SchattenNorm: Difference between revisions

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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
|req=[[kpNorm]]
|rel=[[kpNorm]]<br />[[KyFanNorm]]<br />[[TraceNorm]]
|rel=[[KyFanNorm]]<br />[[TraceNorm]]
|cat=[[List of functions#Norms|Norms]]
|upd=December 1, 2012
|upd=December 1, 2012
|v=1.00}}
|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:
<pre>
<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
</pre>
</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       1443.6

Source code

Click here to view this function's source code on github.