IsPSD - Revision history

Nathaniel: testing syntaxhighlight parameter

2022-05-26T11:52:30Z

testing syntaxhighlight parameter

2014-12-16T18:25:41Z

removed red links

2014-09-22T15:00:23Z

Corrected date

2014-09-22T14:58:11Z

2014-09-21T19:54:52Z

2014-09-21T11:44:50Z

Updated to v1.03

2014-09-19T20:18:24Z

Updating with new GeSHi stuff

2013-01-03T17:26:04Z

2013-01-03T17:25:39Z

Uploaded v1.02

2013-01-02T15:28:01Z

Uploaded v1.01

@@ Line 24: / Line 24: @@
 ===Simple example with low tolerance===
 When <tt>X</tt> is very simple, positive semidefiniteness can be be determined exactly. The following example has the <tt>TOL = 0</tt> (not recommended in general!) to highlight the fact that the script really is checking for positive ''semi''definiteness, not positive definiteness.
-<syntaxhighlight>
+<syntaxhighlight lang="matlab">
 >> X = diag([1 0])
@@ Line 40: / Line 40: @@
 Furthermore, if we make one of the eigenvalues even slightly negative in this case, it is detected as not positive semidefinite:
-<syntaxhighlight>
+<syntaxhighlight lang="matlab">
 >> IsPSD(X-eps*eye(2),0)

@@ Line 1: / Line 1: @@
 {{Function
 |name=IsPSD
-|desc=Determines whether or not a matrix is [[positive semidefinite]]
+|desc=Determines whether or not a matrix is positive semidefinite
 |rel=[[IsCP]]<br />[[IsPPT]]<br />[[IsTotallyPositive]]
 |cat=[[List of functions#Basic_operations|Basic operation]]
-|upd=September 21, 2014
+|upd=September 21, 2014}}
-|v=0.50}}
+<tt>'''IsPSD'''</tt> is a [[List of functions|function]] that determines whether or not a given matrix is positive semidefinite. The input matrix can be either full or sparse and, if requested, a vector that proves that the given matrix is not positive semidefinite can be provided as output.
 ==Syntax==

@@ Line 4: / Line 4: @@
 |rel=[[IsCP]]<br />[[IsPPT]]<br />[[IsTotallyPositive]]
 |cat=[[List of functions#Basic_operations|Basic operation]]
-|upd=September 22, 2014
+|upd=September 21, 2014
 |v=0.50}}
 <tt>'''IsPSD'''</tt> is a [[List of functions|function]] that determines whether or not a given matrix is [[positive semidefinite]]. The input matrix can be either full or sparse and, if requested, a vector that proves that the given matrix is not positive semidefinite can be provided as output.

@@ Line 3: / Line 3: @@
 |desc=Determines whether or not a matrix is [[positive semidefinite]]
 |rel=[[IsCP]]<br />[[IsPPT]]<br />[[IsTotallyPositive]]
-|upd=September 21, 2014
+|cat=[[List of functions#Basic_operations|Basic operation]]
-|v=1.03}}
+|upd=September 22, 2014
 <tt>'''IsPSD'''</tt> is a [[List of functions|function]] that determines whether or not a given matrix is [[positive semidefinite]]. The input matrix can be either full or sparse and, if requested, a vector that proves that the given matrix is not positive semidefinite can be provided as output.

@@ Line 2: / Line 2: @@
 |name=IsPSD
 |desc=Determines whether or not a matrix is [[positive semidefinite]]
 |rel=[[IsCP]]<br />[[IsPPT]]<br />[[IsTotallyPositive]]
 |upd=September 21, 2014

@@ Line 25: / Line 25: @@
 ===Simple example with low tolerance===
 When <tt>X</tt> is very simple, positive semidefiniteness can be be determined exactly. The following example has the <tt>TOL = 0</tt> (not recommended in general!) to highlight the fact that the script really is checking for positive ''semi''definiteness, not positive definiteness.
-<pre>
+<syntaxhighlight>
 >> X = diag([1 0])
@@ Line 38: / Line 38: @@
-</pre>
+</syntaxhighlight>
 Furthermore, if we make one of the eigenvalues even slightly negative in this case, it is detected as not positive semidefinite:
-<pre>
+<syntaxhighlight>
 >> IsPSD(X-eps*eye(2),0)
@@ Line 47: / Line 47: @@
-</pre>
+</syntaxhighlight>
 Note that in general you can not expect this kind of accuracy.
@@ Line 53: / Line 53: @@
 ==Notes==
 Do not request the <tt>WIT</tt> output argument unless you need it. If <tt>WIT</tt> is not requested, positive semidefiniteness is determined by attempting a [http://en.wikipedia.org/wiki/Cholesky_decomposition Cholesky decomposition] of <tt>X</tt>, which is both faster and more accurate than computing its minimum eigenvalue/eigenvector pair.

@@ Line 3: / Line 3: @@
 |desc=Determines whether or not a matrix is [[positive semidefinite]]
 |req=[[opt_args]]
-|rel=[[IsPPT]]<br />[[IsTotallyPositive]]
+|rel=[[IsCP]]<br />[[IsPPT]]<br />[[IsTotallyPositive]]
 |upd=January 3, 2013
 |v=1.02}}

@@ Line 4: / Line 4: @@
 |req=[[opt_args]]
 |rel=[[IsPPT]]<br />[[IsTotallyPositive]]
-|upd=January 2, 2013
+|upd=January 3, 2013
-|v=1.01}}
+|v=1.02}}
 <tt>'''IsPSD'''</tt> is a [[List of functions|function]] that determines whether or not a given matrix is [[positive semidefinite]]. The input matrix can be either full or sparse and, if requested, a vector that proves that the given matrix is not positive semidefinite can be provided as output.
@@ Line 16: / Line 16: @@
 ===Input arguments===
 * <tt>X</tt>: A square matrix.
-* <tt>TOL</tt> (optional, default <tt>sqrt(eps)</tt>): The numerical tolerance used when determining positive semidefiniteness. The matrix will be determined to be positive semidefinite if its minimal eigenvalue is computed to be at least <tt>-TOL</tt>.
+* <tt>TOL</tt> (optional, default <tt>eps^(3/4)</tt>): The numerical tolerance used when determining positive semidefiniteness. The matrix will be determined to be positive semidefinite if its minimal eigenvalue is computed to be at least <tt>-TOL</tt>.
 ===Output arguments===