SchattenNorm: Difference between revisions
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Created page with "{{Function |name=SchattenNorm |desc=Computes the Schatten p-norm of an operator |req=kpNorm |rel=KyFanNorm<br />TraceNorm |upd=December 1, 2012 |..." |
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|name=SchattenNorm | |name=SchattenNorm | ||
|desc=Computes the [[Schatten norm|Schatten p-norm]] of an operator | |desc=Computes the [[Schatten norm|Schatten p-norm]] of an operator | ||
| | |rel=[[kpNorm]]<br />[[KyFanNorm]]<br />[[TraceNorm]] | ||
|cat=[[List of functions#Norms|Norms]] | |||
|upd=December 1, 2012 | |upd=December 1, 2012 | ||
|v= | |v=0.50}} | ||
<tt>'''SchattenNorm'''</tt> is a [[List of functions|function]] that computes the [[Schatten norm|Schatten p-norm]] of an operator (i.e., the p-norm of its vector of singular values). It works with both full and sparse matrices. | <tt>'''SchattenNorm'''</tt> is a [[List of functions|function]] that computes the [[Schatten norm|Schatten p-norm]] of an operator (i.e., the p-norm of its vector of singular values). It works with both full and sparse matrices. | ||
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===Equals the [[Frobenius norm]] when <tt>P = 2</tt>=== | ===Equals the [[Frobenius norm]] when <tt>P = 2</tt>=== | ||
The Shatten 2-norm is simply the Frobenius norm: | The Shatten 2-norm is simply the Frobenius norm: | ||
< | <syntaxhighlight> | ||
>> X = rand(2500); | >> X = rand(2500); | ||
>> [norm(X,'fro'), SchattenNorm(X,2)] | >> [norm(X,'fro'), SchattenNorm(X,2)] | ||
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1443.6 1443.6 | 1443.6 1443.6 | ||
</ | </syntaxhighlight> | ||
{{SourceCode|name=SchattenNorm}} | |||
Revision as of 17:13, 22 September 2014
| SchattenNorm | |
| Computes the Schatten p-norm of an operator | |
| Other toolboxes required | none |
|---|---|
| Related functions | kpNorm KyFanNorm TraceNorm |
| Function category | Norms |
SchattenNorm is a function that computes the Schatten p-norm of an operator (i.e., the p-norm of its vector of singular values). It works with both full and sparse matrices.
Syntax
- NRM = SchattenNorm(X,P)
Argument descriptions
- X: An operator to have its Schatten P-norm computed.
- P: A real number ≥ 1, or Inf.
Examples
Equals the Frobenius norm when P = 2
The Shatten 2-norm is simply the Frobenius norm:
>> X = rand(2500);
>> [norm(X,'fro'), SchattenNorm(X,2)]
ans =
1443.6 1443.6Source code
Click here to view this function's source code on github.