Impala Documentation

template<class ArrayT>

ArrayT* Impala::Core::Matrix::MatCovariance	(	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.

NOTE : this version is an approximation, only valid when the number of rows in m is large.

Definition at line 27 of file MatCovariance.h.

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

Referenced by Impala::Application::Im::DoMatrix(), and MatKLM().

00028 {
00029     typedef typename ArrayT::ArithType ArithT;
00030     typedef typename ArrayT::StorType StorT;
00031 
00032     int nr = MatNrRow(m);
00033     int nc = MatNrCol(m);
00034     ArrayT* cov = MatCreate<ArrayT>(nc, nc);
00035     MatSet(cov, 0);
00036     ArrayT* mean = VecCreate<ArrayT>(nc) ; //means
00037     MatSet(mean, 0);
00038 
00039     for (int k=0; k<nr; k++)
00040     {
00041         StorT* meanPtr = VecE(mean, 0);
00042         StorT* mkPtr = MatE(m, k, 0);
00043         for (int i=0; i<nc; i++)
00044         {
00045             ArithT mkiVal = mkPtr[i];
00046             meanPtr[i] += mkiVal;
00047             StorT* coviPtr = MatE(cov, i, 0);
00048             for (int j=i; j<nc; j++)
00049             {
00050                 coviPtr[j] += mkiVal * mkPtr[j];
00051             }
00052         }
00053     }
00054 
00055     MatDiv(mean, nr);
00056 
00057     for (int i=0; i<nc; i++)
00058     {
00059         StorT* coviPtr = MatE(cov, i, 0);
00060         StorT* meanPtr = VecE(mean, 0);
00061         ArithT meani = meanPtr[i];
00062         for (int j=i; j<nc; j++)
00063         {
00064             ArithT res = coviPtr[j] / nr - meani * meanPtr[j];
00065             coviPtr[j] = res;
00066             *MatE(cov, j, i) = res;
00067         }
00068     }
00069 
00070     if (meanOut != 0)
00071         MatSet(meanOut, mean);
00072     delete mean;
00073 
00074     return cov;
00075 }

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