Programmer Guide/Command Reference/EVAL/svd: Difference between revisions
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;Usage 3: '''<code>svd('''0''', <var>A</var>, <var>trn</var>, <var>U</var>, <var>S</var>, <var>V</var>)</code>''' | ;Usage 3: '''<code>svd('''0''', <var>A</var>, <var>trn</var>, <var>U</var>, <var>S</var>, <var>V</var>)</code>''' | ||
:;<var>U</var>:contains on return the NxM matrix ''U'' | :;<var>U</var>:contains on return the NxM matrix ''U'' | ||
:;<var>S</var>:contains on return the vector ''S'' with M elements; Note: the returned vector contains the diagonal elements of the matrix &Sigma, which are called the ''singular values''. | :;<var>S</var>:contains on return the vector ''S'' with M elements; Note: the returned vector contains the diagonal elements of the matrix Σ, which are called the ''singular values''. | ||
:;<var>V</var>:contains on return the MxM matrix ''V'' | :;<var>V</var>:contains on return the MxM matrix ''V'' | ||
;Result: Computes the SVD of the transformed input matrix ''T''. | ;Result: Computes the SVD of the transformed input matrix ''T''. | ||
:<code>''T'' = ''U'' * | :<code>''T'' = ''U'' * Σ * trn | ||
---- | ---- | ||
Revision as of 09:04, 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).
- Usage 3
svd(
0, A, trn, U, S, V)
- U
- contains on return the NxM matrix U
- S
- contains on return the vector S with M elements; Note: the returned vector contains the diagonal elements of the matrix Σ, which are called the singular values.
- V
- contains on return the MxM matrix V
- Result
- Computes the SVD of the transformed input matrix T.
T = U * Σ * trn