Programmer Guide/Command Reference/EVAL/svd - Revision history

193.171.195.48 at 08:50, 21 April 2011

2011-04-21T08:50:17Z

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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>
	;Result 2: Returns the matrix ''C''=~~<code>~~trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).		;Result 2: Returns the matrix <code>''C''=trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).
	----		----
	;Usage 3: <code>svd('''2''', <var>A</var>, <var>trn</var>, <var>U</var>, <var>S</var>, <var>V</var>)</code>		;Usage 3: <code>svd('''2''', <var>A</var>, <var>trn</var>, <var>U</var>, <var>S</var>, <var>V</var>)</code>

193.171.195.48 at 08:49, 21 April 2011

2011-04-21T08:49:15Z

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	:;<var>V</var>:contains on return the MxM matrix ''V''		:;<var>V</var>:contains on return the MxM matrix ''V''
	;Result 4: Computes the SVD of the transformed and squared input matrix ''T''.		;Result 4: Computes the SVD of the transformed and squared input matrix ''T''.
	::<code>''C'' = trn(''T'') * ''T''		::<code>''C'' = trn(''T'') * ''T''</code>
	::<code>solve: ''C'' = ''V'' * Σ * trn(''V'')</code>		::<code>solve: ''C'' = ''V'' * Σ * trn(''V'')</code>
	:The results are stored in the (optional) numerical tables (references) ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value is the NxM matrix <code>''PC''=''A'' * ''V''</code>.		:The results are stored in the (optional) numerical tables (references) ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value is the NxM matrix <code>''PC''=''A'' * ''V''</code>.

193.171.195.48 at 08:48, 21 April 2011

2011-04-21T08:48:38Z

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	:;<var>S</var>:contains on return the vector ''S'' with M elements; Note: the returned vector contains the diagonal elements of the matrix Σ (''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 (''singular values'').
	:;<var>V</var>:contains on return the MxM matrix ''V''		:;<var>V</var>:contains on return the MxM matrix ''V''
	;Result 6: Computes the SVD of the matrix ''C''. It is assumed that ''C'' is (optional) transformed and squared matrix derived from a NxM data matrix.		;Result 5: Computes the SVD of the matrix ''C''. It is assumed that ''C'' is (optional) transformed and squared matrix derived from a NxM data matrix.
	::<code>solve: ''C'' = ''V'' * Σ * trn(''V'')</code>		::<code>solve: ''C'' = ''V'' * Σ * trn(''V'')</code>
	:The results are stored in the (optional) numerical tables (references) ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value is always '''0'''.		:The results are stored in the (optional) numerical tables (references) ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value is always '''0'''.

193.171.195.48 at 08:47, 21 April 2011

2011-04-21T08:47:57Z

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	{{DISPLAYTITLE:{{SUBPAGENAME}}}}		{{DISPLAYTITLE:{{SUBPAGENAME}}}}
	~~Compute the variance, covariance or covariance-matrix~~.		Singular value decomposition ([http://en.wikipedia.org/wiki/Singular_value_decomposition SVD]).
	----		----
	;Usage 1: ~~'''~~<code>svd('''0''', <var>A</var>, <var>trn</var>)</code>~~'''~~		;Usage 1: <code>svd('''0''', <var>A</var>, <var>trn</var>)</code>
	:;<var>A</var>:the NxM matrix to be transformed		:;<var>A</var>:the NxM matrix to be transformed
	:;<var>trn</var>:transformation to be applied to A		:;<var>trn</var>:transformation to be applied to A
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	;Result 1: The transformed matrix ''T''.		;Result 1: The transformed matrix ''T''.
	----		----
	;Usage 2: ~~'''~~<code>svd('''1''', <var>A</var>, <var>trn</var>)</code>~~'''~~		;Usage 2: <code>svd('''1''', <var>A</var>, <var>trn</var>)</code>
	;Result 2: Returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).		;Result 2: Returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).
	----		----
	;Usage 3: ~~'''~~<code>svd('''2''', <var>A</var>, <var>trn</var>, <var>U</var>, <var>S</var>, <var>V</var>)</code>~~'''~~		;Usage 3: <code>svd('''2''', <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 Σ, 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''.
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	:The results are stored in the (optional) numerical tables (references) ''U'' (NxM), ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value is the NxM matrix <code>''PC''=''U'' * Σ</code>.		:The results are stored in the (optional) numerical tables (references) ''U'' (NxM), ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value is the NxM matrix <code>''PC''=''U'' * Σ</code>.
	----		----
			;Usage 4: <code>svd('''3''', <var>A</var>, <var>trn</var>, <var>U</var>, <var>S</var>, <var>V</var>)</code>
			:;<var>S</var>:contains on return the vector ''S'' with M elements; Note: the returned vector contains the diagonal elements of the matrix Σ (''singular values'').
			:;<var>V</var>:contains on return the MxM matrix ''V''
			;Result 4: Computes the SVD of the transformed and squared input matrix ''T''.
			::<code>''C'' = trn(''T'') * ''T''
			::<code>solve: ''C'' = ''V'' * Σ * trn(''V'')</code>
			:The results are stored in the (optional) numerical tables (references) ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value is the NxM matrix <code>''PC''=''A'' * ''V''</code>.
			----
			;Usage 5: <code>svd('''4''', <var>C</var>, <var>S</var>, <var>V</var>)</code>
			:;<var>C</var>:the MxM input data matrix
			:;<var>S</var>:contains on return the vector ''S'' with M elements; Note: the returned vector contains the diagonal elements of the matrix Σ (''singular values'').
			:;<var>V</var>:contains on return the MxM matrix ''V''
			;Result 6: Computes the SVD of the matrix ''C''. It is assumed that ''C'' is (optional) transformed and squared matrix derived from a NxM data matrix.
			::<code>solve: ''C'' = ''V'' * Σ * trn(''V'')</code>
			:The results are stored in the (optional) numerical tables (references) ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value is always '''0'''.
			----
	;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>]]

193.171.195.48 at 08:36, 21 April 2011

2011-04-21T08:36:26Z

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	\|		\|
	\|}		\|}
	:;Result 1: The transformed matrix ''T''.		;Result 1: The transformed matrix ''T''.
	----		----
	;Usage 2: '''<code>svd('''1''', <var>A</var>, <var>trn</var>)</code>'''		;Usage 2: '''<code>svd('''1''', <var>A</var>, <var>trn</var>)</code>'''
	:;Result 2: Returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).		;Result 2: Returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).
	----		----
	;Usage 3: '''<code>svd('''2''', <var>A</var>, <var>trn</var>, <var>U</var>, <var>S</var>, <var>V</var>)</code>'''		;Usage 3: '''<code>svd('''2''', <var>A</var>, <var>trn</var>, <var>U</var>, <var>S</var>, <var>V</var>)</code>'''
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	:;<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>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''. The results are stored in the (optional) numerical tables (references) ''U'' (NxM), ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value ~~''PC''~~ is the matrix <code>''PC~~''=''U'' * ''S''</code>.~~		;Result 3: Computes the SVD of the transformed input matrix ''T''.
	~~:<code>solve: ''T~~'' = ''U'' * Σ * trn(''V'')</code>		::<code>solve: ''T'' = ''U'' * Σ * trn(''V'')</code>
			:The results are stored in the (optional) numerical tables (references) ''U'' (NxM), ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value is the NxM matrix <code>''PC''=''U'' * Σ</code>.
	----		----

193.171.195.48 at 08:31, 21 April 2011

2011-04-21T08:31:04Z

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	:;Result 2: Returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).		:;Result 2: Returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).
	----		----
	;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('''2''', <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 Σ, 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''. The results are stored in the (optional) numerical tables (references) ''U'' (NxM), ''S'' (Mx1, diagonal of Σ) and ''V'' (MxM). The return value ''PC'' is the matrix <code>''PC''=''U'' * ''S''</code>.
	:<code>''T'' = ''U'' * Σ * trn		:<code>solve: ''T'' = ''U'' * Σ * trn(''V'')</code>
	----		----

193.171.195.48 at 08:04, 21 April 2011

2011-04-21T08:04:34Z

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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'' * ~~''S''~~ * trn		:<code>''T'' = ''U'' * Σ * trn
	----		----

193.171.195.48 at 08:03, 21 April 2011

2011-04-21T08:03:43Z

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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>'''
	:;Result 2: Returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).		:;Result 2: Returns the matrix ''C''=<code>trn(''T'')*''T''</code>. ''C'' is a square matrix with M rows and columns (MxM).
			----
			;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>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>V</var>:contains on return the MxM matrix ''V''
			;Result: Computes the SVD of the transformed input matrix ''T''.
			:<code>''T'' = ''U'' * ''S'' * trn
			----

193.171.195.48 at 07:32, 21 April 2011

2011-04-21T07:32:27Z

@@ Line 31: / Line 31: @@
 ----
 ;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).
 ;See also: [[../var|var]], [[../corr|corr]], [[../dist|dist]], [[../haclust|haclust]], [[../modclust|modclust]]
 [[../#Functions|<function list>]]

193.171.195.48 at 07:30, 21 April 2011

2011-04-21T07:30:15Z

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	:;<var>trn</var>:transformation to be applied to A		:;<var>trn</var>:transformation to be applied to A
	::{\|class="einrahmen"		::{\|class="einrahmen"
	!''trn'' !!transformed matrix ''T'' !!description !! <code>trn(''T'')*''T''</code> (MxM ~~matrix~~)		!''trn'' !!transformed matrix ''T'' (NxM) !!description !! <code>trn(''T'')*''T''</code><BR>(MxM)
	\|-		\|-
	\|0 \|\|''T''[i,j] = ''A''[i,j]		\|0 \|\|''T''[i,j] = ''A''[i,j]