CFLib.org – Common Function Library Project

Description:
Calculates the Pearson correlation for the values in two specified keys in an array of structures.

Return Values:
A structure with the perasonCorrelation and a boolean indicating if the input was valid.

Example:

<!--- An array of structs, with keys "X" and "Y"; all values in X and Y are numeric--->
<cfset variables.arrayOfStructs = arrayNew(1)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 3>
<cfset variables.element.Y = 1> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 6>
<cfset variables.element.Y = 2> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 7>
<cfset variables.element.Y = 3> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 4>
<cfset variables.element.Y = 4> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 5>
<cfset variables.element.Y = 5> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 3>
<cfset variables.element.Y = 6> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 7>
<cfset variables.element.Y = 7> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 6>
<cfset variables.element.Y = 8> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 5>
<cfset variables.element.Y = 9> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 2>
<cfset variables.element.Y = 1> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 3>
<cfset variables.element.Y = 2> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 5>
<cfset variables.element.Y = 3> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 6>
<cfset variables.element.Y = 4> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>
<cfset variables.element = structNew()>
<cfset variables.element.X = 7>
<cfset variables.element.Y = 5> 
<cfset arrayAppend(variables.arrayOfStructs, variables.element)>


<cfset variables.pearsonCorrelation = pearsonCorrelation(
        arrayOfStructs = variables.arrayOfStructs, 
        xKey = "X", 
        yKey = "Y")>


<cfdump var="#variables.pearsonCorrelation#">

Parameters:

Full UDF Source:

/**
 * Calculates the Pearson correlation.
 * 
 * @param arrayOfStructures      An array of structures containing the specified keys for every element. (Required)
 * @param xkey      A string: the structKey containing the first variable. (Required)
 * @param ykey      A string: the structKey containing the second variable. (Required)
 * @return A structure with the perasonCorrelation and a boolean indicating if the input was valid. 
 * @author Martijn van der Woud (martijnvanderwoud@orange.nl) 
 * @version 0, September 27, 2008 
 */
function pearsonCorrelation (arrayOfStructs, xKey, yKey) {
    
    // numeric: holds the mean value for the xKey 
    var xMean = 0;
    // numercic: holds the mean value for the yKey
    var yMean = 0;
    // numeric: just a loop index
    var i=0;
    // numeric: holds the sum of all values for the xKey 
    var xSum = 0;
    // numeric: holds the sum of all values for the yKey 
    var ySum = 0;    
    // numeric: the number of elements in arrayOfStructs    
    var length = arrayLen(arguments.arrayOfStructs);
    // numeric: the sum of squared deviations for the xKey
    var sqDevX = 0;
    // numeric: the sum of squaried deviations for the yKey
    var sqDevY = 0;
    // numeric: the sum of cross-products
    var crossProductSum = 0;
    // numeric: holds the deviation from the mean for the xKey in a specific element
    var xDeviation = 0;
    // numeric: holds the deviation from the mean for the yKey in a specific element
    var yDeviation = 0;
    // numeric: the Pearson correlation
    var pearsonCorrelation = 0;
    // struct: the results to return
    var results = structNew();
    
            
    // loop over elements in argument arrayOfStructs
    for(i = 1; i lte length; i = i+1) {
    
        // add the xKey and yKey values of the current element to their corresponding sum variable
        xSum = xSum + arguments.arrayOfStructs[i][arguments.xKey];
        ySum = ySum + arguments.arrayOfStructs[i][arguments.yKey];
    
    } // end of loop over elements in argument arrayOfStructs
    
    // calculate the means of xKey and yKey
    xMean = xSum / length;
    yMean = ySum / length;


    // again, loop over elements in argument arrayOfStructs
    for(i = 1; i lte length; i = i+1) {
        
        // calculate deviations from the mean for the current element
        xDeviation = arguments.arrayOfStructs[i][arguments.xKey] - xMean;
        yDeviation = arguments.arrayOfStructs[i][arguments.yKey] - yMean;
        
        // update sums of squared deviations and cross-products
        sqDevX = sqDevX + xDeviation^2;
        sqDevY = sqDevY + yDeviation^2;            
        crossProductSum = crossProductSum + xDeviation * yDeviation;
    } // end of loop over elements in argument arrayOfStructs

    
    // if there is no variation in either xKey or yKey, the pearson correlation cannot be computed, so indicate an error
    if (min(sqDevX, sqDevY) eq 0) {
        results.inputValid = false;
        results.pearsonCorrelation = "";
    } else { // otherwise, calculatie the pearson correlation

        
        pearsonCorrelation = (crossProductSum / (length-1));
        pearsonCorrelation = pearsonCorrelation / sqr(sqDevX / (length-1));
        pearsonCorrelation = pearsonCorrelation / sqr(sqDevY / (length-1));
        
        results.inputValid = true;
        results.pearsonCorrelation = pearsonCorrelation;
    
    }
            
    return results;
}