# Function¶

class Function(*args)

Function base class.

Notes

A function acts on points to produce points: .

A function enables to evaluate its gradient and its hessian when mathematically defined.

Examples

Create a Function from a list of analytical formulas and descriptions of the input vector and the output vector :

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x0', 'x1'],
...                         ['x0 + x1', 'x0 - x1'])
>>> print(f([1, 2]))
[3,-1]


Create a Function from strings:

>>> import openturns as ot
>>> f = ot.SymbolicFunction('x', '2.0*sqrt(x)')
>>> print(f(([16],[4])))
[ y0 ]
0 : [ 8  ]
1 : [ 4  ]


Create a Function from a Python function:

>>> def a_function(X):
...     return [X[0] + X[1]]
>>> f = ot.PythonFunction(2, 1, a_function)
>>> print(f(((10, 5),(6, 7))))
[ y0 ]
0 : [ 15 ]
1 : [ 13 ]


See PythonFunction for further details.

Create a Function from a Python class:

>>> class FUNC(OpenTURNSPythonFunction):
...     def __init__(self):
...         super(FUNC, self).__init__(2, 1)
...         self.setInputDescription(['R', 'S'])
...         self.setOutputDescription(['T'])
...     def _exec(self, X):
...         Y = [X[0] + X[1]]
...         return Y
>>> F = FUNC()
>>> myFunc = Function(F)
>>> print(myFunc((1.0, 2.0)))
[3]


See PythonFunction for further details.

Create a Function from another Function:

>>> f = ot.SymbolicFunction(ot.Description.BuildDefault(4, 'x'),
...                         ['x0', 'x0 + x1', 'x0 + x2 + x3'])


Then create another function by setting x1=4 and x3=10:

>>> g = ot.ParametricFunction(f, [3, 1], [10.0, 4.0], True)
>>> print(g.getInputDescription())
[x0,x2]
>>> print(g((1, 2)))
[1,5,13]


Or by setting x0=6 and x2=5:

>>> g = ot.ParametricFunction(f, [3, 1], [6.0, 5.0], False)
>>> print(g.getInputDescription())
[x3,x1]
>>> print(g((1, 2)))
[6,8,12]


Create a Function from another Function and by using a comparison operator:

>>> analytical = ot.SymbolicFunction(['x0','x1'], ['x0 + x1'])
>>> indicator = ot.IndicatorFunction(ot.LevelSet(analytical, ot.Less(), 0.0))
>>> print(indicator([2, 3]))
[0]
>>> print(indicator([2, -3]))
[1]


Create a Function from a collection of functions:

>>> functions = list()
>>> functions.append(ot.SymbolicFunction(['x1', 'x2', 'x3'],
...                                      ['x1^2 + x2', 'x1 + x2 + x3']))
>>> functions.append(ot.SymbolicFunction(['x1', 'x2', 'x3'],
...                                      ['x1 + 2 * x2 + x3', 'x1 + x2 - x3']))
>>> myFunction = ot.AggregatedFunction(functions)
>>> print(myFunction([1.0, 2.0, 3.0]))
[3,6,8,0]


Create a Function which is the linear combination linComb of the functions defined in functionCollection with scalar weights defined in scalarCoefficientColl:

where and then the linear combination is:

>>> myFunction2 = ot.LinearCombinationFunction(functions, [2.0, 4.0])
>>> print(myFunction2([1.0, 2.0, 3.0]))
[38,12]


Create a Function which is the linear combination vectLinComb of the scalar functions defined in scalarFunctionCollection with vectorial weights defined in vectorCoefficientColl:

If where and where

>>> functions=list()
>>> functions.append(ot.SymbolicFunction(['x1', 'x2', 'x3'],
...                                      ['x1 + 2 * x2 + x3']))
>>> functions.append(ot.SymbolicFunction(['x1', 'x2', 'x3'],
...                                      ['x1^2 + x2']))
>>> myFunction2 = ot.DualLinearCombinationFunction(functions, [[2., 4.], [3., 1.]])
>>> print(myFunction2([1, 2, 3]))
[25,35]


Create a Function from values of the inputs and the outputs:

>>> inputSample = [[1.0, 1.0], [2.0, 2.0]]
>>> outputSample = [[4.0], [5.0]]
>>> database = ot.DatabaseFunction(inputSample, outputSample)
>>> x = [1.8]*database.getInputDimension()
>>> print(database(x))
[5]


Create a Function which is the composition function :

>>> g = ot.SymbolicFunction(['x1', 'x2'],
...                         ['x1 + x2','3 * x1 * x2'])
>>> f = ot.SymbolicFunction(['x1', 'x2'], ['2 * x1 - x2'])
>>> composed = ot.ComposedFunction(f, g)
>>> print(composed([3, 4]))
[-22]


Methods

 __call__(*args) Call self as a function. draw(*args) Draw the output of function as a Graph. Accessor to the number of times the function has been called. Accessor to the object's name. Accessor to the description of the inputs and outputs. Accessor to the evaluation function. Accessor to the number of times the function has been called. Accessor to the gradient function. Accessor to the number of times the gradient of the function has been called. Accessor to the hessian function. Accessor to the number of times the hessian of the function has been called. Accessor to the object's id. Accessor to the underlying implementation. Accessor to the description of the input vector. Accessor to the dimension of the input vector. getMarginal(*args) Accessor to marginal. Accessor to the object's name. Accessor to the description of the output vector. Accessor to the number of the outputs. Accessor to the parameter values. Accessor to the parameter description. Accessor to the dimension of the parameter. gradient(inP) Return the Jacobian transposed matrix of the function at a point. hessian(inP) Return the hessian of the function at a point. Accessor to the linearity of the function. Accessor to the linearity of the function with regard to a specific variable. Accessor to the gradient against the parameter. setDescription(description) Accessor to the description of the inputs and outputs. setEvaluation(evaluation) Accessor to the evaluation function. setGradient(gradient) Accessor to the gradient function. setHessian(hessian) Accessor to the hessian function. setInputDescription(inputDescription) Accessor to the description of the input vector. setName(name) Accessor to the object's name. setOutputDescription(inputDescription) Accessor to the description of the output vector. setParameter(parameter) Accessor to the parameter values. setParameterDescription(description) Accessor to the parameter description.
__init__(*args)
draw(*args)

Draw the output of function as a Graph.

Available usages:

draw(inputMarg, outputMarg, centralPoint, xiMin, xiMax, ptNb)

draw(firstInputMarg, secondInputMarg, outputMarg, centralPoint, xiMin_xjMin, xiMax_xjMax, ptNbs)

draw(xiMin, xiMax, ptNb)

draw(xiMin_xjMin, xiMax_xjMax, ptNbs)

Parameters:
outputMarg, inputMargint,

outputMarg is the index of the marginal to draw as a function of the marginal with index inputMarg.

firstInputMarg, secondInputMargint,

In the 2D case, the marginal outputMarg is drawn as a function of the two marginals with indexes firstInputMarg and secondInputMarg.

centralPointsequence of float

Central point with dimension equal to the input dimension of the function.

xiMin, xiMaxfloat

Define the interval where the curve is plotted.

xiMin_xjMin, xiMax_xjMaxsequence of float of dimension 2.

In the 2D case, define the intervals where the curves are plotted.

ptNbint or list of ints of dimension 2

The number of points to draw the curves.

Notes

We note where and , with and .

• In the first usage:

Draws graph of the given 1D outputMarg marginal as a function of the given 1D inputMarg marginal with respect to the variation of in the interval , when all the other components of are fixed to the corresponding components of the centralPoint . Then OpenTURNS draws the graph:

for any where is defined by the equation:

• In the second usage:

Draws the iso-curves of the given outputMarg marginal as a function of the given 2D firstInputMarg and secondInputMarg marginals with respect to the variation of in the interval , when all the other components of are fixed to the corresponding components of the centralPoint . Then OpenTURNS draws the graph:

for any where is defined by the equation:

• In the third usage:

The same as the first usage but only for function .

• In the fourth usage:

The same as the second usage but only for function .

Examples

>>> import openturns as ot
>>> from openturns.viewer import View
>>> f = ot.SymbolicFunction('x', 'sin(2*pi_*x)*exp(-x^2/2)')
>>> graph = f.draw(-1.2, 1.2, 100)
>>> View(graph).show()

getCallsNumber()

Accessor to the number of times the function has been called.

Returns:
calls_numberint

Integer that counts the number of times the function has been called since its creation.

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

The object class name (object.__class__.__name__).

getDescription()

Accessor to the description of the inputs and outputs.

Returns:
descriptionDescription

Description of the inputs and the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y0]

getEvaluation()

Accessor to the evaluation function.

Returns:
functionEvaluationImplementation

The evaluation function.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getEvaluation())
[x1,x2]->[2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6]

getEvaluationCallsNumber()

Accessor to the number of times the function has been called.

Returns:
evaluation_calls_numberint

Integer that counts the number of times the function has been called since its creation.

Returns:
gradientGradientImplementation

Accessor to the number of times the gradient of the function has been called.

Returns:

Integer that counts the number of times the gradient of the Function has been called since its creation. Note that if the gradient is implemented by a finite difference method, the gradient calls number is equal to 0 and the different calls are counted in the evaluation calls number.

getHessian()

Accessor to the hessian function.

Returns:
hessianHessianImplementation

The hessian function.

getHessianCallsNumber()

Accessor to the number of times the hessian of the function has been called.

Returns:
hessian_calls_numberint

Integer that counts the number of times the hessian of the Function has been called since its creation. Note that if the hessian is implemented by a finite difference method, the hessian calls number is equal to 0 and the different calls are counted in the evaluation calls number.

getId()

Accessor to the object’s id.

Returns:
idint

Internal unique identifier.

getImplementation()

Accessor to the underlying implementation.

Returns:
implImplementation

A copy of the underlying implementation object.

getInputDescription()

Accessor to the description of the input vector.

Returns:
descriptionDescription

Description of the input vector.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getInputDescription())
[x1,x2]

getInputDimension()

Accessor to the dimension of the input vector.

Returns:
inputDimint

Dimension of the input vector .

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getInputDimension())
2

getMarginal(*args)

Accessor to marginal.

Parameters:
indicesint or list of ints

Set of indices for which the marginal is extracted.

Returns:
marginalFunction

Function corresponding to either or , with and .

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getOutputDescription()

Accessor to the description of the output vector.

Returns:
descriptionDescription

Description of the output vector.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getOutputDescription())
[y0]

getOutputDimension()

Accessor to the number of the outputs.

Returns:
number_outputsint

Dimension of the output vector .

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getOutputDimension())
1

getParameter()

Accessor to the parameter values.

Returns:
parameterPoint

The parameter values.

getParameterDescription()

Accessor to the parameter description.

Returns:
parameterDescription

The parameter description.

getParameterDimension()

Accessor to the dimension of the parameter.

Returns:
parameterDimensionint

Dimension of the parameter.

Return the Jacobian transposed matrix of the function at a point.

Parameters:
pointsequence of float

Point where the Jacobian transposed matrix is calculated.

Returns:
gradientMatrix

The Jacobian transposed matrix of the function at point.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6','x1 + x2'])
[[ 13.5345   1       ]
[  4.00001  1       ]]

hessian(inP)

Return the hessian of the function at a point.

Parameters:
pointsequence of float

Point where the hessian of the function is calculated.

Returns:
hessianSymmetricTensor

Hessian of the function at point.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6','x1 + x2'])
>>> print(f.hessian([3.14, 4]))
sheet #0
[[ 20          -0.00637061 ]
[ -0.00637061  0          ]]
sheet #1
[[  0           0          ]
[  0           0          ]]

isLinear()

Accessor to the linearity of the function.

Returns:
linearbool

True if the function is linear, False otherwise.

isLinearlyDependent(index)

Accessor to the linearity of the function with regard to a specific variable.

Parameters:
indexint

The index of the variable with regard to which linearity is evaluated.

Returns:
linearbool

True if the function is linearly dependent on the specified variable, False otherwise.

Accessor to the gradient against the parameter.

Returns:
gradientMatrix

setDescription(description)

Accessor to the description of the inputs and outputs.

Parameters:
descriptionsequence of str

Description of the inputs and the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y0]
>>> f.setDescription(['a','b','y'])
>>> print(f.getDescription())
[a,b,y]

setEvaluation(evaluation)

Accessor to the evaluation function.

Parameters:
functionEvaluationImplementation

The evaluation function.

Parameters:
gradient_functionGradientImplementation

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
...  f.getEvaluation()))

setHessian(hessian)

Accessor to the hessian function.

Parameters:
hessian_functionHessianImplementation

The hessian function.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> f.setHessian(ot.CenteredFiniteDifferenceHessian(
...  ot.ResourceMap.GetAsScalar('CenteredFiniteDifferenceHessian-DefaultEpsilon'),
...  f.getEvaluation()))

setInputDescription(inputDescription)

Accessor to the description of the input vector.

Parameters:
descriptionDescription

Description of the input vector.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

setOutputDescription(inputDescription)

Accessor to the description of the output vector.

Parameters:
descriptionDescription

Description of the output vector.

setParameter(parameter)

Accessor to the parameter values.

Parameters:
parametersequence of float

The parameter values.

setParameterDescription(description)

Accessor to the parameter description.

Parameters:
parameterDescription

The parameter description.

## Examples using the class¶

Estimate moments from sample

Estimate moments from sample

Sample manipulation

Sample manipulation

Estimate Wilks and empirical quantile

Estimate Wilks and empirical quantile

Compute squared SRC indices confidence intervals

Compute squared SRC indices confidence intervals

Model a singular multivariate distribution

Model a singular multivariate distribution

Estimate a GEV on the Port Pirie sea-levels data

Estimate a GEV on the Port Pirie sea-levels data

Estimate a GEV on the Fremantle sea-levels data

Estimate a GEV on the Fremantle sea-levels data

Estimate a GEV on race times data

Estimate a GEV on race times data

Kolmogorov-Smirnov : understand the p-value

Kolmogorov-Smirnov : understand the p-value

Kolmogorov-Smirnov : get the statistics distribution

Kolmogorov-Smirnov : get the statistics distribution

Estimate a non stationary covariance function

Estimate a non stationary covariance function

Create a conditional distribution

Create a conditional distribution

Create your own distribution given its quantile function

Create your own distribution given its quantile function

Create a Bayes distribution

Create a Bayes distribution

Generate random variates by inverting the CDF

Generate random variates by inverting the CDF

Transform a distribution

Transform a distribution

Overview of univariate distribution management

Overview of univariate distribution management

Composite random vector

Composite random vector

Create a functional basis process

Create a functional basis process

Add a trend to a process

Add a trend to a process

Create a custom covariance model

Create a custom covariance model

Use the Box-Cox transformation

Use the Box-Cox transformation

Create a process from random vectors and processes

Create a process from random vectors and processes

Draw fields

Draw fields

Trend computation

Trend computation

Compare covariance models

Compare covariance models

Create a mesh

Create a mesh

Create a linear least squares model

Create a linear least squares model

Create a general linear model metamodel

Create a general linear model metamodel

Taylor approximations

Taylor approximations

Create a linear model

Create a linear model

Mixture of experts

Mixture of experts

Perform stepwise regression

Perform stepwise regression

Over-fitting and model selection

Over-fitting and model selection

Apply a transform or inverse transform on your polynomial chaos

Apply a transform or inverse transform on your polynomial chaos

Fit a distribution from an input sample

Fit a distribution from an input sample

Polynomial chaos exploitation

Polynomial chaos exploitation

Polynomial chaos over database

Polynomial chaos over database

Compute grouped indices for the Ishigami function

Compute grouped indices for the Ishigami function

Validate a polynomial chaos

Validate a polynomial chaos

Create a polynomial chaos metamodel by integration on the cantilever beam

Create a polynomial chaos metamodel by integration on the cantilever beam

Create a polynomial chaos metamodel

Create a polynomial chaos metamodel

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Plot enumeration rules

Plot enumeration rules

Polynomial chaos expansion cross-validation

Polynomial chaos expansion cross-validation

Polynomial chaos is sensitive to the degree

Polynomial chaos is sensitive to the degree

Compute Sobol’ indices confidence intervals

Compute Sobol' indices confidence intervals

Kriging: propagate uncertainties

Kriging: propagate uncertainties

Kriging : multiple input dimensions

Kriging : multiple input dimensions

Kriging : draw the likelihood

Kriging : draw the likelihood

Kriging : cantilever beam model

Kriging : cantilever beam model

Kriging: choose an arbitrary trend

Kriging: choose an arbitrary trend

Kriging the cantilever beam model using HMAT

Kriging the cantilever beam model using HMAT

Example of multi output Kriging on the fire satellite model

Example of multi output Kriging on the fire satellite model

Kriging : generate trajectories from a metamodel

Kriging : generate trajectories from a metamodel

Kriging: choose a polynomial trend on the beam model

Kriging: choose a polynomial trend on the beam model

Kriging with an isotropic covariance function

Kriging with an isotropic covariance function

Kriging: metamodel of the Branin-Hoo function

Kriging: metamodel of the Branin-Hoo function

Kriging : quick-start

Kriging : quick-start

Sequentially adding new points to a kriging

Sequentially adding new points to a kriging

Kriging :configure the optimization solver

Kriging :configure the optimization solver

Kriging: choose a polynomial trend

Kriging: choose a polynomial trend

Kriging: metamodel with continuous and categorical variables

Kriging: metamodel with continuous and categorical variables

Viscous free fall: metamodel of a field function

Viscous free fall: metamodel of a field function

Metamodel of a field function

Metamodel of a field function

Estimate moments from Taylor expansions

Estimate moments from Taylor expansions

Simulate an Event

Simulate an Event

Use the post-analytical importance sampling algorithm

Use the post-analytical importance sampling algorithm

Specify a simulation algorithm

Specify a simulation algorithm

Estimate a flooding probability

Estimate a flooding probability

Create a threshold event

Create a threshold event

Exploitation of simulation algorithm results

Exploitation of simulation algorithm results

Use the FORM algorithm in case of several design points

Use the FORM algorithm in case of several design points

Non parametric Adaptive Importance Sampling (NAIS)

Non parametric Adaptive Importance Sampling (NAIS)

Subset Sampling

Subset Sampling

Use the FORM - SORM algorithms

Use the FORM - SORM algorithms

Create a domain event

Create a domain event

Test the design point with the Strong Maximum Test

Test the design point with the Strong Maximum Test

Time variant system reliability problem

Time variant system reliability problem

Create unions or intersections of events

Create unions or intersections of events

An illustrated example of a FORM probability estimate

An illustrated example of a FORM probability estimate

Using the FORM - SORM algorithms on a nonlinear function

Using the FORM - SORM algorithms on a nonlinear function

Estimate Sobol indices on a field to point function

Estimate Sobol indices on a field to point function

Parallel coordinates graph as sensitivity tool

Parallel coordinates graph as sensitivity tool

Estimate Sobol’ indices for a function with multivariate output

Estimate Sobol' indices for a function with multivariate output

Sobol’ sensitivity indices from chaos

Sobol' sensitivity indices from chaos

Use the ANCOVA indices

Use the ANCOVA indices

The HSIC sensitivity indices: the Ishigami model

The HSIC sensitivity indices: the Ishigami model

Example of sensitivity analyses on the wing weight model

Example of sensitivity analyses on the wing weight model

Create a composed function

Create a composed function

Create a parametric function

Create a parametric function

Create an aggregated function

Create an aggregated function

Create a linear combination of functions

Create a linear combination of functions

Create a symbolic function

Create a symbolic function

Increase the output dimension of a function

Increase the output dimension of a function

Create a Python function

Create a Python function

Increase the input dimension of a function

Increase the input dimension of a function

Defining Python and symbolic functions: a quick start introduction to functions

Defining Python and symbolic functions: a quick start introduction to functions

Create multivariate functions

Create multivariate functions

Create a multivariate basis of functions from scalar multivariable functions

Create a multivariate basis of functions from scalar multivariable functions

Value function

Value function

Vertex value function

Vertex value function

Define a connection function with a field output

Define a connection function with a field output

Logistic growth model

Logistic growth model

Function manipulation

Function manipulation

Link to a computer code with coupling tools

Link to a computer code with coupling tools

Generate flooding model observations

Generate flooding model observations

Calibrate a parametric model: a quick-start guide to calibration

Calibrate a parametric model: a quick-start guide to calibration

Generate observations of the Chaboche mechanical model

Generate observations of the Chaboche mechanical model

Calibration without observed inputs

Calibration without observed inputs

Calibration of the logistic model

Calibration of the logistic model

Calibration of the deflection of a tube

Calibration of the deflection of a tube

Calibration of the flooding model

Calibration of the flooding model

Calibration of the Chaboche mechanical model

Calibration of the Chaboche mechanical model

Gibbs sampling of the posterior distribution

Gibbs sampling of the posterior distribution

Sampling from an unnormalized probability density

Sampling from an unnormalized probability density

Posterior sampling using a PythonDistribution

Posterior sampling using a PythonDistribution

Bayesian calibration of a computer code

Bayesian calibration of a computer code

Bayesian calibration of the flooding model

Bayesian calibration of the flooding model

Linear Regression with interval-censored observations

Linear Regression with interval-censored observations

Estimate an integral

Estimate an integral

Iterated Functions System

Iterated Functions System

Compute leave-one-out error of a polynomial chaos expansion

Compute leave-one-out error of a polynomial chaos expansion

Compute confidence intervals of a regression model from data

Compute confidence intervals of a regression model from data

Compute confidence intervals of a univariate noisy function

Compute confidence intervals of a univariate noisy function

Mix/max search and sensitivity from design

Mix/max search and sensitivity from design

Optimization with constraints

Optimization with constraints

Optimization using NLopt

Optimization using NLopt

Mix/max search using optimization

Mix/max search using optimization

Control algorithm termination

Control algorithm termination

Optimization using bonmin

Optimization using bonmin

Multi-objective optimization using Pagmo

Multi-objective optimization using Pagmo

Quick start guide to optimization

Quick start guide to optimization

Optimization of the Rastrigin test function

Optimization of the Rastrigin test function

Optimization using dlib

Optimization using dlib

EfficientGlobalOptimization examples

EfficientGlobalOptimization examples

Plot the log-likelihood contours of a distribution

Plot the log-likelihood contours of a distribution

A quick start guide to graphs

A quick start guide to graphs