Programmer Guide/Command Reference/EVAL/svd

Compute the variance, covariance or covariance-matrix.

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Usage 1

svd(0, A, trn)

A

the NxM matrix to be transformed

trn

transformation to be applied to A

trn	transformed matrix T (NxM)	description	trn(T)*T (MxM)
0	T[i,j] = A[i,j]	no transformation	"Streumatrix"
1	T[i,j] = A[i,j]-avr(A)	subtract matrix mean
2	T[i,j] = A[i,j]-avr(A[*,j])	subtract column mean (center columns)	covariance matrix
3	T[i,j] = (A[i,j]-avr(A[*,j]))/dev(A[*,j])	subtract column mean, devide by column deviation (center and standardize columns)	correlation matrix
4	T[i,j] = A[i,j]-(avr(A[i,*])+avr(A[*,j]))+avr(A)	subtract row and column mean, add matrix mean (center rows and columns)

Result 1

The transformed matrix T.

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Usage 2

svd(1, A, trn)

A

the NxM matrix to be transformed

trn

transformation to be applied to A (see Usage 1)

Result 2

Computes the transformed matrix T and returns the matrix C=trn(T)*T. C is a square matrix with M rows and columns (MxM).

trn	transformation	description	0	T[i,j] = A[i,j]	no transformation
1	T[i,j] = A[i,j]-avr(A)	subtract matrix mean
2	T[i,j] = A[i,j]-avr(A[*,j])	subtract column mean (center columns)
3	T[i,j] = (A[i,j]-avr(A[*,j]))/dev(A[*,j])	subtract column mean, devide by column deviation (center and standardize columns)
4	T[i,j] = A[i,j]-(avr(A[i,*])+avr(A[*,j]))+avr(A)	subtract row and column mean, add matrix mean (center rows and columns)

Result 1

The variance v of vector x.

v = sum( (x-avr(x))?^2 ) / (nrow(x)-1)

v = (x-avr(x))^2 / (nrow(x)-1)

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Usage 2

var(xvector, yvector)

Result 2

The covariance v of the vectors x and y.

v = sum( (x-avr(x) ?* (y-avr(y)) ) / (nrow(x)-1)

v = ((x-avr(x) * (y-avr(y))) / (nrow(x)-1)

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Usage 3

var(xmatrix)

var(xmatrix, yscalar)

var(xmatrix, yvector)

Result 3

The covariance matrix v of the column vectors of x.

v[i,j] = sum( (x[*,i]-a[i]) ?* (x[*,j]-a[j]) ) / (nrow(x)-1) , with: i,j = 0..ncol(x)-1

The column averages a[i] are computed as follows:

y not supplied	a[i] = avr(x[*,i])
yscalar	a[i] = y
yvector	a[i] = y[i]

See also

var, corr, dist, haclust, modclust

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