| Type: | Package |
| Title: | Designs for Computer Experimentations |
| Version: | 1.0.7 |
| Maintainer: | Ashutosh Dalal <ashutosh.dalal97@gmail.com> |
| Description: | In computer experiments space-filling designs are having great impact. Most popularly used space-filling designs are Uniform designs (UDs), Latin hypercube designs (LHDs) etc. For further references one can see Mckay (1979) <doi:10.1080/00401706.1979.10489755> and Fang (1980) https://cir.nii.ac.jp/crid/1570291225616774784. In this package, we have provided algorithms for generate efficient LHDs and UDs. Here, generated LHDs are efficient as they possess lower value of Maxpro measure, Phi_p value and Maximum Absolute Correlation (MAC) value based on the weightage given to each criterion. On the other hand, the produced UDs are having good space-filling property as they always attain the lower bound of Discrete Discrepancy measure. Further, some useful functions added in this package for adding more value to this package. |
| Suggests: | HadamardR |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | no |
| Packaged: | 2025-03-28 16:01:12 UTC; Ashutosh |
| Author: | Ashutosh Dalal [aut, cre], Cini Varghese [aut, ctb], Rajender Parsad [aut, ctb], Mohd Harun [aut, ctb] |
| Repository: | CRAN |
| Date/Publication: | 2025-03-29 00:30:13 UTC |
Find Best Model
Description
This function will try to find out a significant model for each combinations based on adjusted R^2. Then user need to select which model they want to use.
Usage
Best_Model(model, data)
Arguments
model |
Provide a vector that contains all the individual terms present in a full model |
data |
Provide data in a matrix or data frame format where you want to fit the model |
Value
Generate a list of significant models for various combinations of factors.
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
Examples
## Not run:
library(CompExpDes)
# Sample data
data <- data.frame(
x1 = c(1.0, 1.4, 1.8, 2.2, 2.6, 3.0, 3.4, 3.8, 4.2, 4.6, 5.0, 5.4),
x2 = c(50, 25, 5, 30, 55, 45, 20, 10, 35, 60, 40, 15),
x3 = c(2.5, 6.0, 4.0, 1.0, 5.5, 4.5, 3.0, 2.0, 6.5, 3.5, 1.5, 5.0),
x4 = c(45, 25, 55, 35, 65, 15, 70, 20, 50, 30, 60, 40),
y = c(0.0795, 0.0118, 0.0109, 0.0991, 0.1266, 0.0717, 0.1319, 0.0900, 0.1739,
0.1176, 0.1836, 0.1424)
)
# List of terms in the polynomial model
model <- list('x1', 'x2', 'x3', 'x4', 'x1:x2', 'x1:x3', 'x1:x4',
'x2:x3', 'x2:x4', 'x3:x4', 'I(x1^2)',
'I(x2^2)', 'I(x3^2)', 'I(x4^2)')
Best_Model(model,data)
## End(Not run)
Measure of Discrete Discrepancy
Description
Discrete Discrepancy is a measure of uniformity for any uniform design. Lesser the value of Discrete Discrepancy measure, better is the uniform design.
Usage
Discrete_Discrepancy(Design,a,b)
Arguments
Design |
A matrix |
a |
Any value a>b>0. By default it is set to 1. |
b |
Any value a>b>0. By default it is set to 0.5. |
Value
The function calculates the value of Discrete Discrepancy measure and its lower bound for a given design.
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
References
Qin H, Fang KT (2004)<DOI:10.1007/s001840300296> Discrete discrepancy in factorial designs. Metrika, 60, 59-72.
Examples
library(CompExpDes)
lhd1<-matrix(c(1,5,7,3,4,2,6,2,1,4,5,3,7,6,4,5,6,1,2,3,7),nrow=7,ncol=3,byrow=FALSE)
lhd2<-cbind(lhd1[,3],lhd1[,2],lhd1[,1])
ud<-rbind(lhd1,lhd2)
Discrete_Discrepancy(ud, 1, 0.5)
Maximum Absolute Correlation
Description
Maximum Absolute Correlation (MAC) is the maximum absolute value among off diagonal values of a correlation matrix.
Usage
MAC(matrix)
Arguments
matrix |
Input a matrix |
Value
It returns a maximum absolute correlation value for a given matrix.
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
References
Jones, B. and Nachtsheim, C. J. (2011). A class of three-level designs for definitive screening in the presence of second-order effects. Journal of Quality Technology, 43(1), 1-15.
Examples
library(CompExpDes)
lhd<-matrix(c(1,5,7,3,4,2,6,2,1,4,5,3,7,6,4,5,6,1,2,3,7),nrow=7,ncol=3,byrow=FALSE)
MAC(lhd)
Measure of Maxpro criterion
Description
This function calculates Maxpro criterion for a given space-filling design. Lesser the value of it better the design, in the sense that the design has maximum spread in higher dimensional spaces.
Usage
Maxpro_Measure(Design)Arguments
Design |
Provide a design in a matrix format |
Value
Provides Maxpro criterion value given by Joseph et al. (2015).
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
References
Joseph, V.R., Gul, E. and Ba, S. (2015). Maximum projection designs for computer experiments. Biometrika, 102 (2), 371-380.
Examples
library(CompExpDes)
lhd<-matrix(c(1,5,7,3,4,2,6,2,1,4,5,3,7,6,4,5,6,1,2,3,7),nrow=7,ncol=3,byrow=FALSE)
Maxpro_Measure(lhd)
Maximum Coincidence (or Meeting) numbers between rows
Description
Finding out Maximum coincidence (or Meeting) number between unique pair of rows.
Usage
Meeting_Number(matrix)
Arguments
matrix |
Provide any matrix |
Value
This function provides the maximum coincidence number between any pair of rows of for a given matrix.
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
Examples
library(CompExpDes)
mat<-matrix(c(1,2,3,3,2,1,4,2,1),nrow=3,byrow=TRUE)
Meeting_Number(mat)
Nearly Orthogonal Latin Hypercube Designs for Flexible Levels and Factors
Description
This NOLHDs are generated using a new algorithm for a flexible parameter range which possesses a good space-filling property.
Usage
NOLHDs(factors,levels)
Arguments
factors |
Number of factors(>=2) |
levels |
Number of levels(>=factors+3) |
Value
Generates NOLHDs along with its parameters and maximum absolute correlation (MAC) value.
Author(s)
Ashutosh Dalal, Cini varghese, Rajender Parsad and Mohd Harun
References
Cioppa, T.M. and Lucas, T.W.: Efficient nearly orthogonal and space-filling latin hypercubes. Technometrics, 49(1), 45–55 (2007).
Examples
library(CompExpDes)
NOLHDs(2,5)
Two Factor Orthogonal Latin Hypercube Designs
Description
This OLHDs are generated using a new unique algorithm which possesses a good space-filling property.
Usage
OLHDs_2F(levels)
Arguments
levels |
Number of levels, 4t-1, where t =3,4,... |
Value
Generates two factor OLHDs along with its parameters.
Author(s)
Ashutosh Dalal, Cini varghese, Rajender Parsad and Mohd Harun
References
Ye, K.Q.: Orthogonal column Latin hypercubes and their application in computer experiments. Journal of the American Statistical Association, 93(444), 1430–1439 (1998).
Examples
library(CompExpDes)
OLHDs_2F(11)
Phi_p criterion
Description
For a given design Phi_p criterion (Morris and Mitchell, 1995) is calculated using this function. Lesser the value of Phi_p criterion better the design in terms of space-filling.
Usage
PhipMeasure(design,p=15,q=1)
Arguments
design |
A design matrix is needed |
p |
Any positive integer. Default value of p = 15. |
q |
Any positive integer. Default value of q = 1. This implies that we are considering here Euclidean distance. |
Value
Generates Phi_p criterion value
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
References
Morris, M.D. and Mitchell, T.J. (1995). Exploratory designs for computer experiments. Journal of Statistical Planning and Inference, 43, 38-402.
Examples
library(CompExpDes)
lhd<-matrix(c(1,5,7,3,4,2,6,2,1,4,5,3,7,6,4,5,6,1,2,3,7),nrow=7,ncol=3,byrow=FALSE)
PhipMeasure(lhd,p=15,q=2)
Sliced Latin Hypercube Designs with Equal Size of Slices
Description
This sliced LHDs are generated using a different new algorithm for a flexible parameter range which possesses a good space-filling property as whole design as well as for the slices.
Usage
SLHDs(slices,factors,levels)
Arguments
slices |
Number of slices(>=2) |
factors |
Number of factors(>=2) |
levels |
Number of levels(>=3) |
Value
Generates a Sliced LHD along with its parameters.
Author(s)
Ashutosh Dalal, Cini varghese, Rajender Parsad and Mohd Harun
References
Qian, P.Z.G. and Wu, C.F.J. (2009). Sliced space-filling designs. Biometrika, 96(4), 945–956.
Examples
library(CompExpDes)
SLHDs(3,3,3)
Orthogonal Uniform Designs with Two Factors
Description
This series of UDs can be obtained for a composite number of levels, L with always two factors, F. Further, "Excellent" type UDs are Excellent in space-filling with larger number of runs available for L >= 6. On the other hand, "Good" type UDs are good in space-filling and lesser the number of runs, available for L >= 9. Generated designs are UDs under discrete discrepancy measure, as all designs will attain the lower bound value of discrete discrepancy.
Usage
UDesigns_I(levels, type)
Arguments
levels |
Any composite number >=6 (if "Excellent") or >=9 (if "Good") |
type |
"Excellent" or "Good" |
Details
Type "Excellent" or type "Good" both can exist for a same parameter range. For type "Excellent" it will require more runs than designs generated by type "Good". But type "Excellent" provides designs which are having more spread than type "Good" series designs.
Value
Returns a uniform designs along with number of factors, levels, runs, maximum absolute correlation (MAC) value and discrete discrepancy measure along with its lower bound value.
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
References
Fang, K.T. (1980). The uniform design: application of number-theoretic methods in experimental design. Acta Math Appl Sin, 3, 363-372.
Examples
library(CompExpDes)
UDesigns_I(levels=6, type="Excellent")
Uniform Designs with Multiple Factors with Minimal Runs
Description
In this series, the Uniform Designs (UDs) are high dimensional with lesser number of runs will always attain lower bound of discrete discrepancy. They are available for any even number of factors, F (>= 4) with F(F+1) levels each.
Usage
UDesigns_II(factors)
Arguments
factors |
any even number >=4 |
Value
Returns a series of high dimensional UDs along with number of factors, levels, runs, MAC value and discrete discrepancy measure along with its lower bound value.
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
References
Fang, K.T. (1980). The uniform design: application of number-theoretic methods in experimental design. Acta Math Appl Sin, 3, 363-372.
Examples
library(CompExpDes)
UDesigns_II(4)
Nearly Orthogonal Uniform Designs for Two and Four Factors
Description
This function will provide nearly orthogonal uniform designs (UDs) for number of factors, F = 2 and 4 but a flexible number of levels, L >=3.
Usage
UDesigns_III(levels,factors)
Arguments
levels |
Number of levels, L >=3 |
factors |
Number of factors 2 or 4 |
Value
This function will generate 3 Uniform Designs along with the number of levels,factors, runs, MAC value and discrete discrepancy value along with its lower bound value.
Author(s)
Ashutosh Dalal, Cini varghese, Rajender Parsad and Mohd Harun
References
Fang, K.T. (1980). The uniform design: application of number-theoretic methods in experimental design. Acta Math Appl Sin, 3, 363-372.
Examples
## Not run:
library(CompExpDes)
UDesigns_III(3)
## End(Not run)
Weighted Criteria-Based Latin Hypercube Designs (LHDs) for Any Numbers of Factors (>=2)
Description
For any number of factors, F (>=2), this method will generate LHDs with levels, L ranges from F to sC2, where s=2*F+1. Maxpro criterion measure, Phi_p measure also provided as a measure of space-filling and as an orthogonality measure, maximum absolute correlation (MAC) value also provided.
Usage
wtLHDs(levels,factors,weights,iterations,population)
Arguments
levels |
Ranges from F to sC2, where s=2*F+1 |
factors |
F, any number (>=2) |
weights |
Weight should be given to MAC, Phi_p and Maxpro such that sum is 1. Default it is 0.2, 0.4 and 0.4 |
iterations |
Number of iterations. By default it is 300 |
population |
Population size. By default it is 100 |
Value
This function will provide a series of weighted criteria-based LHDs along with space-filling and orthogonality measures for the generated LHDs.
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
References
McKay, M.D., Beckman, R.J. and Conover, W.J. (1979). Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239-245.
Examples
library(CompExpDes)
wtLHDs(20,3,c(0.4,0.2,0.4))
Weighted Criteria-Based Latin Hypercube Designs (LHDs) for Prime Numbers
Description
For prime number of factors, F (>2), this method will generate LHDs with levels, L ranges from F to F^2. Maxpro criterion measure, Phi_p measure also provided as a measure of space-filling and also as an orthogonality measure maximum absolute correlation (MAC) value also provided.
Usage
wtLHDs_prime(levels,factors,weights,iterations)
Arguments
levels |
L,ranges from F to F^2 |
factors |
A prime number, F (>2) |
weights |
Weight should be given to Maxpro, Phi_p and MAC such that sum is 1. Default it is 0.2, 0.4 and 0.4 |
iterations |
Number of iterations. By default it is 300. |
Value
This function will provide a series of weighted criteria-based LHDs along with space-filling and orthogonality measures for the generated LHDs.
Author(s)
Ashutosh Dalal, Cini Varghese, Rajender Parsad and Mohd Harun
References
McKay, M.D., Beckman, R.J. and Conover, W.J. (1979). Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239-245.
Examples
library(CompExpDes)
wtLHDs_prime(9,3,c(0.6,0,0.4))