IsTotallyPositive - Revision history

Nathaniel: removed red links

2014-12-09T18:31:22Z

removed red links

← Older revision		Revision as of 18:31, 9 December 2014
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	{{Function		{{Function
	\|name=IsTotallyPositive		\|name=IsTotallyPositive
	\|desc=Determines whether or not a matrix is [[totally positive]]		\|desc=Determines whether or not a matrix is totally positive
	\|rel=[[IsTotallyNonsingular]]		\|rel=[[IsTotallyNonsingular]]
	\|cat=[[List of functions#Miscellaneous\|Miscellaneous]]		\|cat=[[List of functions#Miscellaneous\|Miscellaneous]]
	\|upd=December 13, 2012		\|upd=December 13, 2012
	\|v=0.50}}		\|v=0.50}}
	<tt>'''IsTotallyPositive'''</tt> is a [[List of functions\|function]] that determines whether or not a given matrix is [[totally positive]] (i.e., all of its square submatrices have positive determinant). The input matrix can be either full or sparse.		<tt>'''IsTotallyPositive'''</tt> is a [[List of functions\|function]] that determines whether or not a given matrix is totally positive (i.e., all of its square submatrices have positive determinant). The input matrix can be either full or sparse.

	==Syntax==		==Syntax==

Nathaniel at 15:44, 29 September 2014

2014-09-29T15:44:26Z

← Older revision		Revision as of 15:44, 29 September 2014
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	\|name=IsTotallyPositive		\|name=IsTotallyPositive
	\|desc=Determines whether or not a matrix is [[totally positive]]		\|desc=Determines whether or not a matrix is [[totally positive]]
	\|~~req~~=[[~~opt_args~~]]		\|rel=[[IsTotallyNonsingular]]
	\|~~rel~~=[[~~IsPSD]]<br />[[IsTotallyNonsingular~~]]		\|cat=[[List of functions#Miscellaneous\|Miscellaneous]]
	\|upd=December 13, 2012		\|upd=December 13, 2012
	\|v=1.00}}		\|v=0.50}}
	<tt>'''IsTotallyPositive'''</tt> is a [[List of functions\|function]] that determines whether or not a given matrix is [[totally positive]] (i.e., all of its square submatrices have positive determinant). The input matrix can be either full or sparse.		<tt>'''IsTotallyPositive'''</tt> is a [[List of functions\|function]] that determines whether or not a given matrix is [[totally positive]] (i.e., all of its square submatrices have positive determinant). The input matrix can be either full or sparse.

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	===Vandermonde matrices===		===Vandermonde matrices===
	It is known that [http://en.wikipedia.org/wiki/Vandermonde_matrix Vandermonde matrices] are totally positive, under certain restrictions on the nodes:		It is known that [http://en.wikipedia.org/wiki/Vandermonde_matrix Vandermonde matrices] are totally positive, under certain restrictions on the nodes:
	<~~pre<noinclude></noinclude>~~>		<syntaxhighlight>
	>> IsTotallyPositive(vander(5:-1:1))		>> IsTotallyPositive(vander(5:-1:1))

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	1		1
	</~~pre<noinclude></noinclude>~~>		</syntaxhighlight>

	==Notes==		==Notes==
	In practice, this function is practical for matrices of size up to about 15-by-15.		In practice, this function is practical for matrices of size up to about 15-by-15.

			{{SourceCode\|name=IsTotallyPositive}}

Nathaniel: Created page with "{{Function |name=IsTotallyPositive |desc=Determines whether or not a matrix is totally positive |req=opt_args |rel=IsPSD
IsTotallyNonsingular |upd=Decembe..."

2012-12-14T04:40:21Z

Created page with "{{Function |name=IsTotallyPositive |desc=Determines whether or not a matrix is totally positive |req=opt_args |rel=IsPSD<br />IsTotallyNonsingular |upd=Decembe..."

New page

{{Function
|name=IsTotallyPositive
|desc=Determines whether or not a matrix is [[totally positive]]
|req=[[opt_args]]
|rel=[[IsPSD]]<br />[[IsTotallyNonsingular]]
|upd=December 13, 2012
|v=1.00}}
<tt>'''IsTotallyPositive'''</tt> is a [[List of functions|function]] that determines whether or not a given matrix is [[totally positive]] (i.e., all of its square submatrices have positive determinant). The input matrix can be either full or sparse.

==Syntax==
* <tt>ITP = IsTotallyPositive(X)</tt>
* <tt>ITP = IsTotallyPositive(X,SUB_SIZES)</tt>
* <tt>ITP = IsTotallyPositive(X,SUB_SIZES,TOL)</tt>
* <tt>[ITP,WIT] = IsTotallyPositive(X,SUB_SIZES,TOL)</tt>

==Argument descriptions==
===Input arguments===
* <tt>X</tt>: A matrix.
* <tt>SUB_SIZES</tt> (optional, default <tt>1:min(size(X))</tt>): A vector specifying the sizes of submatrices to be checked to have positive determinant.
* <tt>TOL</tt> (optional, default <tt>length(X)*eps(norm(X,'fro'))</tt>): The numerical tolerance used when determining positivity.

===Output arguments===
* <tt>ITP</tt>: A flag (either 1 or 0) indicating that <tt>X</tt> is or is not totally positive.
* <tt>WIT</tt> (optional): If <tt>ITP = 0</tt> then <tt>WIT</tt> specifies a submatrix of <tt>X</tt> that has either negative or non-real determinant. More specifically, <tt>WIT</tt> is a matrix with 2 rows such that <tt>det(X(WIT(1,:),WIT(2,:)))</tt> is negative or non-real.

==Examples==
===Vandermonde matrices===
It is known that [http://en.wikipedia.org/wiki/Vandermonde_matrix Vandermonde matrices] are totally positive, under certain restrictions on the nodes:
<pre<noinclude></noinclude>>
>> IsTotallyPositive(vander(5:-1:1))

ans =

1
</pre<noinclude></noinclude>>

==Notes==
In practice, this function is practical for matrices of size up to about 15-by-15.

IsTotallyPositive - Revision history

Nathaniel: removed red links

Nathaniel at 15:44, 29 September 2014

Nathaniel: Created page with "{{Function |name=IsTotallyPositive |desc=Determines whether or not a matrix is totally positive |req=opt_args |rel=IsPSDIsTotallyNonsingular |upd=Decembe..."

Nathaniel: Created page with "{{Function |name=IsTotallyPositive |desc=Determines whether or not a matrix is totally positive |req=opt_args |rel=IsPSD
IsTotallyNonsingular |upd=Decembe..."