Programmer Guide/Command Reference/EVAL/dist

Compute the variance, covariance or covariance-matrix.

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Usage 1

dist(xscalar, yscalar)

dist(xvector, yvector)

Result 1

The euclidan distance d_scalar of x and y. The two arguments must be scalars or vectors with the same length.

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Usage 2

dist(xvector)

dist(xmatrix)

Result 2

The distance matrix d with the euclidian distances of all elements or row vectors of x. The result is a matrix with nrow(x) rows and columns.

xvector	-> d[i,j] = dist(x[i], x[j])
xmatrix	-> di,j = dist(x[i,*], x[j,*])

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Usage 2

dist(x)

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

avr, dev, corr, dist

<function list>

dist

Calculate the distance matrix for all elements in the vector x or for all row vectors in the matrix x. I.e. d(i,j) = distance (x[i,*], x[j,*]). This is a subcommand of the EVAL command.

Usage:

dist(x)

Return Type:

matrix

Calculate the Euclidean distance from x to y. Both arguments must be either scalars or vectors.

Usage:

dist(x, y)

Return Type:

scalar

Calculate the Euclidean distances between all elements of xv or all row vectors of xm to the value ys or the vector yv. The result is a vector with x[!nrow] elements.

Usage:

dist(xv,ys)

dist(xm, yv)

Return Type:

vector