Description of slnorm

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slnorm

PURPOSE

SLNORM Compute the Lp-norms

SYNOPSIS

function An = slnorm(A, p, d)

DESCRIPTION

SLNORM Compute the Lp-norms

 $ Syntax $
   - An = slnorm(A)
   - An = slnorm(A, p)
   - An = slnorm(A, [], d)
   - An = slnorm(A, p, d)

 $ Arguments $
   - A:        the input array
   - p:        the order of the norm (default = 2)
   - d:        the dimension of subarrays (default = 1, column vectors)
   - An:       the resultant array

 $ Description $
   - An = slnorm(A) computes the L2 norm of column vectors of A. If A is
     an array of size d1 x d2 x ... dn, then An would be of size 
     1 x d2 x ... dn. Each value of An is the L2 norm of corresponding
     column vector.

   - An = slnorm(A, p) computes the Lp norm of column vectors of A. If A 
     is an array of size d1 x d2 x ... dn, then An would be of size 
     1 x d2 x ... dn. Each value of An is the Lp norm of corresponding
     column vector.

   - An = slnorm(A, [], d) computes the L2 norm of sub-arrays along the 
     dimensions specified by d. For example, if A is a d1 x d2 x ... dn
     array, and d = [1, 2], then An would be an array of size
     1 x 1 x d3 x ... x dn. Each value of An is the square root of square-
     sum of values in corresponding plane.

   - An = slnorm(A, p, d) computes the Lp norm of sub-arrays along the 
     dimensions specified by d.

 $ Remarks $
   # Lp norm is the pth order-root of the sum of p-th power of all values
     in a subspace. 
   # p can be inf or -inf. If p = inf, then the Lp norm is simply the
     maximum magnitude value; while if p = -inf, then the Lp norm is the 
     minimum magnitude value.

 $ History $
   - Created by Dahua Lin on Nov 19th, 2005

CROSS-REFERENCE INFORMATION

This function calls:

• slmax SLMAX Compute the maximum of values in subarrays
• slmin SLMIN Compute the minimum of values in subarrays
• slsum SLSUM Compute the sum of values in subarrays

This function is called by:

• sldiscrep SLDISCREP Evaluates the discrepancy of two arrays
• slnormalize SLNORMALIZE Normalize the sub-arrays

SOURCE CODE

0001 function An = slnorm(A, p, d)
0002 %SLNORM Compute the Lp-norms
0003 %
0004 % $ Syntax $
0005 %   - An = slnorm(A)
0006 %   - An = slnorm(A, p)
0007 %   - An = slnorm(A, [], d)
0008 %   - An = slnorm(A, p, d)
0009 %
0010 % $ Arguments $
0011 %   - A:        the input array
0012 %   - p:        the order of the norm (default = 2)
0013 %   - d:        the dimension of subarrays (default = 1, column vectors)
0014 %   - An:       the resultant array
0015 %
0016 % $ Description $
0017 %   - An = slnorm(A) computes the L2 norm of column vectors of A. If A is
0018 %     an array of size d1 x d2 x ... dn, then An would be of size
0019 %     1 x d2 x ... dn. Each value of An is the L2 norm of corresponding
0020 %     column vector.
0021 %
0022 %   - An = slnorm(A, p) computes the Lp norm of column vectors of A. If A
0023 %     is an array of size d1 x d2 x ... dn, then An would be of size
0024 %     1 x d2 x ... dn. Each value of An is the Lp norm of corresponding
0025 %     column vector.
0026 %
0027 %   - An = slnorm(A, [], d) computes the L2 norm of sub-arrays along the
0028 %     dimensions specified by d. For example, if A is a d1 x d2 x ... dn
0029 %     array, and d = [1, 2], then An would be an array of size
0030 %     1 x 1 x d3 x ... x dn. Each value of An is the square root of square-
0031 %     sum of values in corresponding plane.
0032 %
0033 %   - An = slnorm(A, p, d) computes the Lp norm of sub-arrays along the
0034 %     dimensions specified by d.
0035 %
0036 % $ Remarks $
0037 %   # Lp norm is the pth order-root of the sum of p-th power of all values
0038 %     in a subspace.
0039 %   # p can be inf or -inf. If p = inf, then the Lp norm is simply the
0040 %     maximum magnitude value; while if p = -inf, then the Lp norm is the
0041 %     minimum magnitude value.
0042 %
0043 % $ History $
0044 %   - Created by Dahua Lin on Nov 19th, 2005
0045 %
0046 
0047 %% parse and verify input arguments
0048 if nargin < 2 || isempty(p)
0049     p = 2;
0050 end
0051 if nargin < 3 || isempty(d)
0052     d = 1;
0053 end
0054 if ~isscalar(p)
0055     error('sltoolbox:notscalar', 'p should be a scalar');
0056 end
0057 if p == 0
0058     error('sltoolbox:zeroerr', 'p should not be zero');
0059 end
0060 
0061 
0062 %% compute
0063 An = abs(A);
0064 if p == 1
0065     An = slsum(An, d);
0066 elseif p == 2
0067     An = sqrt(slsum(An .* An ,d));
0068 elseif p == inf
0069     An = slmax(An, d);
0070 elseif p == (-inf)
0071     An = slmin(An, d);
0072 else
0073     An = slsum(An.^p, d) .^ (1/p);
0074 end
0075 
0076 
0077     
0078 
0079 
0080     
0081     
0082 
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0087

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