Miscellaneous Functions

Partition Construction

Although perhaps not computationally useful, SnFFT does export the function to construct the set of paritions of 1:N. Generally, this is useful for giving the output of other code easier to interpret.

partitions(N)

# Parameters:
#       N::Int
#       - the problem size
# Return Values:
#       P::Array{Array{Array{Int, 1}, 1}, 1} (Partitions)
#       - P[n][p] contains the pth Partition of n
#       WI::Array{Int, 2} (Width Information)
#       - WI[n, w] contains the number of Paritions of n whose first element is less than or equal to w

Preference Matrices

Constructs the preference matrix for a permutation.

preferencematrix(P)

# Parameters:
#       P::Array{Int, 1}
#       - a permutation
# Return Values:
#       Q::Array{Int, 2}
#       - the preference matrix for P
#       - Q[i,j] = 1 if and only if j precedes i in P

Kendall Tau Distance

Computes the Kendall Tau distance between two permutations using the permutation’s preference matrices.

kendalldistance(Q1, Q2)

# Parameters:
#       Q1::Array{Int, 2}
#       - the preference matrix for the first permutation
#       Q2::Array{Int, 2}
#       - the preference matrix for the second permutation
# Return Values:
#       D::Int
#       - the Kendall Tau Distance between two permutations
#       - the the number of pairs (i, j) such that: P1[i] < P1[j] and P2[i] > P2[j]

Mallow’s Distribution

Constructs a Mallow’s Distribution centered around a specified permutation with a given spreading factor.

mallowsdistribution(P, Gamma)

# Parameters:
#       P::Array{Int, 1}
#       - a permutation
#       Gamma::Float64
#       - the spreading factor
# Return Values:
#       MD::Array{Float64, 1}
#       - the mallows distribution with spreading factor Gamma centered at P

Printing Methods

permutation_string(Permutation)

# Parameters:
#       Permutation::Array{Int, 1}
#       - a permutation
# Return Values:
#       ST::String
#       - the string representation of permutation

partition_strign(Partition)

# Parameters:
#       Partition::Array{Int, 1}
#       - a partition
# Return Values:
#       ST::String
#       - the string representation of partition