Difference between revisions of "KpNorm"
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{{Function | {{Function | ||
|name=kpNorm | |name=kpNorm | ||
| − | |desc=Computes the | + | |desc=Computes the (k,p)-norm of a vector or matrix |
|rel=[[kpNormDual]]<br />[[KyFanNorm]]<br />[[SchattenNorm]]<br />[[TraceNorm]] | |rel=[[kpNormDual]]<br />[[KyFanNorm]]<br />[[SchattenNorm]]<br />[[TraceNorm]] | ||
|cat=[[List of functions#Norms|Norms]] | |cat=[[List of functions#Norms|Norms]] | ||
| − | |upd= | + | |upd=October 22, 2014 |
|v=0.50}} | |v=0.50}} | ||
<tt>'''kpNorm'''</tt> is a [[List of functions|function]] that computes the [[(k,p)-norm]] of a vector or matrix. In the case of a vector, this is the p-norm of the vector's k largest (in magnitude) entries. In the case of a matrix, this is the p-norm of the vector of its k largest singular values. It works with both full and sparse vectors and matrices. | <tt>'''kpNorm'''</tt> is a [[List of functions|function]] that computes the [[(k,p)-norm]] of a vector or matrix. In the case of a vector, this is the p-norm of the vector's k largest (in magnitude) entries. In the case of a matrix, this is the p-norm of the vector of its k largest singular values. It works with both full and sparse vectors and matrices. | ||
Revision as of 02:07, 23 October 2014
| kpNorm | |
| Computes the (k,p)-norm of a vector or matrix | |
| Other toolboxes required | none |
|---|---|
| Related functions | kpNormDual KyFanNorm SchattenNorm TraceNorm |
| Function category | Norms |
kpNorm is a function that computes the (k,p)-norm of a vector or matrix. In the case of a vector, this is the p-norm of the vector's k largest (in magnitude) entries. In the case of a matrix, this is the p-norm of the vector of its k largest singular values. It works with both full and sparse vectors and matrices.
Syntax
- NRM = kpNorm(X,K,P)
Argument descriptions
- X: A vector or matrix to have its (K,P)-norm computed.
- K: A positive integer.
- P: A real number ≥ 1, or Inf.
Examples
Generalizes the operator, trace, Ky Fan, and Schatten norms
The (K,P)-norm of a matrix is simply the usual operator norm when K = 1 or P = Inf:
>> X = rand(3);
>> [norm(X), kpNorm(X,1,Inf), kpNorm(X,2,Inf), kpNorm(X,3,Inf), kpNorm(X,1,5)]
ans =
1.0673 1.0673 1.0673 1.0673 1.0673When P = 1 and K is the size of X, this norm reduces to the trace norm:
>> [kpNorm(X,3,1), TraceNorm(X)]
ans =
1.6482 1.6482More generally, when P = 1 this norm reduces to the Ky Fan K-norm:
>> [kpNorm(X,2,1), KyFanNorm(X,2)]
ans =
1.5816 1.5816Similarly, when K = min(size(X)) this norm reduces to the Schatten P-norm:
>> [kpNorm(X,3,4), SchattenNorm(X,4)]
ans =
1.0814 1.0814Source code
Click here to view this function's source code on github.