Vector norm

Returns the vector norm for a specified dimension (e.g. row/col) of a matrix

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Updated Wed, 26 Apr 2006 15:18:06 +0000

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% VNORM - Return the vector norm along specified dimension of A
%
% VNORM(A) returns the 2-norm along the first non-singleton
% dimension of A
% VNORM(A,dim) return the 2-norm along the dimension 'dim'
% VNORM(A,dim,normtype) returns the norm specified by normtype
% along the dimension 'dim'
% VNORM(A,[],normtype) returns the norm specified by normtype along
% the first non-singleton dimension of A
%
% normtype may be one of {inf,-inf,positive integer}.
% For a given vector, v, these norms are defined as
% inf: max(abs(v))
% -inf: min(abs(v))
% p (where p is a positive integer): sum(abs(v).^p)^(1/p)
%
% Examples:
% A = [8 1 6; 3 5 7; 4 -9 2];
%
% %Columnwise 2-norm (Euclidean norm)
% vnorm(A,1) = [9.4340 10.3441 9.4340];
% vnorm(A,[],2) % Same as above (since first non-singleton dimensions
% % is columnwise and default norm is 2-norm.
% vnorm(A,[],[])% Again, same as above
%
% % Row-wise maximum of absolute values
% vnorm(A,2,inf) = [8 7 9]';
%
% % Columnwise minimum of absolute values
% vnorm(A,[],-inf) = [3 1 2];
%
% % Error: Use the inf type and not the string 'inf'
% vnorm(A,[],'inf') % Wrong
% vnorm(A,[],inf) % Correct

Cite As

Winston Smith (2023). Vector norm (https://www.mathworks.com/matlabcentral/fileexchange/10708-vector-norm), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R14SP3
Compatible with any release
Platform Compatibility
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Version Published Release Notes
1.0.0.0

Improved help with examples and special cased the 1-norm.