Description of slnormalize

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slnormalize

PURPOSE

SLNORMALIZE Normalize the sub-arrays

SYNOPSIS

function An = slnormalize(A, p, d)

DESCRIPTION

SLNORMALIZE Normalize the sub-arrays

 $ Syntax $
   - An = slnormalize(A)
   - An = slnormalize(A, p)
   - An = slnormalize(A, [], d)
   - An = slnormalize(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 normalized array

 $ Description $
   - An = slnormalize(A) normalizes the column vectors of A by 2nd-order.

   - An = slnormalize(A, p) normalizes the column vectors of a by
     pth-order.

   - An = slnormalize(A, [], d) normalizes the subarrays of A along 
     dimensions specified by d by 2nd-order.

   - An = slnormalize(A, p, d) normalizes the subarrays of A along
     dimensions specified by d by pth-order.

 $ Remarks $
   # Normalize an array by pth order means dividing the elements of 
     the array by its p-th norm.
   # 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
   - Modified by Dahua Lin on Sep 10th, 2006
       - replace slmul by slmulvec to increase efficiency

CROSS-REFERENCE INFORMATION

This function calls:

• slenforce SLENFORCE Enforce some property on the array A
• slmulvec SLMULVEC multiplies a vector to columns or rows of a matrix
• slnorm SLNORM Compute the Lp-norms

This function is called by:

• sllocaltanspace SLLOCALTANSPACE Solves the local tangent spaces
• slregcov SLREGCOV Regularizes covariance matrices
• slwhiten_from_samples SLWHITEN_FROM_SAMPLES Compute the whitening matrix from sample matrix
• slpca SLPCA Learns a PCA model from training samples

SOURCE CODE

0001 function An = slnormalize(A, p, d)
0002 %SLNORMALIZE Normalize the sub-arrays
0003 %
0004 % $ Syntax $
0005 %   - An = slnormalize(A)
0006 %   - An = slnormalize(A, p)
0007 %   - An = slnormalize(A, [], d)
0008 %   - An = slnormalize(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 normalized array
0015 %
0016 % $ Description $
0017 %   - An = slnormalize(A) normalizes the column vectors of A by 2nd-order.
0018 %
0019 %   - An = slnormalize(A, p) normalizes the column vectors of a by
0020 %     pth-order.
0021 %
0022 %   - An = slnormalize(A, [], d) normalizes the subarrays of A along
0023 %     dimensions specified by d by 2nd-order.
0024 %
0025 %   - An = slnormalize(A, p, d) normalizes the subarrays of A along
0026 %     dimensions specified by d by pth-order.
0027 %
0028 % $ Remarks $
0029 %   # Normalize an array by pth order means dividing the elements of
0030 %     the array by its p-th norm.
0031 %   # p can be inf or -inf. If p = inf, then the Lp norm is simply the
0032 %     maximum magnitude value; while if p = -inf, then the Lp norm is the
0033 %     minimum magnitude value.
0034 %
0035 % $ History $
0036 %   - Created by Dahua Lin on Nov 19th, 2005
0037 %   - Modified by Dahua Lin on Sep 10th, 2006
0038 %       - replace slmul by slmulvec to increase efficiency
0039 %
0040 
0041 %% parse and verify input arguments
0042 if nargin < 2 || isempty(p)
0043     p = 2;
0044 end
0045 if nargin < 3 || isempty(d)
0046     d = 1;
0047 end
0048 if ~isscalar(p)
0049     error('sltoolbox:notscalar', 'p should be a scalar');
0050 end
0051 if p == 0
0052     error('sltoolbox:zeroerr', 'p should not be zero');
0053 end
0054 
0055 %% compute
0056 nrms = slnorm(A, p, d);
0057 nrms = slenforce(nrms, 'positive');
0058 An = slmulvec(A, 1 ./ nrms);
0059 
0060 
0061

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