Impala Documentation

template<class ArrayT>

ArrayT* Impala::Core::Matrix::MatCovarianceExact	(	ArrayT *	m,
		ArrayT *	meanOut = `0`
	)			`[inline]`

Covariance matrix.

Compute the covariance matrix of the observed data Output: [nc x nc] covariance matrix and (optionally) a vector of mean-values for each dimension.

This version is exact, also for a small number of rows in m. Straightforward implementation, so slower than the other version

Definition at line 88 of file MatCovariance.h.

References MatDiv(), MatE(), MatNrCol(), MatNrRow(), MatSet(), and VecE().

Referenced by Impala::Core::Tracking::Classifier::SetBackground().

00089 {
00090     typedef typename ArrayT::ArithType ArithT;
00091     typedef typename ArrayT::StorType StorT;
00092 
00093     int nr = MatNrRow(m);
00094     int nc = MatNrCol(m);
00095     ArrayT* cov = MatCreate<ArrayT>(nc, nc);
00096     MatSet(cov, 0);
00097     ArrayT* mean = VecCreate<ArrayT>(nc) ; //means
00098     MatSet(mean, 0);
00099 
00100     int k;
00101     for ( k=0; k<nr; k++)
00102     {
00103         StorT* meanPtr = VecE(mean, 0);
00104         StorT* mkPtr = MatE(m, k, 0);
00105         for (int i=0; i<nc; i++)
00106         {
00107             ArithT mkiVal = mkPtr[i];
00108             meanPtr[i] += mkiVal;
00109             /*
00110             StorT* coviPtr = MatE(cov, i, 0);
00111             for (int j=i; j<nc; j++) {
00112                 coviPtr[j] += mkiVal * mkPtr[j];
00113             }
00114             */
00115         }
00116     }
00117 
00118     MatDiv(mean, nr);
00119 
00120     for ( k=0; k<nr; k++) {
00121         StorT* meanPtr = VecE(mean, 0);
00122         StorT* mkPtr = MatE(m, k, 0);
00123         for (int i=0; i<nc; i++)
00124         {
00125             //ArithT mkiVal = mkPtr[i];
00126             StorT* coviPtr = MatE(cov, i, 0);
00127             for (int j=i; j<nc; j++)
00128             {
00129                 coviPtr[j] += (mkPtr[i] - meanPtr[i]) * (mkPtr[j] - meanPtr[j]);
00130             }
00131         }
00132     }
00133 
00134     for (int i=0; i<nc; i++) {
00135         StorT* coviPtr = MatE(cov, i, 0);
00136         //StorT* meanPtr = VecE(mean, 0);
00137         //ArithT meani = meanPtr[i];
00138         for (int j=i; j<nc; j++)
00139         {
00140             ArithT res = coviPtr[j] / (nr - 1);
00141             coviPtr[j] = res;
00142             *MatE(cov, j, i) = res;
00143         }
00144     }
00145 
00146     if (meanOut != 0)
00147         MatSet(meanOut, mean);
00148     delete mean;
00149 
00150     return cov;
00151 }

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