zero_out_smalls

Contents

• Zero Out Smalls
• Default criterion for smalls
• Validate the inputs
• Replace the smalls with zeros for a full or a sparse matrix

function A=zero_out_smalls(A, small_cri)

Zero Out Smalls

To zero out the small elements in an input vector or matrix whose absolute values are smaller than a given criterion, specified by small_cri. By default, small_cri=eps. Due to operations on floating point numbers, many quantities should be zero mathematically but are actually not. If these "fuzzy" quantities are carried over in further calculations, erroneous results may arise. They will also unnecessarily increase the number of non-zero elements in sparse matrices and slow down the calculations.

Inputs: A, the vector or matrix of which the small elements are desired to be zeroed out. small_cri is an optional input as a criterion for being small, its default value is EPS.

Output: A, the same vector or matrix as the input but with the small elements zeroed out.

% Zhigang Xu, May 2008, [e-mail], updated on July 5, 2008 for the help message.

Default criterion for smalls

if nargin < 2
    small_cri=eps;
end

Validate the inputs

if small_cri < 0
    error('The small_cri should be a non negtive number.')
end

Replace the smalls with zeros for a full or a sparse matrix

When A is non-sparse, to replace the small elements with zero is easy. When A is sparse, we have to be cautious for the replacement. It is necessary to avoid indexing on A on the left side of the equation sign, otherwise Matlab will get very slow when the size of A is very large! (cf http://blogs.mathworks.com/loren/2007/03/01/creating-sparse-finite-element-matrices-in-matlab/#1. )

if ~issparse(A)
    id=abs(A)<=small_cri;
    A(id)=0;
else
   B=abs(A)>small_cri;
   A=A.*B;
end

Published with MATLAB® 7.6