KyFanNorm - Revision history

Nathaniel: added CVX parameter

2014-12-24T16:39:49Z

added CVX parameter

2014-10-23T13:45:07Z

2014-10-23T13:43:28Z

Can be used with CVX

2014-10-23T13:42:44Z

2014-10-23T13:42:17Z

2014-10-23T02:19:10Z

Examples: Added CVX example

2014-09-22T17:11:58Z

2014-09-22T16:38:00Z

Equals the operator norm when K = 1 (but faster!)

2014-09-22T16:37:08Z

2012-12-01T17:56:38Z

@@ Line 5: / Line 5: @@
 |cat=[[List of functions#Norms|Norms]]
 |upd=December 1, 2012
-|v=0.50}}
+|cvx=yes (convex)}}
 <tt>'''KyFanNorm'''</tt> is a [[List of functions|function]] that computes the Ky Fan k-norm of an operator (i.e., the sum of its k largest singular values):
 : <math>\|X\|_{(k)} := \sum_{j=1}^k \sigma_j^{\downarrow}(X).</math>

@@ Line 6: / Line 6: @@
 |upd=December 1, 2012
 |v=0.50}}
-<tt>'''KyFanNorm'''</tt> is a [[List of functions|function]] that computes the Ky Fan k-norm of an operator (i.e., the sum of its k largest singular values). It works with both full and sparse matrices, and can be used in the objective function or constraints of a CVX optimization problem.
+<tt>'''KyFanNorm'''</tt> is a [[List of functions|function]] that computes the Ky Fan k-norm of an operator (i.e., the sum of its k largest singular values):
 ==Syntax==

@@ Line 40: / Line 40: @@
 ===Can be used with CVX===
-This function can be used directly in constraints or the objective function of CVX problems. The following code snippet computes the minimum value of $\mathrm{Tr}(S\rho)$ over all density matrices $\rho$ satisfying $\|\rho\|_{(k)} \leq 3/4$, where $S$ is the [[SwapOperator|swap operator]].
+This function can be used directly in constraints or the objective function of CVX problems. The following code snippet computes the minimum value of $\mathrm{Tr}(S\rho)$ over all density matrices $\rho$ satisfying $\|\rho\|_{(2)} \leq 3/4$, where $S$ is the [[SwapOperator|swap operator]].
 <syntaxhighlight>
 >> cvx_begin sdp quiet

@@ Line 1: / Line 1: @@
 {{Function
 |name=KyFanNorm
-|desc=Computes the [[Ky Fan norm|Ky Fan k-norm]] of an operator
+|desc=Computes the Ky Fan norm|Ky Fan k-norm of an operator
 |rel=[[kpNorm]]<br />[[SchattenNorm]]<br />[[TraceNorm]]
 |cat=[[List of functions#Norms|Norms]]
 |upd=December 1, 2012
 |v=0.50}}
-<tt>'''KyFanNorm'''</tt> is a [[List of functions|function]] that computes the [[Ky Fan norm|Ky Fan k-norm]] of an operator (i.e., the sum of its k largest singular values). It works with both full and sparse matrices, and can be used in the objective function or constraints of a CVX optimization problem.
+<tt>'''KyFanNorm'''</tt> is a [[List of functions|function]] that computes the Ky Fan k-norm of an operator (i.e., the sum of its k largest singular values). It works with both full and sparse matrices, and can be used in the objective function or constraints of a CVX optimization problem.
 ==Syntax==

@@ Line 6: / Line 6: @@
 |upd=December 1, 2012
 |v=0.50}}
-<tt>'''KyFanNorm'''</tt> is a [[List of functions|function]] that computes the [[Ky Fan norm|Ky Fan k-norm]] of an operator (i.e., the sum of its k largest singular values). It works with both full and sparse matrices.
+<tt>'''KyFanNorm'''</tt> is a [[List of functions|function]] that computes the [[Ky Fan norm|Ky Fan k-norm]] of an operator (i.e., the sum of its k largest singular values). It works with both full and sparse matrices, and can be used in the objective function or constraints of a CVX optimization problem.
 ==Syntax==
@@ Line 40: / Line 40: @@
 ===Can be used with CVX===
-This function can be used directly in constraints or the objective function of cvx problems. The following code snippet computes the minimum value of $\mathrm{Tr}(S\rho)$ over all density matrices $\rho$ satisfying $\|\rho\|_{(k)} \leq 3/4$, where $S$ is the [[SwapOperator|swap operator]].
+This function can be used directly in constraints or the objective function of CVX problems. The following code snippet computes the minimum value of $\mathrm{Tr}(S\rho)$ over all density matrices $\rho$ satisfying $\|\rho\|_{(k)} \leq 3/4$, where $S$ is the [[SwapOperator|swap operator]].
 <syntaxhighlight>
 >> cvx_begin sdp quiet

@@ Line 37: / Line 37: @@
 Elapsed time is 4.288788 seconds.
 </syntaxhighlight>
 {{SourceCode|name=KyFanNorm}}

@@ Line 17: / Line 17: @@
 ==Examples==
 ===Equals the operator norm when <tt>K = 1</tt> (but faster!)===
-The Ky Fan 1-norm is just the operator norm, which is implemented in MATLAB by the <tt>[http://www.mathworks.com/help/symbolic/norm.html norm]</tt> function. However, the <tt>KyFanNorm</tt> function is typically faster than the <tt>norm</tt> function:
+The Ky Fan 1-norm is just the operator norm, which is implemented in MATLAB by the <tt>[http://www.mathworks.com/help/matlab/ref/norm.html norm]</tt> function. However, the <tt>KyFanNorm</tt> function is typically much faster than the <tt>norm</tt> function:
 <syntaxhighlight>
 >> X = rand(2500);

@@ Line 28: / Line 28: @@
 Elapsed time is 0.861377 seconds.
 >> tic; norm(X)
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