Matrices

\d .gmb.mat
//null aware primitives from Nick Psaris's Funq
noflip:{system"g"}              / redefine to customize behavior
ncount:{count[x]-$[type x;sum null x;0i {x+null y}/ x]}
nsum:{$[type x;sum x;0i {x+0i^y}/ x]}
navg:{$[type x;avg x;nsum[x]%ncount x]}
nwavg:{[w;x]$[type x;w wavg x;(%/){x+y*(0f^z;not null z)}/[0 0f;w;x]]}
nvar:{$[type x;var x;navg[x*x]-m*m:navg x]}
ndev:{sqrt nvar::}
nsvar:{$[type x;svar x;(n*nvar x)%-1+n:ncount x]}
nsdev:{sqrt nsvar::}
//Matrix functions & primitives from Nick Psaris's Funq
f2nd:{[f;X]$[noflip[];(f value::) peach flip (count[X]#`)!X;f peach flip X]} //avoids flips when garbage collection is on --Nick Psaris Funq
mm:{$[;y] peach x} //X mmu Y replacement
mmt:{(y$) peach x} // X mmu flip Y replacement 
mtm:{f2nd[$[;y];x]} //flip X mmu Y replacement 

// My custom Matrix Functions
nSCovMatrix:{[matrix]
    //takes table or array
    //null aware Sample Covariance Matrix
    $[98h=type matrix;matrix:"f"$(flip matrix[cols matrix]);matrix:"f"$matrix];
    corMatrix:u cor/:\:u: flip matrix;
    sd:sqrt nsvar[matrix]; //standard dev of each variable
    diagMatrix:sd*{x=/:x}til first count each matrix;
    :covMatrix:(diagMatrix) mmu corMatrix mmu (diagMatrix);
 };


chiSquareDistanceRow:{[table]
    //takes table of categorical variables, returns chisquare distance matrix of rows(observations)
    n:count table;
    p:count cols table;
    cDT:flip value flip .gmb.preprocessing.oneHotEncoder[table][`CDT];
    step1:{[x;y]y[x]<>/:y}\:[til n;cDT]; //diff of CDT entries squared
    step2:{[step1;cDT]step1[til count cDT]%\:(sum cDT)}\:[step1;cDT]; //step2 divide each entry by sum of columns of CDT
    :({[x;y]sum each y[x]}\:[til count cDT;step2])*n%p; //matrix of chi squared distance between rows
    };

chiSquareDistanceColumn:{[table]
    //takes table of categorical variables, returns chisquare distance matrix of cols(variables)
    n:count table;
    cDT:flip value flip .gmb.preprocessing.oneHotEncoder[table][`CDT];
    //n* sums squar diffs between CDT columns
    :n*sum each {[n;cDT] flip((flip cDT)[n] <>/: (flip cDT)[til count flip cDT])}\:[til count flip cDT;cDT]; 
 };

covarianceMatrix:{(x+flip(not n=\:n)*x:(n#'0.0),'(x$/:'(n:til count x)_\:x)%count first x)-a*\:a:avg each x} //from .stat.q

getDiagonal:{[x]
    //retrieves diagonal from a matrix
    :x@'til count x;
    }; 

mahalanobisDistance:{[dataSet]
    //takes a table OR array, null aware, uses sample cov
    //each observation is included in set of observations
    //room for improvement on finding covariance table
    $[98h=type dataSet;matrix:"f"$(value flip dataSet);matrix:"f"$dataSet];
    observation:(flip matrix);
    step1: 0f^(observation -\: (navg peach matrix));
    covMatrix:nSCovMatrix[0^observation]; 
    step2: $[;inv covMatrix] peach step1;
    step3:sqrt (step2 mmu/: step1);
    :getDiagonal[step3];
    };