mathmodels: A Powerful R Toolkit for Mathematical Modeling

An R package providing a versatile toolkit for mathematical modeling, developed as a companion to the book Mathematical Modeling: Algorithms and Programming Implementation (China Machine Press). It focuses on implementing rigorous algorithms in a user-friendly manner.

Current Version (0.0.5) Focus: Evaluation algorithms, including data preprocessing, subjective (AHP) and objective (Entropy, CRITIC, PCA) weighting methods, weight combination techniques, comprehensive evaluation (TOPSIS, Fuzzy, RSR, DEA), inequality measures (Gini, Theil), and grey prediction models (GM(1,1), GM(1,N), Verhulst).

Key Features

• Rigorous & Comprehensive: Implements core algorithms for evaluation and analysis with attention to detail.
• User-Friendly Interface: Simplifies complex workflows with intuitive function design and intelligent handling of data preprocessing (standardization, normalization, directionality).
• Tidyverse Integration: Seamlessly works with |> and tidyverse tools for smooth data manipulation and batch processing.

Installation

You can install the latest development version of mathmodels directly from GitHub use:

remotes::install_github("zhjx19/mathmodels")

Or download to current path, unzip and use:

# install.packages("deaR")    # Install the dependency packages first
install.packages("mathmodels-main", repos=NULL, type="source")

Getting Started

library(mathmodels)
A = matrix(c(1,   1/2, 4, 3,   3,
             2,   1,   7, 5,   5,
             1/4, 1/7, 1, 1/2, 1/3,
             1/3, 1/5, 2, 1,   1,
             1/3, 1/5, 3, 1,   1), byrow = TRUE, nrow = 5)
# Analytic Hierarchy Process
AHP(A)
## $w
## [1] 0.26360349 0.47583538 0.05381460 0.09806829 0.10867824
## 
## $CR
## [1] 0.01609027
## 
## $Lmax
## [1] 5.072084
## 
## $CI
## [1] 0.0180211

Learning More

For detailed documentation, tutorials, and in-depth examples on using the mathmodels package, please refer to the comprehensive online manual:

📘 mathmodels Package Manual - Simplifying Mathematical Modeling (Online Book, In Chinese)

This online book is the definitive guide to the package's functionalities. Currently, only evaluation algorithms are fully implemented, including:

• Indicator data preprocessing
• AHP
• Entropy weighting
• CRITIC weighting
• PCA weighting
• Combination of subjective and objective weighting
• TOPSIS
• Grey Relational Analysis (GRA)
• Rank Sum Ratio (RSR) method
• Fuzzy Comprehensive Evaluation (FCE)
• Data Envelopment Analysis (CCR/BCC/SBM, Malmquist)
• Inequality Measures (Gini, Theil Index)
• Regional Economics (LQ/HHI/EG Index)
• Coupling coordination degree and obstacle degree