optimizer, default: 0
pareto (bool, optional) – Load pareto file (default: False)

opal.analysis.SamplerStatistics module¶

class opal.analysis.SamplerStatistics.SamplerStatistics[source]¶

Bases: object

find_matches(ids1, ids2, **kwargs)[source]¶

Compare two lists

Compare two lists with indices ids1 and ids2 in order to check if they are independent (i.e. not many matches).

Parameters

ids1 (list) – Indices of 1st sample set
ids2 (list) – Indices of 2nd sample set
matches (bool, optional) – If true, the input values of the matches are returned as well, (default: False)

Returns

int – Number of matches
list – Values of matched input (only if matches is True)

opal.analysis.Statistics module¶

class opal.analysis.Statistics.Statistics[source]¶

Bases: object

Base class for all statistic functions on datasets.

It also provides functions on plain data.

__init__()[source]¶: Initialize self. See help(type(self)) for accurate signature.

gaussian_kde(data)[source]¶

Calculate the kernel density estimator directly on data.

Parameters: data (array_like) – Plain data
Returns: scipy kernel density estimator
Return type: scipy.stats.gaussian_kde

histogram(data, **kwargs)[source]¶

Compute a histogram of a dataset

Parameters

data (array_like) – Plain data
bins (int or str, optional) – Binning type or nr of bins (default: ‘sturges’) (see https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.histogram.html)
density (bool, optional) – Normalize such that integral over range is 1 (default: True).

Returns

numpy.histogram (array) – The values of the histogram. See density and weights for a description of the possible semantics.
bin_edges (array of dtype float) – Return the bin edges (length(hist)+1).

Notes

See https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.histogram.html

kurtosis(data)[source]¶

Compute the kurtosis (Fisher or Pearson) directly on data.

Parameters: data (array_like) – Plain data
Returns: kurtosis
Return type: float

mean(data)[source]¶

Calculate the arithmetic mean directly on data.

Parameters: data (array_like) – Plain data
Returns: arithmetic mean
Return type: float

moment(data, k)[source]¶

Calculate the k-th central moment directly on data.

Parameters

data (array_like) – Plain data
k (int) – The moment number, k = 1 is central mean

Returns

k-th central moment

Return type

float

skew(data)[source]¶

Calculate the skewness directly on data.

Parameters: data (array_like) – Plain data
Returns: skewness
Return type: float

opal.analysis.StdOpalOutputAnalysis module¶

class opal.analysis.StdOpalOutputAnalysis.StdOpalOutputAnalysis[source]¶

Bases: object

calcRFphases(RFcavity)[source]¶

Calculate the phases of individual cavities in the simulation

Parameters: RFcavity (str) – Name of the RFcavity as specifed in the input file
Returns: Phases
Return type: list

Examples

Check Cyclotron.ipynb in the opal/test directory

opal.analysis.TrackOrbitAnalysis module¶

class opal.analysis.TrackOrbitAnalysis.TrackOrbitAnalysis[source]¶

Bases: object

calcTurnSeparation(nsteps=- 1, angle=0.0)[source]¶

Calculate turn separation from OPAL xxx–trackOrbit.dat file

Parameters

nsteps (int) – Number of steps per turn
angle (float) – Angle of reference line in radians

Returns

float – Turn separation
float – Energy
float – Radial angle phi_r
float – Radius

Examples

Check Cyclotron.ipynb in the opal/test directory

opal.analysis.cyclotron module¶

opal.analysis.cyclotron.calcCenteringExtraction(radius, turnCorrection=1.35, phaseCorrection=0.0, amplitudeCorrection=1)[source]¶

Calculate betatron tune values and zentrierung

Based on Fortran routine from Martin Humbel “Bestimmung der horizontalen Betatronschwingungsgroessen R0, DR, A und B mit der Methode der Normalengleichung”

Parameters

radius (array_like) – Radii of turns
turnCorrection (float, optional) – Betatron oscillations per turn (tune), default value (1.35) based on PSI Ring
phaseCorrection (float, optional) – Phase correction for betatron calculation in grad (radial angle between measurement and extraction, default: 0)
amplitudeCorrection (float, optional) – Amplitude correction for betatron calculation (default: 1)

Returns

The centering values

Return type

array

Examples

Check Cyclotron.ipynb in the opal/test directory

opal.analysis.cyclotron.detect_peaks(x, mph=None, mpd=1, threshold=0, edge='rising', kpsh=False, valley=False, show=False, ax=None)[source]¶

Detect peaks in data based on their amplitude and other features.

Parameters

x (array_like) – 1D data.
mph (None or number, optional) – Detect peaks that are greater than minimum peak height (default: None).
mpd (int, optional) – detect peaks that are at least separated by minimum peak distance (in number of data, default = 1).
threshold (int, optional) – Detect peaks (valleys) that are greater (smaller) than threshold in relation to their immediate neighbors (default = 0).
edge (None or str) – {None, ‘rising’, ‘falling’, ‘both’}, optional (default = ‘rising’) for a flat peak, keep only the rising edge (‘rising’), only the falling edge (‘falling’), both edges (‘both’), or don’t detect a flat peak (None).
kpsh (bool, optional) – keep peaks with same height even if they are closer than mpd (default = False).
valley (bool, optional) – If True, detect valleys (local minima) instead of peaks.
show (bool, optional) – If True, plot data in matplotlib figure.
ax (matplotlib.axes.Axes instance, optional) –

Returns

ind – indices of the peaks in x.

Return type

array_like

Notes

The detection of valleys instead of peaks is performed internally by simply negating the data: ind_valleys = detect_peaks(-x)

The function can handle NaN’s

See this IPython Notebook 1.

References

1: http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/DetectPeaks.ipynb

Examples

>>> from detect_peaks import detect_peaks
>>> x = np.random.randn(100)
>>> x[60:81] = np.nan
>>> # detect all peaks and plot data
>>> ind = detect_peaks(x, show=True)
>>> print(ind)

>>> x = np.sin(2*np.pi*5*np.linspace(0, 1, 200)) + np.random.randn(200)/5
>>> # set minimum peak height = 0 and minimum peak distance = 20
>>> detect_peaks(x, mph=0, mpd=20, show=True)

>>> x = [0, 1, 0, 2, 0, 3, 0, 2, 0, 1, 0]
>>> # set minimum peak distance = 2
>>> detect_peaks(x, mpd=2, show=True)

>>> x = np.sin(2*np.pi*5*np.linspace(0, 1, 200)) + np.random.randn(200)/5
>>> # detection of valleys instead of peaks
>>> detect_peaks(x, mph=0, mpd=20, valley=True, show=True)

>>> x = [0, 1, 1, 0, 1, 1, 0]
>>> # detect both edges
>>> detect_peaks(x, edge='both', show=True)

>>> x = [-2, 1, -2, 2, 1, 1, 3, 0]
>>> # set threshold = 2
>>> detect_peaks(x, threshold = 2, show=True)

opal.analysis.cyclotron.eval_radial_momentum(px, py, theta)[source]¶

Evaluate the radial momentum

Parameters

px (float or array) – Data of momentum in x
py (float or array) – Data of momentum in y
theta (float) – Azimuthal angle (in radian)

Returns

Radial momentum

Return type

float

Notes

\[\begin{split}\begin{align} x & = r \sin(\theta) \\ y & = r \cos(\theta) \\ r & = \sqrt(x^2 + y^2) \\ \frac{dr}{dt} & = \frac{dr}{dx} \frac{dx}{dt} + \frac{dr}{dy} \frac{dy}{dt} \\ \frac{dr}{dt} & \sim \textrm{radial momentum}~p_r \\ \frac{dx}{dt} & \sim \textrm{horizontal momentum}~p_x \\ \frac{dy}{dt} & \sim \textrm{longitudinal momentum}~p_y \\ \frac{dr}{dx} & = \frac{1}{2 r} * 2 * x = \frac{x}{r} = \cos(\theta) \\ \frac{dr}{dy} & = \frac{1}{2 r} * 2 * y = \frac{y}{r} = \sin(\theta) \\ \rightarrow p_r & = p_x \cos(\theta) + p_y \sin(\theta) \end{align}\end{split}\]

opal.analysis.cyclotron.eval_radius(x, y)[source]¶

Evaluate the radius

\[r = \sqrt{x^2 + y^2}\]

Parameters

x (float or array) – Data of x-direction
y (float or array) – Data of y-direction

Returns

Radius

Return type

float

opal.analysis.pareto_fronts module¶

opal.analysis.pareto_fronts.delete_repeats(x, y, z=0)[source]¶

Delete repeated pareto front values, if any.

Parameters

x (array_like) – 1D array of first objective values
y (array_like) – 1D array of second objective values
z (array_like, optional) – ND array of second design variables

Returns

Return type

df (pandas db) database with out repeats

opal.analysis.pareto_fronts.get_all_data_db(dbpath)[source]¶

Get objectives and design variables

Get all objectives and design variables from every generation in an optimzation database. Databases are made using OPAL output from json files or stat files. Functions to make databases can be found in mldb.py.

Parameters: db (str) – Path to pickle file containing database made with mldb.py
Returns: data – Dictonary containing all objectives and design values in optimization database.
Return type: dict

opal.analysis.pareto_fronts.pareto_pts(x, y)[source]¶

Find Pareto points

Find Pareto points for 2 objectives, given all data recorded by optimization run. These points are calculated independent of generation. i.e. best points from all generations are found and saved.

Parameters

x (array_like) – 1D array of first objective values
y (array_like) – 1D array of second objective values
dvars (array_like, optional) – ND array of design variables

Returns

pfdict – Dictionary that holds pareto front values and corresponding design values

Return type

dict

opal.analysis.pareto_fronts.scaleData(vals)[source]¶

Scale 1D data array from 0 to 1.

Used to compare objectives with different units.

Parameters: vals (array_like) – 1D array that holds any opal data
Returns: sacaled_vals – 1D array scaled from 0 to 1
Return type: array_like