Design of Experiment API

`UQPyL.doe`

The doe module generates design samples from a Problem input space. Samplers first generate samples in unit space, then map them to the problem bounds through problem.unit_to_space().

Import

python

from UQPyL.doe import LHS, Random, FFD, Sobol

Public Objects

Object	Role
`Sampler`	Base class for DOE samplers.
`Random`	Uniform random sampling.
`LHS`	Latin hypercube sampling.
`FFD`	Full factorial design.
`Sobol`	Sobol low-discrepancy sequence sampling.
`SaltelliDesign`	Saltelli design for Sobol sensitivity analysis.
`FASTDesign`	FAST design for sensitivity analysis.
`MorrisDesign`	Morris trajectory design for sensitivity analysis.

`Sampler`

Sampler is the base interface used by most DOE classes.

Methods

Method	Returns	Meaning
`sample(problem, nSamples=None, seed=None, nt=None)`	`np.ndarray`	Generate samples in the problem space.
`sampleWithMeta(problem, nSamples=None, seed=None, nt=None)`	`(np.ndarray, dict)`	Generate samples and metadata.

Parameter	Meaning
`problem`	A `ProblemBase` instance, such as `Problem`, `ModelProblem`, or a benchmark problem.
`nSamples`	Number of samples or base sample size, depending on the sampler.
`seed`	Optional random seed.
`nt`	Legacy alias for `nSamples`. If both are provided, they must match.

Example:

python

from UQPyL.doe import LHS
from UQPyL.problem import Sphere


problem = Sphere(nInput=3)
sampler = LHS()

X = sampler.sample(problem, nSamples=10, seed=123)
print(X.shape)

Use sampleWithMeta() when downstream methods need design metadata:

python

X, meta = sampler.sampleWithMeta(problem, nSamples=10, seed=123)

print(meta["designType"])

`Random`

Uniform random sampler.

python

Random()

Method	Meaning
`sample(problem, nSamples=None, seed=None, nt=None)`	Generate random samples in the problem space.
`sampleWithMeta(problem, nSamples=None, seed=None, nt=None)`	Generate random samples with metadata.

Metadata:

Key	Meaning
`designType`	Always `"random"`.
`seed`	Seed used to initialize the random generator.

`LHS`

Latin hypercube sampler.

python

LHS(criterion="classic", iterations=5)

Parameter	Meaning
`criterion`	LHS criterion. One of `"classic"`, `"center"`, `"maximin"`, `"center_maximin"`, or `"correlation"`.
`iterations`	Number of candidate designs tested by optimized criteria.

Method	Meaning
`sample(problem, nSamples=None, seed=None, nt=None)`	Generate LHS samples in the problem space.
`sampleWithMeta(problem, nSamples=None, seed=None, nt=None)`	Generate LHS samples with metadata.

Metadata:

Key	Meaning
`designType`	Always `"lhs"`.
`criterion`	Criterion used by the sampler.
`iterations`	Iteration count for optimized criteria.
`seed`	Seed used to initialize the random generator.

Example:

python

from UQPyL.doe import LHS
from UQPyL.problem import Sphere


problem = Sphere(nInput=2)
sampler = LHS(criterion="maximin", iterations=10)

X, meta = sampler.sampleWithMeta(problem, nSamples=20, seed=123)
print(X.shape)
print(meta["criterion"])

`FFD`

Full factorial design.

python

FFD()

Unlike most samplers, FFD uses levels instead of nSamples.

Method	Returns	Meaning
`sample(problem, levels, seed=None)`	`np.ndarray`	Generate the full factorial grid in the problem space.
`sampleWithMeta(problem, levels, seed=None)`	`(np.ndarray, dict)`	Generate the grid with metadata.

Parameter	Meaning
`levels`	Scalar level count applied to all variables, or one level count per variable.
`seed`	Accepted for API consistency. It does not affect the deterministic grid.

Metadata:

Key	Meaning
`designType`	Always `"full_fact"`.
`levels`	Level count used for each variable.
`seed`	Always `None`.

Example:

python

from UQPyL.doe import FFD
from UQPyL.problem import Sphere


problem = Sphere(nInput=2)
sampler = FFD()

X, meta = sampler.sampleWithMeta(problem, levels=[3, 4])
print(X.shape)
print(meta["levels"])

`Sobol`

Sobol low-discrepancy sequence sampler.

python

Sobol(scramble=True, skipValue=0)

Parameter	Meaning
`scramble`	Whether to scramble the Sobol sequence.
`skipValue`	Number of initial Sobol points to skip.

Method	Meaning
`sample(problem, nSamples=None, seed=None, nt=None)`	Generate Sobol samples in the problem space.
`sampleWithMeta(problem, nSamples, seed=None)`	Generate Sobol samples with metadata.

Metadata:

Key	Meaning
`designType`	Always `"sobol_sequence"`.
`scramble`	Whether scrambling was enabled.
`skipValue`	Number of skipped initial points.
`seed`	Seed used when `scramble=True`; otherwise `None`.

nSamples should usually be a power of 2 for balanced Sobol samples. skipValue must be a non-negative integer and cannot exceed nSamples.

`SaltelliDesign`

Saltelli design for Sobol sensitivity analysis.

python

SaltelliDesign(scramble=True, skipValue=0, secondOrder=False)

Parameter	Meaning
`scramble`	Whether to scramble the Sobol base sequence.
`skipValue`	Number of initial Sobol points to skip.
`secondOrder`	Whether to generate the second-order design.

Method	Meaning
`sample(problem, nSamples=None, seed=None, nt=None)`	Generate the design in the problem space.
`sampleWithMeta(problem, N, seed=None)`	Generate the design with metadata.

For a problem with D inputs and base sample size N, output shape is:

`secondOrder`	Shape
`False`	`((D + 2) * N, D)`
`True`	`((2 * D + 2) * N, D)`

Metadata:

Key	Meaning
`designType`	Always `"saltelli"`.
`N`	Base sample size.
`secondOrder`	Whether second-order design was generated.
`skipValue`	Number of skipped Sobol points.
`scramble`	Whether scrambling was enabled.
`blockSize`	Number of rows per base sample.
`seed`	Seed used when `scramble=True`; otherwise `None`.

N should usually be a power of 2. skipValue must be a non-negative integer and cannot exceed N.

`FASTDesign`

FAST design for sensitivity analysis.

python

FASTDesign(M=4)

Parameter	Meaning
`M`	FAST interference parameter. Must be a positive integer.

Method	Meaning
`sample(problem, nSamples=None, seed=None, nt=None)`	Generate the FAST design in the problem space.
`sampleWithMeta(problem, N, seed=None)`	Generate the FAST design with metadata.

For a problem with D inputs and base sample size N, output shape is:

text

(N * D, D)

N must satisfy:

text

N > 4 * M^2

Metadata:

Key	Meaning
`designType`	Always `"fast"`.
`N`	Base sample size.
`M`	FAST interference parameter.
`blockSize`	Rows per input variable.
`seed`	Seed used to initialize the random generator.

`MorrisDesign`

Morris trajectory design for sensitivity analysis.

python

MorrisDesign(numLevels=4)

Parameter	Meaning
`numLevels`	Number of Morris levels. Must be an even integer greater than or equal to 4.

Method	Meaning
`sample(problem, nSamples=None, seed=None, nt=None)`	Generate Morris trajectories in the problem space.
`sampleWithMeta(problem, numTrajectory, seed=None)`	Generate Morris trajectories with metadata.

For a problem with D inputs and numTrajectory trajectories, output shape is:

text

(numTrajectory * (D + 1), D)

Metadata:

Key	Meaning
`designType`	Always `"morris"`.
`numTrajectory`	Number of trajectories.
`numLevels`	Number of Morris levels.
`trajectorySize`	Rows per trajectory, equal to `D + 1`.
`seed`	Seed used to initialize the random generator.

Example:

python

from UQPyL.doe import MorrisDesign
from UQPyL.problem import Sphere


problem = Sphere(nInput=3)
sampler = MorrisDesign(numLevels=4)

X, meta = sampler.sampleWithMeta(problem, numTrajectory=10, seed=21)
print(X.shape)
print(meta["trajectorySize"])

Design of Experiment API

Design of Experiment API ​

UQPyL.doe ​

Import ​

Public Objects ​

Sampler ​

Methods ​

Random ​

LHS ​

FFD ​

Sobol ​

SaltelliDesign ​

FASTDesign ​

MorrisDesign ​

Design of Experiment API

`UQPyL.doe`

Import

Public Objects

`Sampler`

Methods

`Random`

`LHS`

`FFD`

`Sobol`

`SaltelliDesign`

`FASTDesign`

`MorrisDesign`