# API reference¶

## Markov Methods¶

 `giddy.markov.Markov`(class_ids[, classes, ...]) Classic Markov Chain estimation. `giddy.markov.Spatial_Markov`(y, w[, k, m, ...]) Markov transitions conditioned on the value of the spatial lag. `giddy.markov.LISA_Markov`(y, w[, ...]) Markov for Local Indicators of Spatial Association `giddy.markov.FullRank_Markov`(y[, ...]) Full Rank Markov in which ranks are considered as Markov states rather than quantiles or other discretized classes. `giddy.markov.GeoRank_Markov`(y[, ...]) Geographic Rank Markov. Kullback information based test of Markov Homogeneity. Prais conditional mobility measure. `giddy.markov.homogeneity`(transition_matrices) Test for homogeneity of Markov transition probabilities across regimes. `giddy.markov.sojourn_time`(p[, summary]) Calculate sojourn time based on a given transition probability matrix. `giddy.ergodic.steady_state`(P[, ...]) Generalized function for calculating the steady state distribution for a regular or reducible Markov transition matrix P. `giddy.ergodic.mfpt`(P[, fill_empty_classes]) Generalized function for calculating mean first passage times for an ergodic or non-ergodic transition probability matrix. Variances of mean first passage times for an ergodic transition probability matrix.

## Directional LISA¶

 `giddy.directional.Rose`(Y, w[, k]) Rose diagram based inference for directional LISAs.

## Economic Mobility Indices¶

 `giddy.mobility.markov_mobility`(p[, measure, ini]) Markov-based mobility index.

## Exchange Mobility Methods¶

 `giddy.rank.Theta`(y, regime[, permutations]) Regime mobility measure. `giddy.rank.Tau`(x, y) Kendall's Tau is based on a comparison of the number of pairs of n observations that have concordant ranks between two variables. `giddy.rank.SpatialTau`(x, y, w[, permutations]) Spatial version of Kendall's rank correlation statistic. Local version of the classic Tau. `giddy.rank.Tau_Local_Neighbor`(x, y, w[, ...]) Neighbor set LIMA. `giddy.rank.Tau_Local_Neighborhood`(x, y, w[, ...]) Neighborhood set LIMA. `giddy.rank.Tau_Regional`(x, y, regime[, ...]) Inter and intraregional decomposition of the classic Tau.

## Alignment-based Sequence Methods¶

 `giddy.sequence.Sequence`(y[, subs_mat, ...]) Pairwise sequence analysis.

## Utility Functions¶

 Random permutation of rows and columns of a matrix `giddy.util.get_lower`(matrix) Flattens the lower part of an n x n matrix into an n*(n-1)/2 x 1 vector. Assign 1 to diagonal elements which fall in rows full of 0s to ensure the transition probability matrix is a stochastic one.