Sporth - Revision history

Nathaniel at 16:30, 29 September 2014

2014-09-29T16:30:05Z

← Older revision		Revision as of 16:30, 29 September 2014
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	\|desc=Returns a sparse orthonormal basis for the range		\|desc=Returns a sparse orthonormal basis for the range
	\|upd=December 13, 2012		\|upd=December 13, 2012
	\|v=1.01		\|v=0.50
	\|rel=[[spnull]]		\|rel=[[spnull]]
			\|cat=[[List of functions#Helper_functions\|Helper functions]]
	\|lic=1		\|lic=1
	\|helper=1}}		\|helper=1}}
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	==Examples==		==Examples==
	The following example gives a 4-by-4 matrix whose range is spanned by the two vectors $[1,0,0,0]^T$ and $[0,0,1,0]^T$:		The following example gives a 4-by-4 matrix whose range is spanned by the two vectors $[1,0,0,0]^T$ and $[0,0,1,0]^T$:
	<~~pre~~>		<syntaxhighlight>
	>> S = sparse(4,4);		>> S = sparse(4,4);
	>> S(1,1) = 1; S(3,2) = 1;		>> S(1,1) = 1; S(3,2) = 1;
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	(1,1) 1		(1,1) 1
	(3,2) 1		(3,2) 1
	</~~pre~~>		</syntaxhighlight>

	Note that the output is sparse because <tt>S</tt> is sparse. If the input is full then the output will be full as well:		Note that the output is sparse because <tt>S</tt> is sparse. If the input is full then the output will be full as well:
	<~~pre~~>		<syntaxhighlight>
	>> sporth(full(S))		>> sporth(full(S))

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	0 -1		0 -1
	0 0		0 0
	</~~pre~~>		</syntaxhighlight>

	If we just want to compute the rank of <tt>S</tt>, we can do the following:		If we just want to compute the rank of <tt>S</tt>, we can do the following:
	<~~pre~~>		<syntaxhighlight>
	>> [~,r] = sporth(S)		>> [~,r] = sporth(S)

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	2		2
	</~~pre~~>		</syntaxhighlight>

			{{SourceCode\|name=sporth\|helper=1}}

	==External links==		==External links==
	* [http://www.mathworks.com/matlabcentral/fileexchange/27550-sparse-null-space-and-orthogonal Sparse null space and orthogonal]: The source of this file on MATLAB File Exchange		* [http://www.mathworks.com/matlabcentral/fileexchange/27550-sparse-null-space-and-orthogonal Sparse null space and orthogonal]: The source of this file on MATLAB File Exchange

Nathaniel: Uploaded v1.01

2012-12-14T01:55:38Z

Uploaded v1.01

← Older revision		Revision as of 01:55, 14 December 2012
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	\|name=sporth		\|name=sporth
	\|desc=Returns a sparse orthonormal basis for the range		\|desc=Returns a sparse orthonormal basis for the range
	\|upd=~~May 10~~, ~~2010~~		\|upd=December 13, 2012
	\|v=1.00		\|v=1.01
	\|rel=[[spnull]]		\|rel=[[spnull]]
	\|lic=1		\|lic=1
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	==Syntax==		==Syntax==
	* <tt>Q = sporth(S)</tt>		* <tt>Q = sporth(S)</tt>
	* <tt>[Q,r] = sporth(S)</tt>		* <tt>Q = sporth(S,TOL)</tt>
			* <tt>[Q,r] = sporth(S,TOL)</tt>

	==Argument descriptions==		==Argument descriptions==
	===Input arguments===		===Input arguments===
	* <tt>S</tt>: The matrix to have its range computed.		* <tt>S</tt>: The matrix to have its range computed.
			* <tt>TOL</tt> (optional, default <tt>norm(S,'fro') * eps(class(S))</tt>): The numerical tolerance used.

	===Output arguments===		===Output arguments===

Nathaniel at 01:34, 14 December 2012

2012-12-14T01:34:49Z

← Older revision		Revision as of 01:34, 14 December 2012
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	\|upd=May 10, 2010		\|upd=May 10, 2010
	\|v=1.00		\|v=1.00
			\|rel=[[spnull]]
	\|lic=1		\|lic=1
	\|helper=1}}		\|helper=1}}

Nathaniel: Created page with "{{Function |name=sporth |desc=Returns a sparse orthonormal basis for the range |upd=May 10, 2010 |v=1.00 |lic=1 |helper=1}} `'''sporth'''` is a [[List of functions|func..."

2012-12-05T18:14:06Z

Created page with "{{Function |name=sporth |desc=Returns a sparse orthonormal basis for the range |upd=May 10, 2010 |v=1.00 |lic=1 |helper=1}} <tt>'''sporth'''</tt> is a [[List of functions|func..."

New page

{{Function
|name=sporth
|desc=Returns a sparse orthonormal basis for the range
|upd=May 10, 2010
|v=1.00
|lic=1
|helper=1}}
<tt>'''sporth'''</tt> is a [[List of functions|function]] that computes an orthonormal basis for the range of a full or sparse matrix. When the matrix is sparse, this computation is performed via the [http://en.wikipedia.org/wiki/QR_decomposition QR decomposition] and is typically much faster than using <tt>orth(full(S))</tt>. This function is useful in particular for computing the rank of a sparse matrix without having to use the (slow) <tt>rank(full(S))</tt> or the (often inaccurate) <tt>[http://www.mathworks.com/help/matlab/ref/sprank.html sprank(S)]</tt>.

==Syntax==
* <tt>Q = sporth(S)</tt>
* <tt>[Q,r] = sporth(S)</tt>

==Argument descriptions==
===Input arguments===
* <tt>S</tt>: The matrix to have its range computed.

===Output arguments===
* <tt>Q</tt>: A matrix whose columns form an orthonormal basis for the range of <tt>S</tt>.
* <tt>r</tt> (optional): The rank of <tt>S</tt>.

==Examples==
The following example gives a 4-by-4 matrix whose range is spanned by the two vectors $[1,0,0,0]^T$ and $[0,0,1,0]^T$:
<pre>
>> S = sparse(4,4);
>> S(1,1) = 1; S(3,2) = 1;
>> sporth(S)

ans =

(1,1) 1
(3,2) 1
</pre>

Note that the output is sparse because <tt>S</tt> is sparse. If the input is full then the output will be full as well:
<pre>
>> sporth(full(S))

ans =

1 0
0 0
0 -1
0 0
</pre>

If we just want to compute the rank of <tt>S</tt>, we can do the following:
<pre>
>> [~,r] = sporth(S)

r =

2
</pre>

==External links==
* [http://www.mathworks.com/matlabcentral/fileexchange/27550-sparse-null-space-and-orthogonal Sparse null space and orthogonal]: The source of this file on MATLAB File Exchange

Sporth - Revision history

Nathaniel at 16:30, 29 September 2014

Nathaniel: Uploaded v1.01

Nathaniel at 01:34, 14 December 2012

Nathaniel: Created page with "{{Function |name=sporth |desc=Returns a sparse orthonormal basis for the range |upd=May 10, 2010 |v=1.00 |lic=1 |helper=1}} '''sporth''' is a [[List of functions|func..."

Nathaniel: Created page with "{{Function |name=sporth |desc=Returns a sparse orthonormal basis for the range |upd=May 10, 2010 |v=1.00 |lic=1 |helper=1}} `'''sporth'''` is a [[List of functions|func..."