Programmer Guide/Command Reference/EVAL/dist: Difference between revisions

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:'''<code>dist(''x''<sub>vector</sub>)</code>'''
:'''<code>dist(''x''<sub>vector</sub>)</code>'''
:'''<code>dist(''x''<sub>matrix</sub>)</code>'''
:'''<code>dist(''x''<sub>matrix</sub>)</code>'''
;Result 2: The distance matrix ''d'' with the euclidian distances of all elements or row vectors of ''x''. The result is a matrix with <code>nrow(''x'')</code> rows and columns.  
;Result 2: The matrix ''d'' with the euclidian distances of all elements or row vectors of ''x''. The result is a matrix with <code>nrow(''x'')</code> rows and columns.  
:{|class="keinrahmen"
:{|class="keinrahmen"
|''x''<sub>vector</sub> ||-> ''d''[i,j] = dist(''x''[i], ''x''[j])
|''x''<sub>vector</sub> ||-> ''d''[i,j] = dist(''x''[i], ''x''[j])
|-
|-
|''x''<sub>matrix</sub> ||-> ''d''<sub>i,j</sub> = dist(''x''[i,*], ''x''[j,*])
|''x''<sub>matrix</sub> ||-> ''d''[i,j] = dist(''x''[i,*], ''x''[j,*])
|-
| || with: i,j = 0 .. <code>ncol(''x'')</code>
|}
|}
----
----
;Usage 2: '''<code>dist(''x'')</code>'''
;Usage 3:  
;Result 2:
:'''<code>dist(''x''<sub>vector</sub>, ''y''<sub>scalar</sub>)</code>'''
The covariance ''v'' of the vectors ''x'' and ''y''.
:'''<code>dist(''x''<sub>matrix</sub>, ''y''<sub>vector</sub>)</code>'''
:<code>''v'' = sum( (''x''-avr(''x'') ?* (''y''-avr(''y'')) ) / (nrow(''x'')-1)</code>
;Result 3: The vector ''d'' with the euclidian distances of all elements or row vectors of ''x'' to ''y''. The result is a vector with <code>nrow(''x'')</code> rows and columns.
:<code>''v'' = ((''x''-avr(''x'') * (''y''-avr(''y''))) / (nrow(''x'')-1)</code>
:{|class="keinrahmen"
----
|''x''<sub>vector</sub>,''y''<sub>scalar</sub> ||-> ''d''[i] = dist(''x''[i], ''y'')
;Usage 3: '''<code>var(''x''<sub>matrix</sub>)</code>'''
:'''<code>var(''x''<sub>matrix</sub>, ''y''<sub>scalar</sub>)</code>'''
:'''<code>var(''x''<sub>matrix</sub>, ''y''<sub>vector</sub>)</code>'''
;Result 3: The covariance matrix ''v'' of the column vectors of ''x''.
:<code>''v''[i,j] = sum( (''x''[*,i]-a[i]) ?* (''x''[*,j]-a[j]) ) / (nrow(''x'')-1) , with: i,j = 0..ncol(''x'')-1</code>
:The column averages a[i] are computed as follows:
::{|class="einrahmen"
|''y'' not supplied || a[i] = avr(''x''[*,i])
|-
|-
|''y''<sub>scalar</sub> || a[i] = ''y''
|''x''<sub>matrix</sub>,''y''<sub>vector</sub> ||-> ''d''[i,j] = dist(''x''[i,*], ''y'')  (<code>ncol(''x'') = nrow(''y'')</code>
|-
|-
|''y''<sub>vector</sub> || a[i] = ''y''[i]
| || with: i = 0 .. <code>ncol(''x'')</code>
|}
----
;Usage 4:
:'''<code>dist(''x''<sub>matrix</sub>, ''flag'')</code>'''
;Result 3: The matrix ''d'' with the euclidian distances of the row vectors (''flag''='''0''') or column vectors (''flag''='''1''') or ''x''.
:{|class="keinrahmen"
|''flag''=0 ||-> ''d''[i,j] = dist(''x''[i,*], ''x[j,*]'') ||, with: i,j = 0 .. <code>nrow(''x'')</code>
|-
|-
|''flag''=1 ||-> ''d''[i,j] = dist(''x''[*,i], ''x[*,j]'') ||, with: i,j = 0 .. <code>ncol(''x'')</code>
|}
|}


;See also: [[Programmer_Guide/Command_Reference/EVAL/avr|avr]], [[Programmer_Guide/Command_Reference/EVAL/dev|dev]], [[Programmer_Guide/Command_Reference/EVAL/corr|corr]], [[Programmer_Guide/Command_Reference/EVAL/dist|dist]]
 
;See also: [[Programmer_Guide/Command_Reference/EVAL/var|var]], [[Programmer_Guide/Command_Reference/EVAL/corr|corr]]


[[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]]
[[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]]
{{DISPLAYTITLE:{{SUBPAGENAME}}}}
=====dist=====
Calculate the distance matrix for all elements in the vector <var>x</var> or for all row vectors in the matrix <var>x</var>. I.e. d(i,j) = distance (<var>x</var>[i,*], <var>x</var>[j,*]). This is a subcommand of the <code>[[Programmer Guide/Command Reference/EVAL/EVAL|EVAL]]</code> command.
=====Usage:=====
<code>dist(<var>x</var>)</code>
=====Return Type:=====
matrix
Calculate the Euclidean distance from <var>x</var> to <var>y</var>. Both arguments must be either scalars or vectors.
=====Usage:=====
<code>dist(<var>x</var>, <var>y</var>)</code>
=====Return Type:=====
scalar
Calculate the Euclidean distances between all elements of <var>x</var>v or all row vectors of <var>x</var>m to the value <var>y</var>s or the vector <var>y</var>v. The result is a vector with x[!nrow] elements.
=====Usage:=====
<code>dist(<var>xv,ys</var>)</code>
<code>dist(<var>x</var>m, <var>y</var>v)</code>
=====Return Type:=====
vector

Revision as of 09:45, 11 April 2011

Compute the variance, covariance or covariance-matrix.

Usage 1
dist(xscalar, yscalar)
dist(xvector, yvector)
Result 1
The euclidan distance dscalar of x and y. The two arguments must be scalars or vectors with the same length.
Usage 2
dist(xvector)
dist(xmatrix)
Result 2
The 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 -> d[i,j] = dist(x[i,*], x[j,*])
with: i,j = 0 .. ncol(x)
Usage 3
dist(xvector, yscalar)
dist(xmatrix, yvector)
Result 3
The vector d with the euclidian distances of all elements or row vectors of x to y. The result is a vector with nrow(x) rows and columns.
xvector,yscalar -> d[i] = dist(x[i], y)
xmatrix,yvector -> d[i,j] = dist(x[i,*], y) (ncol(x) = nrow(y)
with: i = 0 .. ncol(x)
Usage 4
dist(xmatrix, flag)
Result 3
The matrix d with the euclidian distances of the row vectors (flag=0) or column vectors (flag=1) or x.
flag=0 -> d[i,j] = dist(x[i,*], x[j,*]) , with: i,j = 0 .. nrow(x)
flag=1 -> d[i,j] = dist(x[*,i], x[*,j]) , with: i,j = 0 .. ncol(x)


See also
var, corr

<function list>

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