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

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----
----
;Usage 2: '''<code>svd('''1''', <var>A</var>, <var>trn</var>)</code>'''
;Usage 2: '''<code>svd('''1''', <var>A</var>, <var>trn</var>)</code>'''
:;<var>A</var>:the NxM matrix to be transformed
:;Result 2: Returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).
:;<var>trn</var>:transformation to be applied to A (see '''Usage 1''')
:;Result 2: Computes the transformed matrix ''T'' and returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).


::{|class="einrahmen"
!''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''.
:<code>''v'' = sum( (''x''-avr(''x''))?^2 ) / (nrow(''x'')-1)</code>
:<code>''v'' = (''x''-avr(''x''))^2 / (nrow(''x'')-1)</code>
----
;Usage 2: '''<code>var(''x''<sub>vector</sub>, ''y''<sub>vector</sub>)</code>'''
;Result 2: The covariance ''v'' of the vectors ''x'' and ''y''.
:<code>''v'' = sum( (''x''-avr(''x'') ?* (''y''-avr(''y'')) ) / (nrow(''x'')-1)</code>
:<code>''v'' = ((''x''-avr(''x'') * (''y''-avr(''y''))) / (nrow(''x'')-1)</code>
----
;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''
|-
|''y''<sub>vector</sub> || a[i] = ''y''[i]
|-
|}


;See also: [[../var|var]], [[../corr|corr]], [[../dist|dist]], [[../haclust|haclust]], [[../modclust|modclust]]
;See also: [[../var|var]], [[../corr|corr]], [[../dist|dist]], [[../haclust|haclust]], [[../modclust|modclust]]


[[../#Functions|<function list>]]
[[../#Functions|<function list>]]

Revision as of 08:32, 21 April 2011

Compute the variance, covariance or covariance-matrix.

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.
Usage 2
svd(1, A, trn)
Result 2
Returns the matrix C=trn(T)*T. C is a square matrix with M rows and columns (MxM).


See also
var, corr, dist, haclust, modclust

<function list>

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