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

Christian at 18:08, 21 April 2011

2011-04-21T18:08:32Z

← Older revision		Revision as of 20:08, 21 April 2011
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	:The function DGESV (ZGESV) solves a linear equation system.		:The function DGESV (ZGESV) solves a linear equation system.
	::<code>''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>		::<code>''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>
	:The function DGELS (ZGELS) can be used to find the least squares solution of an overdetermined system (M>=N) or the minimum norm solution of an underdetermined system (M<N).		:The function DGELS (ZGELS) can be used to find the least squares solution of an overdetermined system (M≥N) or the minimum norm solution of an underdetermined system (M<N).
	::<code>'''M>=N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>		::<code>'''M≥N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>
	::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>		::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>
	:A detailed description of the LAPACK functions can be found at [http://www.netlib.org/lapack www.netlib.org].		:A detailed description of the LAPACK functions can be found at [http://www.netlib.org/lapack www.netlib.org].

193.171.195.48 at 10:36, 21 April 2011

2011-04-21T10:36:21Z

← Older revision		Revision as of 12:36, 21 April 2011
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	:A detailed description of the LAPACK functions can be found at [http://www.netlib.org/lapack www.netlib.org].		:A detailed description of the LAPACK functions can be found at [http://www.netlib.org/lapack www.netlib.org].
	;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.		;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.
	;See also: [[../rpolyreg\|rpolyreg]], [[../complex arithmetic\|complex arithmetic]]		;See also: [[../rpolyreg\|rpolyreg]], [[../complex arithmetic\|complex arithmetic]], [[../svd\|svd]]

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

193.171.195.48 at 10:35, 21 April 2011

2011-04-21T10:35:56Z

← Older revision		Revision as of 12:35, 21 April 2011
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	:A detailed description of the LAPACK functions can be found at [http://www.netlib.org/lapack www.netlib.org].		:A detailed description of the LAPACK functions can be found at [http://www.netlib.org/lapack www.netlib.org].
	;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.		;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.


	;See also: [[../rpolyreg\|rpolyreg]], [[../complex arithmetic\|complex arithmetic]]		;See also: [[../rpolyreg\|rpolyreg]], [[../complex arithmetic\|complex arithmetic]]

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

Toni at 06:18, 13 April 2011

2011-04-13T06:18:54Z

← Older revision		Revision as of 08:18, 13 April 2011
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	{{DISPLAYTITLE:rleqs, cleqs}}		{{DISPLAYTITLE:rleqs, cleqs}}
	These functions implements an interface for the [http://www.netlib.org/lapack LAPACK] functions DGESV, ZGESV, DGELS and ZGELS.		These functions implements an interface for the [http://www.netlib.org/lapack LAPACK] functions DGESV, ZGESV, DGELS and ZGELS.
	;Usage: <code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>:		;Usage:
			:{\|class="keinrahmen"
			\|<code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>
			\|... uses functions DGESV and DGELS;
			\|arguments ''A'', ''B'' and result ''X'' are real
			\|-
			\|<code>cleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>
			\|... uses functions ZGESV and ZGELS;
			\|arguments ''A'', ''B'' and result ''X'' are complex
			\|}
	:;<var>A</var>: left side MxN matrix ''x''		:;<var>A</var>: left side MxN matrix ''x''
	:;<var>B</var>: right side vector with M elements (one solution) or MxNHRS matrix (multiple solutions)		:;<var>B</var>: right side vector with M elements (one solution) or MxNHRS matrix (multiple solutions)
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	;~~Notes~~:		;See also: [[../rpolyreg\|rpolyreg]], [[../complex arithmetic\|complex arithmetic]]
	~~:*The function <code>cleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code> has the same arguments and result as <code>rleqs</code>, but the vectors/matrices ''A'', ''B'' and ''X'' are~~ [[~~Programmer_Guide~~/~~Command_Reference/EVAL/complex arithmetic~~\|~~complex~~]].
	~~:*<code>rleqs</code> calls the LAPACK functions DGESV and DGELS~~, ~~while <code>cleqs</code> calls ZGESV and ZGELS~~


	~~;See also:~~ [[~~Programmer_Guide~~/~~Command_Reference/EVAL/rpolyreg~~\|~~rpolyreg~~]]

	[[~~Programmer_Guide~~/~~Command_Reference/EVAL~~#Functions\|<function list>]]		[[../#Functions\|<function list>]]

Toni at 06:14, 13 April 2011

2011-04-13T06:14:26Z

← Older revision		Revision as of 08:14, 13 April 2011
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	:The function DGESV (ZGESV) solves a linear equation system.		:The function DGESV (ZGESV) solves a linear equation system.
	::<code>''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>		::<code>''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>
	:The function DGELS (ZGELS) can be used to find the least solution of an overdetermined system (M>=N) or the minimum norm solution of an underdetermined system (M<N).		:The function DGELS (ZGELS) can be used to find the least squares solution of an overdetermined system (M>=N) or the minimum norm solution of an underdetermined system (M<N).
	::<code>'''M>=N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>		::<code>'''M>=N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>
	::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>		::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>

Toni at 06:13, 13 April 2011

2011-04-13T06:13:41Z

← Older revision		Revision as of 08:13, 13 April 2011
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	::<code>'''M>=N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>		::<code>'''M>=N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>
	::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>		::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>
	:A detailed description of the functions can be found at [http://www.netlib.org/lapack www.netlib.org].		:A detailed description of the LAPACK functions can be found at [http://www.netlib.org/lapack www.netlib.org].
	;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.		;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.

Toni at 06:13, 13 April 2011

2011-04-13T06:13:15Z

← Older revision		Revision as of 08:13, 13 April 2011
Line 18:		Line 18:
	::<code>'''M>=N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>		::<code>'''M>=N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>
	::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>		::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>
	:A detailed description of the functions can be found ~~here:~~ [http://www.netlib.org/lapack]		:A detailed description of the functions can be found at [http://www.netlib.org/lapack www.netlib.org].
	;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.		;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.

Toni at 06:12, 13 April 2011

2011-04-13T06:12:16Z

← Older revision		Revision as of 08:12, 13 April 2011
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	{{DISPLAYTITLE:rleqs, cleqs}}		{{DISPLAYTITLE:rleqs, cleqs}}
	These functions implements an interface for the ~~LAPACK~~ [http://www.netlib.org/lapack] functions DGESV, ZGESV, DGELS and ZGELS.		These functions implements an interface for the [http://www.netlib.org/lapack LAPACK] functions DGESV, ZGESV, DGELS and ZGELS.
	;Usage: <code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>:		;Usage: <code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>:
	:;<var>A</var>: left side MxN matrix ''x''		:;<var>A</var>: left side MxN matrix ''x''
Line 18:		Line 18:
	::<code>'''M>=N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>		::<code>'''M>=N:''' minimize \|\| ''B[M x NRHS] - ''A''[M x N] ''X''[M x NRHS] \|\|</code>
	::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>		::<code>'''M<N:''' ''A''[M x M] ''X''[M x NRHS] = ''B''[M x NRHS]</code>
	:A detailed description of the functions can be found here: [[http://www.netlib.org/lapack]]		:A detailed description of the functions can be found here: [http://www.netlib.org/lapack]
	;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.		;Result: The result ''X'' has the same type as the argument ''B'' and contains one solution per column.

Toni at 06:10, 13 April 2011

2011-04-13T06:10:05Z

← Older revision		Revision as of 08:10, 13 April 2011
Line 1:		Line 1:
	{{DISPLAYTITLE:rleqs, cleqs}}		{{DISPLAYTITLE:rleqs, cleqs}}
	These functions implements an interface for the [http://www.netlib.org/lapack~~\|LAPACK~~] functions DGESV, ZGESV, DGELS and ZGELS.		These functions implements an interface for the LAPACK [http://www.netlib.org/lapack] functions DGESV, ZGESV, DGELS and ZGELS.
	;Usage: <code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>:		;Usage: <code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>:
	:;<var>A</var>: left side MxN matrix ''x''		:;<var>A</var>: left side MxN matrix ''x''

Toni at 06:08, 13 April 2011

2011-04-13T06:08:42Z

← Older revision		Revision as of 08:08, 13 April 2011
Line 1:		Line 1:
	{{DISPLAYTITLE:rleqs, cleqs}}		{{DISPLAYTITLE:rleqs, cleqs}}
	These functions implements an interface for the [[http://www.netlib.org/lapack\|LAPACK]] functions DGESV, ZGESV, DGELS and ZGELS.		These functions implements an interface for the [http://www.netlib.org/lapack\|LAPACK] functions DGESV, ZGESV, DGELS and ZGELS.
	;Usage: <code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>:		;Usage: <code>rleqs(<var>A</var>, <var>B</var> {, <var>alg</var>})</code>:
	:;<var>A</var>: left side MxN matrix ''x''		:;<var>A</var>: left side MxN matrix ''x''