GetisOrdGiStar.js

// Functions: 
// GetisOrdGi()     - includes values from locations j connected to location i
//                    but excludes the value at i in the calculation. 
// GetisOrdGiStar() - includes the value at location (i).
// GetisOrdGiStarZ()- produces a standard (z) score reather than the Gi or GiStar
//                    statistic.
// GetisOrdGiStarZ_nulls() - same as GetisOrdGiStarZ but handles null values in
//                           the data array (the connections matrix should include
//                           all locations, regardless of whether or not data
//                           are missing for a variable at that locaion).
// GetisOrdGiZ()   - standard (z) score transformation of Gi statistic.

// Functions for spatial randomization test of Gi*:
// permuteGetisOrdGiStar(), testGetisOrdGiStar()

// Authors: Corey Devin Anderson and Kirankumar Batchu

//------------------------------------------------------------------------------//

// Description: 

// Calculates Getis-Ord statistics (Gi* and Gi) for determining local hot (and 
// cold) spots. Getis-Ord Gi* includes the focal location (i) in the calculation
// whereas Gi does not. The functions GetisOrdGiStarZ() and GetisOrdGiZ() return
// standard variates (z-scores) based on observed and expected Getis-Ord
// statistics. Currently, one function (GetisOrdGiStarZ_nulls) can handle null 
// values, and others will be added in the near future. Such functions essentially
// return the same result as if you dropped the location prior to building weights
// and calculating the test statistics.

//------------------------------------------------------------------------------//

// Parameters:
// dataArray    : a 1D Array containing the values at each location.
// weightMatrix : a square matrix (n x n) represented as a 2D Array containing 
//                the pairwise weights. Each 1D Array within the 2D Array 
//                represents the connections for a particular location and should
//                be in the same order as the data values in yourArray.
// nsim         : number of permutations (for testGetisOrdGiStar).

// Notes: increasing the number of permutations (nsim) may cause an infinite
// loop error in codepen.io, or loading delays.

// Parameters for main functions:

// GetisOrdGiStar(dataArray, weightMatrix)
// GetisOrdGi(dataArray, weightMatrix)
// GetisOrdGiStarZ(dataArray, weightMatrix)
// GetisOrdGiZ(dataArray, weightMatrix)

// permuteGetisOrdGiStar(dataArray, weightMatrix)
// testGetisOrdGiStar(dataArray, weightMatrix, nsim = 999)
// rowStandardize(weightMatrix)

//------------------------------------------------------------------------------//

// Getis-Ord Gi*
// Gi* includes location i in the summations; Gi does not.

// Getis-Ord Gi*
// Returns an Array containing the Gi* statistics for each location.

// Requires GetisOrdG_helpers.js

// START
function GetisOrdGiStar(dataArray, weightMatrix) {
    let n = weightMatrix.length;  // row count = number of locations (n)
    let totalSum = sumArray(dataArray);  // sum values in data array
    let giStarOut = new Array(n);  // make blank array to populate
    for (let i = 0; i < n; i++) { // calculate Gi* statistics for each location
      let sumjConnectedToiIncludingi = sumArray(multiplyArrays(dataArray, weightMatrix[i]))
      giStarOut[i] =  sumjConnectedToiIncludingi / totalSum; 
    }
  return giStarOut;  // return array of Gi* values
  }
  // END
  
  // Example calls:
  // console.log(GetisOrdGiStar(peakValleyFlat, bMat));
  // console.log(GetisOrdGiStar(peakValleyFlat, rowStandardize(bMat)));
  
  // For larger data set:
  // console.log(GetisOrdGiStar(jsonObject1, rowStandardize(jsonObject2)));
  // let t0 = performance.now();
  // GetisOrdGiStar(jsonObject1, rowStandardize(jsonObject2));
  // let t1 = performance.now();
  // console.log("Time taken: " + ((t1 - t0) / 1000) + " seconds")
  // Half a second to calculate all Gi* values.