SnFFT Package

The SnFFT package is Julia package designed to facilitate harmonic analysis on the symmetric group of order n, denoted S_n . Out of the box, SnFFT implements:

• Group operations and factorizations for S_n
• Functionality to set up functions over S_n
• The fast Fourier transform with additional options if the function is sparse or bandlimited
• The inverse fast Fourier transform with additional options if the function is bandlimited or the user is only interested in the result from the top few components
• The convolution and correlation of two Fourier transforms

Contents:

• Getting Started
  • Installation
  • Set Up
  • Parallelism
• Examples
  • General Notes:
  • Example Function Explanations
• Symmetric Group Functionality
  • Group Operations
  • Group Element Constructors
  • Factorizations and Related Operations on the Left-Coset Tree
  • Young’s Orthogonal Representation of a Permutation
• Functions over the Symmetric Group
  • Dense Functions
  • Bandlimited Functions
  • Sparse Functions
• Young’s Orthogonal Representations
  • Dense and Sparse Functions
  • Bandlimited Functions
• Fast Fourier Transforms
  • Dense Fast Fourier Transform
  • Bandlimited Fast Fourier Transform
  • Sparse Fast Fourier Transform
• Inverse Fast Fourier Transform
  • Dense Inverse Fast Fourier Transform
  • Bandlimited Inverse Fast Fourier Transform
  • Partial Inverse Fast Fourier Transform
• Convolution and Correlation
• Miscellaneous Functions
  • Partition Construction
  • Preference Matrices
  • Kendall Tau Distance
  • Mallow’s Distribution
  • Printing Methods
• Machine Learning Applications
  • Clustering Ranked Data - Synthetic Data
  • Multi-Object Tracking
  • Disease Progresion
• Supplement

Indices and tables

• Index
• Module Index
• Search Page