API Documentation

Documentation for ExperimentalDesign.jl's API.

API Documentation

Index

ExperimentalDesign.AbstractDesign
ExperimentalDesign.AbstractFactorialDesign
ExperimentalDesign.AbstractOptimalDesign
ExperimentalDesign.AbstractScreeningDesign
ExperimentalDesign.BoxBehnken
ExperimentalDesign.BoxBehnken
ExperimentalDesign.BoxBehnken
ExperimentalDesign.CategoricalFactor
ExperimentalDesign.CategoricalFactor
ExperimentalDesign.CentralComposite
ExperimentalDesign.CentralComposite
ExperimentalDesign.CentralComposite
ExperimentalDesign.DesignDistribution
ExperimentalDesign.DesignDistribution
ExperimentalDesign.DesignDistribution
ExperimentalDesign.DesignDistribution
ExperimentalDesign.DesignDistribution
ExperimentalDesign.FractionalFactorial2Level
ExperimentalDesign.FractionalFactorial2Level
ExperimentalDesign.FullFactorial
ExperimentalDesign.FullFactorial
ExperimentalDesign.FullFactorial
ExperimentalDesign.FullFactorial
ExperimentalDesign.FullFactorial
ExperimentalDesign.OptimLHCDesign
ExperimentalDesign.OptimLHCDesign
ExperimentalDesign.OptimLHCDesign
ExperimentalDesign.OptimalDesign
ExperimentalDesign.OptimalDesign
ExperimentalDesign.PlackettBurman
ExperimentalDesign.PlackettBurman
ExperimentalDesign.PlackettBurman
ExperimentalDesign.RandomLHCDesign
ExperimentalDesign.RandomLHCDesign
ExperimentalDesign.RandomLHCDesign
Base.rand
Base.rand
ExperimentalDesign.boxbehnken
ExperimentalDesign.boxbehnken
ExperimentalDesign.ccdesign
ExperimentalDesign.d_criterion
ExperimentalDesign.explicit_fullfactorial
ExperimentalDesign.explicit_fullfactorial
ExperimentalDesign.fold!
ExperimentalDesign.fold!
ExperimentalDesign.fullfactorial
ExperimentalDesign.isplackettburman
ExperimentalDesign.kl_exchange
ExperimentalDesign.next_offset_divisible_prime
ExperimentalDesign.paley
ExperimentalDesign.plackettburman
ExperimentalDesign.random_design!

API

ExperimentalDesign.AbstractDesign — Type

abstract type AbstractDesign

source

ExperimentalDesign.AbstractFactorialDesign — Type

abstract type AbstractFactorialDesign <: AbstractDesign

source

ExperimentalDesign.AbstractOptimalDesign — Type

abstract type AbstractOptimalDesign <: AbstractDesign

source

ExperimentalDesign.AbstractScreeningDesign — Type

abstract type AbstractScreeningDesign <: AbstractDesign

source

ExperimentalDesign.BoxBehnken — Type

struct BoxBehnken <: ExperimentalDesign.AbstractResponseSurfaceDesign

Box-Behnken design for response surface methodology.

matrix::DataFrame
factors::Tuple
formula::FormulaTerm

source

ExperimentalDesign.BoxBehnken — Method

BoxBehnken(formula::FormulaTerm; center) -> BoxBehnken

julia> BoxBehnken(@formula( y ~ -1 + factor1 & factor1 + factor2 & factor2 + factor3 & factor3 + factor1 & factor2 + factor1 & factor3 + factor2 & factor3 + factor1 + factor2 + factor3), center=3)
BoxBehnken
Dimension: (15, 3)
Factors: (:factor1, :factor2, :factor3)
Formula: y ~ -1 + factor1 + factor2 + factor3 + factor1 & factor1 + factor2 & factor2 + factor3 & factor3 + factor1 & factor2 + factor1 & factor3 + factor2 & factor3
Design Matrix:
15×3 DataFrame
 Row │ factor1  factor2  factor3
     │ Float64  Float64  Float64
─────┼───────────────────────────
   1 │    -1.0     -1.0      0.0
   2 │     1.0     -1.0      0.0
   3 │    -1.0      1.0      0.0
   4 │     1.0      1.0      0.0
   5 │    -1.0      0.0     -1.0
   6 │     1.0      0.0     -1.0
   7 │    -1.0      0.0      1.0
   8 │     1.0      0.0      1.0
   9 │     0.0     -1.0     -1.0
  10 │     0.0      1.0     -1.0
  11 │     0.0     -1.0      1.0
  12 │     0.0      1.0      1.0
  13 │     0.0      0.0      0.0
  14 │     0.0      0.0      0.0
  15 │     0.0      0.0      0.0

source

ExperimentalDesign.BoxBehnken — Method

BoxBehnken(factors::Int64; center) -> BoxBehnken

julia> BoxBehnken(3, center=3)
BoxBehnken
Dimension: (15, 3)
Factors: (:factor1, :factor2, :factor3)
Formula: y ~ -1 + factor1 & factor1 + factor2 & factor2 + factor3 & factor3 + factor1 & factor2 + factor1 & factor3 + factor2 & factor3 + factor1 + factor2 + factor3
Design Matrix:
15×3 DataFrame
 Row │ factor1  factor2  factor3
     │ Float64  Float64  Float64
─────┼───────────────────────────
   1 │    -1.0     -1.0      0.0
   2 │     1.0     -1.0      0.0
   3 │    -1.0      1.0      0.0
   4 │     1.0      1.0      0.0
   5 │    -1.0      0.0     -1.0
   6 │     1.0      0.0     -1.0
   7 │    -1.0      0.0      1.0
   8 │     1.0      0.0      1.0
   9 │     0.0     -1.0     -1.0
  10 │     0.0      1.0     -1.0
  11 │     0.0     -1.0      1.0
  12 │     0.0      1.0      1.0
  13 │     0.0      0.0      0.0
  14 │     0.0      0.0      0.0
  15 │     0.0      0.0      0.0

source

ExperimentalDesign.CategoricalFactor — Type

struct CategoricalFactor <: Distribution{Univariate, Discrete}

values::Vector{N} where N
distribution::DiscreteUniform

A simple wrapper for a DiscreteUniform distribution over non-numerical arrays.

source

ExperimentalDesign.CategoricalFactor — Method

CategoricalFactor(values::Array{N, 1}) -> CategoricalFactor

julia> a = CategoricalFactor([:a, :b, 2, 1.0])
CategoricalFactor(
values: Any[:a, :b, 2, 1.0]
distribution: DiscreteUniform(a=1, b=4)
)

source

ExperimentalDesign.CentralComposite — Type

struct CentralComposite <: ExperimentalDesign.AbstractResponseSurfaceDesign

Encapsulates a central composite design.

matrix::DataFrame
factors::Tuple
formula::FormulaTerm
alpha::Symbol
face::Symbol

source

ExperimentalDesign.CentralComposite — Method

CentralComposite(formula::FormulaTerm; center, alpha, face) -> CentralComposite

julia> CentralComposite(@formula(y ~ -1 + factor1 & factor1 + factor2 & factor2 + factor3 & factor3 + factor1 & factor2 + factor1 & factor3 + factor2 & factor3 + factor1 + factor2 + factor3))
CentralComposite
Dimension: (22, 3)
Factors: (:factor1, :factor2, :factor3)
Formula: y ~ -1 + factor1 + factor2 + factor3 + factor1 & factor1 + factor2 & factor2 + factor3 & factor3 + factor1 & factor2 + factor1 & factor3 + factor2 & factor3
Alpha: orthogonal
Face: circumscribed
Design Matrix:
22×3 DataFrame
 Row │ factor1   factor2   factor3
     │ Float64   Float64   Float64
─────┼──────────────────────────────
   1 │ -1.0      -1.0      -1.0
   2 │  1.0      -1.0      -1.0
   3 │ -1.0       1.0      -1.0
   4 │  1.0       1.0      -1.0
   5 │ -1.0      -1.0       1.0
   6 │  1.0      -1.0       1.0
   7 │ -1.0       1.0       1.0
   8 │  1.0       1.0       1.0
  ⋮  │    ⋮         ⋮         ⋮
  16 │  0.0       1.82574   0.0
  17 │  0.0       0.0      -1.82574
  18 │  0.0       0.0       1.82574
  19 │  0.0       0.0       0.0
  20 │  0.0       0.0       0.0
  21 │  0.0       0.0       0.0
  22 │  0.0       0.0       0.0
                      7 rows omitted

source

ExperimentalDesign.CentralComposite — Method

CentralComposite(factors::Int64; center, alpha, face) -> CentralComposite

julia> CentralComposite(3)
CentralComposite
Dimension: (22, 3)
Factors: (:factor1, :factor2, :factor3)
Formula: y ~ -1 + factor1 & factor1 + factor2 & factor2 + factor3 & factor3 + factor1 & factor2 + factor1 & factor3 + factor2 & factor3 + factor1 + factor2 + factor3
Alpha: orthogonal
Face: circumscribed
Design Matrix:
22×3 DataFrame
 Row │ factor1   factor2   factor3
     │ Float64   Float64   Float64
─────┼──────────────────────────────
   1 │ -1.0      -1.0      -1.0
   2 │  1.0      -1.0      -1.0
   3 │ -1.0       1.0      -1.0
   4 │  1.0       1.0      -1.0
   5 │ -1.0      -1.0       1.0
   6 │  1.0      -1.0       1.0
   7 │ -1.0       1.0       1.0
   8 │  1.0       1.0       1.0
  ⋮  │    ⋮         ⋮         ⋮
  16 │  0.0       1.82574   0.0
  17 │  0.0       0.0      -1.82574
  18 │  0.0       0.0       1.82574
  19 │  0.0       0.0       0.0
  20 │  0.0       0.0       0.0
  21 │  0.0       0.0       0.0
  22 │  0.0       0.0       0.0
                      7 rows omitted

source

ExperimentalDesign.DesignDistribution — Type

struct DesignDistribution

factors::NamedTuple
formula::FormulaTerm

Encapsulates one or more Distributions, generating random designs. Receives a NamedTuple of factor names associated with Distributions from the the Distributions package. After instantiating a DesignDistribution, you must request samples from it using rand, which generates a RandomDesign

source

ExperimentalDesign.DesignDistribution — Method

DesignDistribution(factors::Array) -> DesignDistribution

julia> DesignDistribution([Uniform(2, 3), DiscreteUniform(-1, 5), Uniform(5, 10)])
DesignDistribution
Formula: 0 ~ factor1 + factor2 + factor3
Factor Distributions:
factor1: Uniform{Float64}(a=2.0, b=3.0)
factor2: DiscreteUniform(a=-1, b=5)
factor3: Uniform{Float64}(a=5.0, b=10.0)

source

ExperimentalDesign.DesignDistribution — Method

DesignDistribution(factors::NamedTuple) -> DesignDistribution

julia> DesignDistribution((f1 = Uniform(2, 3), f2 = DiscreteUniform(-1, 5), f3 = Uniform(5, 10)))
DesignDistribution
Formula: 0 ~ f1 + f2 + f3
Factor Distributions:
f1: Uniform{Float64}(a=2.0, b=3.0)
f2: DiscreteUniform(a=-1, b=5)
f3: Uniform{Float64}(a=5.0, b=10.0)

source

ExperimentalDesign.DesignDistribution — Method

DesignDistribution(factors::Tuple) -> DesignDistribution

julia> DesignDistribution((Uniform(2, 3), DiscreteUniform(-1, 5), Uniform(5, 10)))
DesignDistribution
Formula: 0 ~ factor1 + factor2 + factor3
Factor Distributions:
factor1: Uniform{Float64}(a=2.0, b=3.0)
factor2: DiscreteUniform(a=-1, b=5)
factor3: Uniform{Float64}(a=5.0, b=10.0)

source

ExperimentalDesign.DesignDistribution — Method

DesignDistribution(distribution::Distribution, n::Int64) -> DesignDistribution

julia> DesignDistribution(DiscreteNonParametric([-1, 1], [0.5, 0.5]), 6)
DesignDistribution
Formula: 0 ~ factor1 + factor2 + factor3 + factor4 + factor5 + factor6
Factor Distributions:
factor1: DiscreteNonParametric{Int64, Float64, Vector{Int64}, Vector{Float64}}(support=[-1, 1], p=[0.5, 0.5])
factor2: DiscreteNonParametric{Int64, Float64, Vector{Int64}, Vector{Float64}}(support=[-1, 1], p=[0.5, 0.5])
factor3: DiscreteNonParametric{Int64, Float64, Vector{Int64}, Vector{Float64}}(support=[-1, 1], p=[0.5, 0.5])
factor4: DiscreteNonParametric{Int64, Float64, Vector{Int64}, Vector{Float64}}(support=[-1, 1], p=[0.5, 0.5])
factor5: DiscreteNonParametric{Int64, Float64, Vector{Int64}, Vector{Float64}}(support=[-1, 1], p=[0.5, 0.5])
factor6: DiscreteNonParametric{Int64, Float64, Vector{Int64}, Vector{Float64}}(support=[-1, 1], p=[0.5, 0.5])

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ExperimentalDesign.FractionalFactorial2Level — Type

struct FractionalFactorial2Level <: AbstractFactorialDesign

matrix::DataFrame
factors::NamedTuple
formula::FormulaTerm

source

ExperimentalDesign.FractionalFactorial2Level — Method

FractionalFactorial2Level(formula::FormulaTerm) -> FractionalFactorial2Level

julia> FractionalFactorial2Level(@formula(y ~ a + b + a&b + c + a&c+ b&c + a&b&c))
FractionalFactorial2Level
Dimension: (8, 7)
Factors: (a = [-1, 1], b = [-1, 1], c = [-1, 1])
Formula: y ~ a + b + c + a & b + a & c + b & c + a & b & c
Design Matrix:
8×7 DataFrame
 Row │ a      b      c      a_b    a_c    b_c    a_b_c
     │ Int64  Int64  Int64  Int64  Int64  Int64  Int64
─────┼─────────────────────────────────────────────────
   1 │    -1     -1     -1      1      1      1     -1
   2 │     1     -1     -1     -1     -1      1      1
   3 │    -1      1     -1     -1      1     -1      1
   4 │     1      1     -1      1     -1     -1     -1
   5 │    -1     -1      1      1     -1     -1      1
   6 │     1     -1      1     -1      1     -1     -1
   7 │    -1      1      1     -1     -1      1     -1
   8 │     1      1      1      1      1      1      1

source

ExperimentalDesign.FullFactorial — Type

struct FullFactorial <: AbstractFactorialDesign

Encapsulates an explicit full factorial design, where all experiments are completely computed and stored. Use IterableFullFactorial to obtain an implicit factorial design with arbitrary access to the elements of a full factorial design.

matrix::DataFrame
factors::NamedTuple
formula::FormulaTerm

source

ExperimentalDesign.FullFactorial — Method

FullFactorial(factors::Array) -> FullFactorial

julia> FullFactorial(fill([-1, 1], 3))
FullFactorial
Dimension: (8, 3)
Factors: (factor1 = [-1, 1], factor2 = [-1, 1], factor3 = [-1, 1])
Formula: 0 ~ factor1 + factor2 + factor3
Design Matrix:
8×3 DataFrame
 Row │ factor1  factor2  factor3
     │ Int64    Int64    Int64
─────┼───────────────────────────
   1 │      -1       -1       -1
   2 │       1       -1       -1
   3 │      -1        1       -1
   4 │       1        1       -1
   5 │      -1       -1        1
   6 │       1       -1        1
   7 │      -1        1        1
   8 │       1        1        1

source

ExperimentalDesign.FullFactorial — Method

FullFactorial(factors::NamedTuple, formula::FormulaTerm) -> FullFactorial

julia> FullFactorial((A = [1, 2, 4], B = [:a, :b], C = [1.0, -1.0]), @formula(y ~ A + B +C))
FullFactorial
Dimension: (12, 3)
Factors: (A = [1, 2, 4], B = [:a, :b], C = [1.0, -1.0])
Formula: y ~ A + B + C
Design Matrix:
12×3 DataFrame
 Row │ A    B    C
     │ Any  Any  Any
─────┼────────────────
   1 │ 1    a    1.0
   2 │ 2    a    1.0
   3 │ 4    a    1.0
   4 │ 1    b    1.0
   5 │ 2    b    1.0
   6 │ 4    b    1.0
   7 │ 1    a    -1.0
   8 │ 2    a    -1.0
   9 │ 4    a    -1.0
  10 │ 1    b    -1.0
  11 │ 2    b    -1.0
  12 │ 4    b    -1.0

source

ExperimentalDesign.FullFactorial — Method

FullFactorial(factors::NamedTuple) -> FullFactorial

julia> FullFactorial((A = [1, 2, 4], B = [:a, :b], C = [1.0, -1.0]))
FullFactorial
Dimension: (12, 3)
Factors: (A = [1, 2, 4], B = [:a, :b], C = [1.0, -1.0])
Formula: 0 ~ A + B + C
Design Matrix:
12×3 DataFrame
 Row │ A    B    C
     │ Any  Any  Any
─────┼────────────────
   1 │ 1    a    1.0
   2 │ 2    a    1.0
   3 │ 4    a    1.0
   4 │ 1    b    1.0
   5 │ 2    b    1.0
   6 │ 4    b    1.0
   7 │ 1    a    -1.0
   8 │ 2    a    -1.0
   9 │ 4    a    -1.0
  10 │ 1    b    -1.0
  11 │ 2    b    -1.0
  12 │ 4    b    -1.0

source

ExperimentalDesign.FullFactorial — Method

FullFactorial(factors::Tuple) -> FullFactorial

julia> FullFactorial(([1, 2, 4], [:a, :b], [1.0, -1.0]))
FullFactorial
Dimension: (12, 3)
Factors: (factor1 = [1, 2, 4], factor2 = [:a, :b], factor3 = [1.0, -1.0])
Formula: 0 ~ factor1 + factor2 + factor3
Design Matrix:
12×3 DataFrame
 Row │ factor1  factor2  factor3
     │ Any      Any      Any
─────┼───────────────────────────
   1 │ 1        a        1.0
   2 │ 2        a        1.0
   3 │ 4        a        1.0
   4 │ 1        b        1.0
   5 │ 2        b        1.0
   6 │ 4        b        1.0
   7 │ 1        a        -1.0
   8 │ 2        a        -1.0
   9 │ 4        a        -1.0
  10 │ 1        b        -1.0
  11 │ 2        b        -1.0
  12 │ 4        b        -1.0

source

ExperimentalDesign.OptimLHCDesign — Type

struct OptimLHCDesign <: ExperimentalDesign.AbstractRandomDesign

matrix::DataFrame
factors::Tuple
fitness::Vector{Float64}

source

ExperimentalDesign.OptimLHCDesign — Method

OptimLHCDesign(n::Int64, d::Int64, gens) -> OptimLHCDesign

julia> OptimLHCDesign(5,3,4)
OptimLHCDesign
Dimension: (5, 3)
Factors: (:factor1, :factor2, :factor3)
Fitness: [1.3760238272524201, 1.3760238272524201, 1.3760238272524201, 1.3760238272524201, 1.3760238272524201]
Design Matrix:
5×3 DataFrame
 Row │ factor1  factor2  factor3
     │ Int64    Int64    Int64
─────┼───────────────────────────
   1 │       3        5        2
   2 │       5        1        3
   3 │       4        4        5
   4 │       2        2        1
   5 │       1        3        4

source

ExperimentalDesign.OptimLHCDesign — Method

OptimLHCDesign(n::Int64, factors::Tuple, gens) -> OptimLHCDesign

julia> OptimLHCDesign(5,Tuple((:A,:B,:C)),4)
OptimLHCDesign
Dimension: (5, 3)
Factors: (:A, :B, :C)
Fitness: [1.3760238272524201, 1.3760238272524201, 1.3760238272524201, 1.3760238272524201, 1.3760238272524201]
Design Matrix:
5×3 DataFrame
 Row │ A      B      C
     │ Int64  Int64  Int64
─────┼─────────────────────
   1 │     3      5      2
   2 │     5      1      3
   3 │     4      4      5
   4 │     2      2      1
   5 │     1      3      4

source

ExperimentalDesign.OptimalDesign — Type

struct OptimalDesign <: AbstractOptimalDesign

matrix::DataFrame
factors::NamedTuple
formula::FormulaTerm
selected_experiments::Array{Int64, N} where N
criteria::Dict{Symbol, Float64}

Contains a set of candidate experiments, a target optimality criterion, and a model prior formula. A set of experiments that maximizes a given optimality criterion can selected from a candidate set using the kl_exchange algorithm.

source

ExperimentalDesign.OptimalDesign — Method

OptimalDesign(candidates::AbstractDesign, formula::FormulaTerm, experiments::Int64; tolerance, seed_design_size, max_iterations, design_k, candidates_l) -> OptimalDesign

julia> design_distribution = DesignDistribution((f1 = Uniform(2, 3), f2 = DiscreteUniform(-1, 5), f3 = Uniform(5, 10)))
DesignDistribution
Formula: 0 ~ f1 + f2 + f3
Factor Distributions:
f1: Uniform{Float64}(a=2.0, b=3.0)
f2: DiscreteUniform(a=-1, b=5)
f3: Uniform{Float64}(a=5.0, b=10.0)

julia> design = rand(design_distribution, 400);

julia> f = @formula 0 ~ f1 + f2 + f3 + f2 ^ 2;

julia> OptimalDesign(design, f, 10)
OptimalDesign
Dimension: (10, 3)
Factors: (f1 = Uniform{Float64}(a=2.0, b=3.0), f2 = DiscreteUniform(a=-1, b=5), f3 = Uniform{Float64}(a=5.0, b=10.0))
Formula: 0 ~ f1 + f2 + f3 + :(f2 ^ 2)
Selected Candidate Rows: [244, 49, 375, 43, 369, 44, 16, 346, 175, 205]
Optimality Criteria: Dict(:D => 2.3940431912232483)
Design Matrix:
10×3 DataFrame
 Row │ f1       f2       f3
     │ Float64  Float64  Float64
─────┼───────────────────────────
   1 │ 2.99329      1.0  5.09246
   2 │ 2.96899      5.0  9.39802
   3 │ 2.96274     -1.0  5.31426
   4 │ 2.00285      2.0  5.40398
   5 │ 2.8491       1.0  9.90621
   6 │ 2.00309     -1.0  9.49394
   7 │ 2.20051      2.0  9.75605
   8 │ 2.06422      5.0  5.1759
   9 │ 2.037       -1.0  9.13114
  10 │ 2.82612      5.0  9.66349

source

ExperimentalDesign.PlackettBurman — Type

struct PlackettBurman <: AbstractScreeningDesign

Encapsulates a Plackett-Burman screening design constructed using Paley's method. Factor levels are encoded as :high and :low symbols, and extra dummy variables, possibly aliasing interactions between factors, will be added to pad a design.

matrix::DataFrame
factors::Tuple
dummy_factors::Tuple
formula::FormulaTerm

source

ExperimentalDesign.PlackettBurman — Method

PlackettBurman(formula::FormulaTerm; symbol_encoding) -> PlackettBurman

julia> PlackettBurman(@formula(y ~ x1 + x2 + x3 + x4))
PlackettBurman
Dimension: (8, 7)
Factors: (:x1, :x2, :x3, :x4)
Dummy Factors: (:dummy1, :dummy2, :dummy3)
Formula: y ~ -1 + x1 + x2 + x3 + x4 + dummy1 + dummy2 + dummy3
Design Matrix:
8×7 DataFrame
 Row │ x1     x2     x3     x4     dummy1  dummy2  dummy3
     │ Int64  Int64  Int64  Int64  Int64   Int64   Int64
─────┼────────────────────────────────────────────────────
   1 │     1      1      1      1       1       1       1
   2 │    -1      1     -1      1       1      -1      -1
   3 │     1     -1      1      1      -1      -1      -1
   4 │    -1      1      1     -1      -1      -1       1
   5 │     1      1     -1     -1      -1       1      -1
   6 │     1     -1     -1     -1       1      -1       1
   7 │    -1     -1     -1      1      -1       1       1
   8 │    -1     -1      1     -1       1       1      -1

source

ExperimentalDesign.PlackettBurman — Method

PlackettBurman(factors::Int64) -> PlackettBurman

julia> PlackettBurman(4)
PlackettBurman
Dimension: (8, 7)
Factors: (:factor1, :factor2, :factor3, :factor4)
Dummy Factors: (:dummy1, :dummy2, :dummy3)
Formula: 0 ~ -1 + factor1 + factor2 + factor3 + factor4 + dummy1 + dummy2 + dummy3
Design Matrix:
8×7 DataFrame
 Row │ factor1  factor2  factor3  factor4  dummy1  dummy2  dummy3
     │ Int64    Int64    Int64    Int64    Int64   Int64   Int64
─────┼────────────────────────────────────────────────────────────
   1 │       1        1        1        1       1       1       1
   2 │      -1        1       -1        1       1      -1      -1
   3 │       1       -1        1        1      -1      -1      -1
   4 │      -1        1        1       -1      -1      -1       1
   5 │       1        1       -1       -1      -1       1      -1
   6 │       1       -1       -1       -1       1      -1       1
   7 │      -1       -1       -1        1      -1       1       1
   8 │      -1       -1        1       -1       1       1      -1

source

ExperimentalDesign.RandomLHCDesign — Type

struct RandomLHCDesign <: ExperimentalDesign.AbstractRandomDesign

matrix::DataFrame
factors::Tuple

source

ExperimentalDesign.RandomLHCDesign — Method

RandomLHCDesign(n::Int64, d::Int64) -> RandomLHCDesign

julia> RandomLHCDesign(4,3)
RandomLHCDesign
Dimension: (4, 3)
Factors: (:factor1, :factor2, :factor3)
Design Matrix:
4×3 DataFrame
 Row │ factor1  factor2  factor3
     │ Int64    Int64    Int64
─────┼───────────────────────────
   1 │       1        4        4
   2 │       2        1        2
   3 │       3        3        3
   4 │       4        2        1

source

ExperimentalDesign.RandomLHCDesign — Method

RandomLHCDesign(n::Int64, factors::Tuple) -> RandomLHCDesign

julia> RandomLHCDesign(4,Tuple((:A,:B,:C)))
RandomLHCDesign
Dimension: (4, 3)
Factors: (:A, :B, :C)
Design Matrix:
4×3 DataFrame
 Row │ A      B      C
     │ Int64  Int64  Int64
─────┼─────────────────────
   1 │     1      4      4
   2 │     2      1      2
   3 │     3      3      3
   4 │     4      2      1

source

Base.rand — Function

rand(distribution::DesignDistribution) -> ExperimentalDesign.RandomDesign
rand(distribution::DesignDistribution, n::Int64) -> ExperimentalDesign.RandomDesign

julia> rand(DesignDistribution((f1 = Uniform(2, 3), f2 = DiscreteUniform(-1, 5), f3 = Uniform(5, 10))), 12)
ExperimentalDesign.RandomDesign
Dimension: (12, 3)
Factors: (f1 = Uniform{Float64}(a=2.0, b=3.0), f2 = DiscreteUniform(a=-1, b=5), f3 = Uniform{Float64}(a=5.0, b=10.0))
Formula: 0 ~ f1 + f2 + f3
Design Matrix:
12×3 DataFrame
 Row │ f1       f2       f3
     │ Float64  Float64  Float64
─────┼───────────────────────────
   1 │ 2.04922     -1.0  9.62061
   2 │ 2.59117      3.0  5.79254
   3 │ 2.77148     -1.0  6.22902
   4 │ 2.25659      4.0  6.00256
   5 │ 2.64968      2.0  9.21818
   6 │ 2.31523      5.0  8.80749
   7 │ 2.86526      2.0  8.47297
   8 │ 2.44753      0.0  6.11722
   9 │ 2.08284     -1.0  6.34626
  10 │ 2.81201     -1.0  6.44508
  11 │ 2.64232      3.0  5.57183
  12 │ 2.08189      1.0  8.72759

source

Base.rand — Function

rand(distribution::CategoricalFactor) -> Vector{_A} where _A
rand(distribution::CategoricalFactor, n::Int64) -> Vector{_A} where _A

julia> rand(CategoricalFactor([:a, :b, 2, 1.0]), 6)
6-element Vector{Any}:
 2
 1.0
  :b
 2
 2
 1.0

source

ExperimentalDesign.boxbehnken — Method

boxbehnken(matrix_size::Int64, center::Int64) -> Any

Constructs a Box-Behnken design with size matrix_size with specified number of center points.

julia> boxbehnken(4,0)
24×4 transpose(::Matrix{Float64}) with eltype Float64:
 -1.0  -1.0   0.0   0.0
  1.0  -1.0   0.0   0.0
 -1.0   1.0   0.0   0.0
  1.0   1.0   0.0   0.0
 -1.0   0.0  -1.0   0.0
  1.0   0.0  -1.0   0.0
 -1.0   0.0   1.0   0.0
  1.0   0.0   1.0   0.0
 -1.0   0.0   0.0  -1.0
  1.0   0.0   0.0  -1.0
  ⋮
  0.0   1.0   1.0   0.0
  0.0  -1.0   0.0  -1.0
  0.0   1.0   0.0  -1.0
  0.0  -1.0   0.0   1.0
  0.0   1.0   0.0   1.0
  0.0   0.0  -1.0  -1.0
  0.0   0.0   1.0  -1.0
  0.0   0.0  -1.0   1.0
  0.0   0.0   1.0   1.0

source

ExperimentalDesign.boxbehnken — Method

boxbehnken(matrix_size::Int64) -> Any

Constructs a Box-Behnken design with size matrix_size.

julia> boxbehnken(4)
27×4 transpose(::Matrix{Float64}) with eltype Float64:
 -1.0  -1.0   0.0   0.0
  1.0  -1.0   0.0   0.0
 -1.0   1.0   0.0   0.0
  1.0   1.0   0.0   0.0
 -1.0   0.0  -1.0   0.0
  1.0   0.0  -1.0   0.0
 -1.0   0.0   1.0   0.0
  1.0   0.0   1.0   0.0
 -1.0   0.0   0.0  -1.0
  1.0   0.0   0.0  -1.0
  ⋮
  0.0  -1.0   0.0   1.0
  0.0   1.0   0.0   1.0
  0.0   0.0  -1.0  -1.0
  0.0   0.0   1.0  -1.0
  0.0   0.0  -1.0   1.0
  0.0   0.0   1.0   1.0
  0.0   0.0   0.0   0.0
  0.0   0.0   0.0   0.0
  0.0   0.0   0.0   0.0

source

ExperimentalDesign.ccdesign — Function

ccdesign(n::Int64) -> Any
ccdesign(n::Int64, center::Array{Int64, N} where N) -> Any
ccdesign(n::Int64, center::Array{Int64, N} where N, alpha::Symbol) -> Any
ccdesign(n::Int64, center::Array{Int64, N} where N, alpha::Symbol, face::Symbol) -> Any

Constructs a central composite design.

julia> ccdesign(3)
22×3 Matrix{Float64}:
 -1.0      -1.0      -1.0
  1.0      -1.0      -1.0
 -1.0       1.0      -1.0
  1.0       1.0      -1.0
 -1.0      -1.0       1.0
  1.0      -1.0       1.0
 -1.0       1.0       1.0
  1.0       1.0       1.0
  0.0       0.0       0.0
  0.0       0.0       0.0
  ⋮
  1.82574   0.0       0.0
  0.0      -1.82574   0.0
  0.0       1.82574   0.0
  0.0       0.0      -1.82574
  0.0       0.0       1.82574
  0.0       0.0       0.0
  0.0       0.0       0.0
  0.0       0.0       0.0
  0.0       0.0       0.0

source

ExperimentalDesign.d_criterion — Method

d_criterion(model_matrix; tolerance) -> Any

Criterion of D-optimality, which seeks to minimize $|(X^T · X) − I*tol| / N^{1/b}$, or equivalently maximize the determinant of the information matrix $X^T · X$ of the design. This criterion results in maximizing the differential Shannon information content of the parameter estimates.

source

ExperimentalDesign.explicit_fullfactorial — Method

explicit_fullfactorial(iterator::Base.Iterators.ProductIterator) -> Any

Receives a Base.Iterators.ProductIterator and computes an explicit full factorial design. The generated array is exponentially large.

julia> explicit_fullfactorial(fullfactorial(([-1, 1], [:a, :b, :c])))
6×2 Matrix{Any}:
 -1  :a
  1  :a
 -1  :b
  1  :b
 -1  :c
  1  :c

source

ExperimentalDesign.explicit_fullfactorial — Method

explicit_fullfactorial(factors::Tuple) -> Any

Receives a tuple of arrays representing categorical factor levels, and computes an explicit full factorial design. The generated array is exponentially large.

julia> explicit_fullfactorial(([-1, 1], [:a, :b, :c], [1, 2]))
12×3 Matrix{Any}:
 -1  :a  1
  1  :a  1
 -1  :b  1
  1  :b  1
 -1  :c  1
  1  :c  1
 -1  :a  2
  1  :a  2
 -1  :b  2
  1  :b  2
 -1  :c  2
  1  :c  2

source

ExperimentalDesign.fold! — Method

fold!(design::FractionalFactorial2Level) -> DataFrame

julia> fold!(FractionalFactorial2Level(@formula(y ~ a + b + a&b + c + a&c+ b&c + a&b&c)))
16×7 DataFrame
 Row │ a      b      c      a_b    a_c    b_c    a_b_c 
     │ Int64  Int64  Int64  Int64  Int64  Int64  Int64 
─────┼─────────────────────────────────────────────────
   1 │    -1     -1     -1      1      1      1     -1
   2 │     1     -1     -1     -1     -1      1      1
   3 │    -1      1     -1     -1      1     -1      1
   4 │     1      1     -1      1     -1     -1     -1
   5 │    -1     -1      1      1     -1     -1      1
   6 │     1     -1      1     -1      1     -1     -1
   7 │    -1      1      1     -1     -1      1     -1
   8 │     1      1      1      1      1      1      1
   9 │     1      1      1     -1     -1     -1      1
  10 │    -1      1      1      1      1     -1     -1
  11 │     1     -1      1      1     -1      1     -1
  12 │    -1     -1      1     -1      1      1      1
  13 │     1      1     -1     -1      1      1     -1
  14 │    -1      1     -1      1     -1      1      1
  15 │     1     -1     -1      1      1     -1      1
  16 │    -1     -1     -1     -1     -1     -1     -1

source

ExperimentalDesign.fold! — Method

fold!(design::PlackettBurman) -> DataFrame

julia> fold!(PlackettBurman(2))
8×3 DataFrame
 Row │ factor1  factor2  dummy1
     │ Int64    Int64    Int64
─────┼──────────────────────────
   1 │       1        1       1
   2 │       1       -1      -1
   3 │      -1       -1       1
   4 │      -1        1      -1
   5 │      -1       -1      -1
   6 │      -1        1       1
   7 │       1        1      -1
   8 │       1       -1       1

source

ExperimentalDesign.fullfactorial — Method

fullfactorial(factors::Tuple) -> Base.Iterators.ProductIterator

Receives a tuple of arrays representing categorical factor levels, and returns a Base.Iterators.ProductIterator. This allows full factorial designs to be arbitrarily large and only be computed as needed. To compute an explicit full factorial design, use explicit_fullfactorial.

julia> fullfactorial(Tuple([-1, 1] for i = 1:10))
Base.Iterators.ProductIterator{NTuple{10, Vector{Int64}}}(([-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1]))

source

ExperimentalDesign.isplackettburman — Method

isplackettburman(d::Matrix{Int64}) -> Bool

To check if a given design is a Plackett-Burman design, we must check for the following properties, obtained in the original Plackett-Burman paper:

Each component is replicated at each of its values the same number of times, that is, the sum of elements in each column is zero
Each pair of components occur together at every combination of values the same number of times, that is, the sum of each pair of columns will produce a column with the same number of occurrences of $2$ and $-2$, and twice that number of occurrences of $0$

Plackett, R.L. and Burman, J.P., 1946. The design of optimum multifactorial experiments. Biometrika, 33(4), pp.305-325.

julia> isplackettburman(plackettburman(2))
true

julia> isplackettburman(plackettburman(4))
true

julia> isplackettburman(plackettburman(16))
true

julia> isplackettburman(rand(Int, 4,4))
false

source

ExperimentalDesign.kl_exchange — Method

kl_exchange(formula::FormulaTerm, candidate_set::DataFrame; tolerance, seed_design_size, max_iterations, experiments, design_k, candidates_l)

Builds optimum designs using the KL exchange algorithm, as described by Atkinson et al.. The ideia is to iteratively swap $K$ design elements with $L$ candidate elements, in order to maximize an optimality criterion. Although any criteria based on information matrices could be used here, the KL exchange algorithm leverages determinant properties to optimize the d_criterion.

Atkinson, A., Donev, A., & Tobias, R. (2007). Optimum experimental designs, with SAS (Vol. 34). Oxford University Press, Chapter 12.

julia> candidates = FullFactorial(fill([-1, 0, 1], 5));

julia> candidates_formula = ConstantTerm(0) ~ sum(Term.(Symbol.(names(candidates.matrix))));

julia> candidates_formula = FormulaTerm(candidates_formula.lhs,
                                        candidates_formula.rhs +
                                        (@formula 0 ~ factor3 ^ 2).rhs);

julia> selected_rows = kl_exchange(candidates_formula,
                                   candidates.matrix,
                                   seed_design_size = 2,
                                   experiments = 11,
                                   design_k = 11,
                                   candidates_l = size(candidates.matrix, 1) - 11);

julia> d_criterion(selected_rows)
0.730476820204009

julia> candidates.matrix[selected_rows.indices[1], :]
11×5 DataFrames.DataFrame
│ Row │ factor1 │ factor2 │ factor3 │ factor4 │ factor5 │
│     │ Int64   │ Int64   │ Int64   │ Int64   │ Int64   │
├─────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│ 1   │ -1      │ 1       │ -1      │ 1       │ 1       │
│ 2   │ 1       │ -1      │ 1       │ 1       │ 1       │
│ 3   │ 1       │ 1       │ 0       │ -1      │ 1       │
│ 4   │ -1      │ 1       │ 1       │ -1      │ 1       │
│ 5   │ -1      │ -1      │ 0       │ 1       │ 1       │
│ 6   │ 1       │ 1       │ 1       │ 1       │ -1      │
│ 7   │ -1      │ -1      │ 1       │ -1      │ -1      │
│ 8   │ 1       │ -1      │ 0       │ 1       │ -1      │
│ 9   │ -1      │ 1       │ -1      │ 1       │ -1      │
│ 10  │ -1      │ 1       │ 0       │ -1      │ -1      │
│ 11  │ 1       │ -1      │ -1      │ -1      │ -1      │

julia> n_candidates = 3000;

julia> n_factors = 30;

julia> design_generator = DesignDistribution(Uniform(0, 1), n_factors);

julia> candidates = rand(design_generator, n_candidates);

julia> selected_rows = kl_exchange(candidates.formula,
                                   candidates.matrix,
                                   experiments = n_factors + 2,
                                   design_k = n_factors,
                                   candidates_l = round(Int, (n_candidates - n_factors) / 2));

julia> d_criterion(selected_rows)
0.07904918814259465

julia> candidates.matrix[selected_rows.indices[1], :]
32×30 DataFrame. Omitted printing of 24 columns
│ Row │ factor1    │ factor2   │ factor3   │ factor4   │ factor5   │ factor6   │
│     │ Float64    │ Float64   │ Float64   │ Float64   │ Float64   │ Float64   │
├─────┼────────────┼───────────┼───────────┼───────────┼───────────┼───────────┤
│ 1   │ 0.832487   │ 0.875035  │ 0.433788  │ 0.805738  │ 0.481517  │ 0.382364  │
│ 2   │ 0.761498   │ 0.0398811 │ 0.998741  │ 0.632286  │ 0.29121   │ 0.55497   │
│ 3   │ 0.639793   │ 0.49432   │ 0.678795  │ 0.685274  │ 0.269203  │ 0.896397  │
│ 4   │ 0.00370418 │ 0.5139    │ 0.0630861 │ 0.175531  │ 0.570244  │ 0.60512   │
│ 5   │ 0.698514   │ 0.207593  │ 0.766977  │ 0.0719112 │ 0.665055  │ 0.499193  │
│ 6   │ 0.412744   │ 0.785263  │ 0.432861  │ 0.909976  │ 0.642545  │ 0.832013  │
│ 7   │ 0.353518   │ 0.116685  │ 0.140352  │ 0.929095  │ 0.0484366 │ 0.838524  │
⋮
│ 25  │ 0.577343   │ 0.790529  │ 0.763994  │ 0.548131  │ 0.402066  │ 0.293336  │
│ 26  │ 0.0941214  │ 0.52891   │ 0.293733  │ 0.92224   │ 0.982713  │ 0.929744  │
│ 27  │ 0.0256128  │ 0.723072  │ 0.23927   │ 0.993221  │ 0.521335  │ 0.407319  │
│ 28  │ 0.221631   │ 0.375189  │ 0.67251   │ 0.658613  │ 0.272448  │ 0.230501  │
│ 29  │ 0.843885   │ 0.375497  │ 0.116069  │ 0.989937  │ 0.935444  │ 0.0466424 │
│ 30  │ 0.181611   │ 0.956062  │ 0.98997   │ 0.80352   │ 0.994557  │ 0.203797  │
│ 31  │ 0.738407   │ 0.25753   │ 0.929704  │ 0.407498  │ 0.0934688 │ 0.99359   │
│ 32  │ 0.228975   │ 0.81272   │ 0.803107  │ 0.931826  │ 0.598371  │ 0.588823  │

source

ExperimentalDesign.next_offset_divisible_prime — Method

next_offset_divisible_prime(n::Int64, offset::Int64, divisor::Int64, tries::Int64) -> Int64

Gets the next prime p, starting from n, for which (p + offset) % divisor == 0 holds.

julia> next_offset_divisible_prime(3, 1, 4, 1000)
3

julia> next_offset_divisible_prime(5, 1, 4, 1000)
7

julia> next_offset_divisible_prime(4, 1, 4, 1000)
7

source

ExperimentalDesign.paley — Method

paley(matrix::Matrix{Int64}) -> Matrix{Int64}

The Paley construction is a method for constructing Hadamard matrices using finite fields.

julia> paley(Matrix{Int}(undef, 8, 8))
8×8 Matrix{Int64}:
 -1   1   1  -1   1   1   1  -1
  1   1  -1   1   1   1  -1  -1
  1  -1   1   1   1  -1  -1   1
 -1   1   1   1  -1  -1   1   1
  1   1   1  -1  -1   1   1  -1
  1   1  -1  -1   1   1  -1   1
  1  -1  -1   1   1  -1   1   1
 -1  -1   1   1  -1   1   1   1

source

ExperimentalDesign.plackettburman — Method

plackettburman(matrix_size::Int64) -> Matrix{Int64}

Constructs a Plackett-Burman design with size matrix_size if possible, or to the closest, largest, number for which it is possible.

julia> plackettburman(4)
8×7 Matrix{Int64}:
  1   1   1   1   1   1   1
 -1   1  -1   1   1  -1  -1
  1  -1   1   1  -1  -1  -1
 -1   1   1  -1  -1  -1   1
  1   1  -1  -1  -1   1  -1
  1  -1  -1  -1   1  -1   1
 -1  -1  -1   1  -1   1   1
 -1  -1   1  -1   1   1  -1

source

ExperimentalDesign.random_design! — Method

random_design!(distributions::Tuple, n::Int64) -> Any

julia> random_design!((Uniform(2, 3), DiscreteUniform(-1, 5), Uniform(5, 10)), 10)
10×3 Matrix{Float64}:
 2.04922  -1.0  8.21161
 2.59117   3.0  5.40944
 2.77148  -1.0  9.62061
 2.25659   4.0  5.79254
 2.64968   2.0  6.22902
 2.31523   5.0  6.00256
 2.86526   2.0  9.21818
 2.44753   0.0  8.80749
 2.08284  -1.0  8.47297
 2.81201  -1.0  6.11722

source

API Documentation

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