The Python package p7ot for pSeven Core integration in OpenTURNS

The purpose of this package is to make pSeven Core capabilities compatible with OpenTURNS (OT):

1. To be able to use pSeven Core GTOpt in OpenTURNS for solving optimization problems that are defined and post-processed with the dedicated OT classes: OptimizationProblem, OptimizationSolver, and OptimizationResult.
2. To be able to import surrogate models generated by pSeven Core GTApprox into OpenTURNS as an OT NumericalMathFunction.
3. To be able to use pSeven Core GTDoE in OpenTURNS through the dedicated OT class Experiment.

REQUIREMENTS

• pSeven Core 6.9
• OpenTURNS 1.7 or 1.8 (OpenTURNS 1.8 for ExperimentImplementation exchange)
• numpy 1.6.1

p7ot has been tested with OpenTURNS 1.7 and 1.8 on Linux operating systems.

QUICK START

Just write in Python

>>> import openturns as ot
>>> import p7ot

Design of Experiment

Sequential design of experiment:

>>> experiment = p7ot.Sequence(bounds=ot.Interval([0]*3, [10]*3), count=10, technique="SobolSeq")
>>> print experiment.generate()
0 : [ 0     0     0     ]
1 : [ 5     5     5     ]
2 : [ 7.5   2.5   2.5   ]
3 : [ 2.5   7.5   7.5   ]
4 : [ 3.75  3.75  6.25  ]
5 : [ 8.75  8.75  1.25  ]
6 : [ 6.25  1.25  8.75  ]
7 : [ 1.25  6.25  3.75  ]
8 : [ 1.875 3.125 9.375 ]
9 : [ 6.875 8.125 4.375 ]

Latin Hypercube Sampling (LHS) design of experiment:

>>> experiment = p7ot.LHS(bounds=ot.Interval([0]*3, [10]*3), count=10, useOptimized=True)
>>> print experiment.generate()
0 : [ 1.5 7.5 6.5 ]
1 : [ 5.5 8.5 4.5 ]
2 : [ 4.5 4.5 8.5 ]
3 : [ 0.5 1.5 7.5 ]
4 : [ 8.5 6.5 2.5 ]
5 : [ 3.5 5.5 1.5 ]
6 : [ 6.5 0.5 3.5 ]
7 : [ 2.5 9.5 9.5 ]
8 : [ 7.5 3.5 0.5 ]
9 : [ 9.5 2.5 5.5 ]

Adaptive Blackbox-Based design of experiment:

>>> blackbox = ot.NumericalMathFunction(['x1', 'x2', 'x3'], ['x1^2 + x2^2 + x3^2'])
>>> experiment = p7ot.AdaptiveBlackbox(blackbox=blackbox, bounds=ot.Interval([0]*3, [10]*3), count=10)
>>> print experiment.generate()
0 : [ 8.33333   5         0.555556  ]
1 : [ 0.555556  7.22222   1.66667   ]
2 : [ 6.11111   3.88889   5         ]
3 : [ 9.44444   8.33333   7.22222   ]
4 : [ 5         9.44444   6.11111   ]
5 : [ 1.66667   2.77778   9.44444   ]
6 : [ 7.22222   0.555556  8.33333   ]
7 : [ 3.88889   6.11111   3.88889   ]
8 : [ 2.77778   1.66667   2.77778   ]
9 : [ 0.0334393 9.99071   9.97424   ]

Approximation model

>>> from da.p7core import gtapprox
>>> import numpy as np
>>> x = np.random.random((10, 2))
>>> y = [x1 * x2 for x1, x2 in x]
>>> p7_model = gtapprox.Builder().build(x,y)  # p7core model
>>> print p7_model.calc([0.2, 0.3])
[ 0.06139608]
>>> p7ot_function = p7ot.ModelFunction(p7_model)  # p7ot function
>>> print p7ot_function([0.2, 0.3])
[0.0613961]
>>> ot_function = ot.NumericalMathFunction(p7ot_function)  # OpenTURNS function
>>> print ot_function([0.2, 0.3])  
[0.0613961]

Optimization

>>> rosenbrock_function = ot.NumericalMathFunction(['x1', 'x2', 'x3', 'x4'], ['100*(x4-x3^2)^2+(x3-1)^2+' +
...                                                                           '100*(x3-x2^2)^2+(x2-1)^2+' +
...                                                                           '100*(x2-x1^2)^2+(x1-1)^2'])
>>> bounds = ot.Interval([-500]*4, [500]*4)
>>> problem = ot.OptimizationProblem()
>>> problem.setObjective(rosenbrock_function)
>>> problem.setBounds(bounds)
>>> solver = p7ot.GTOpt(problem)  # p7core optimization algorithm
>>> solver.setStartingPoint(bounds.getUpperBound())
>>> solver.run()
>>> result = solver.getResult()
>>> print result.getIterationNumber()
1096
>>> print result.getOptimalPoint()
[0.999933,0.999867,0.999735,0.999468]
>>> print result.getOptimalValue()
[9.29851e-08]

DOCUMENTATION

For any additional information about algorithms used and options description see pSeven Core Documentation

LICENSE

p7ot is distributed under the Lesser General Public License.
Please see the LICENSE.GPL, LICENSE.LGPL files for details of the license.