Description of sllogdet

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sllogdet

PURPOSE

SLLOGDET Computes the logarithm of determinant of a matrix in a robust way

SYNOPSIS

function r = sllogdet(A)

DESCRIPTION

SLLOGDET Computes the logarithm of determinant of a matrix in a robust way

 $ Syntax $
   - r = sllogdet(A)

 $ Arguments $
   - A:       the square matrix whose log-determinant is to be solved
   - r:       the log-determinant of A

 $ Description $
   - r = sllogdet(A) computes the logarithm of (absolute )determinant of a square
     matrix A in a robust way, to reduce the risk of underflow or overflow.

 $ Remarks $
   - If the matrix is singular, inf or -inf would be return.

 $ History $
   - Created by Dahua Lin on Dec 28th, 2005

CROSS-REFERENCE INFORMATION

This function calls:

• slignorevars SLIGNOREVARS Ignores the input variables

This function is called by:

• slgausspdf SLGAUSSPDF Computes the probability density of Gaussian models

SOURCE CODE

0001 function r = sllogdet(A)
0002 %SLLOGDET Computes the logarithm of determinant of a matrix in a robust way
0003 %
0004 % $ Syntax $
0005 %   - r = sllogdet(A)
0006 %
0007 % $ Arguments $
0008 %   - A:       the square matrix whose log-determinant is to be solved
0009 %   - r:       the log-determinant of A
0010 %
0011 % $ Description $
0012 %   - r = sllogdet(A) computes the logarithm of (absolute )determinant of a square
0013 %     matrix A in a robust way, to reduce the risk of underflow or overflow.
0014 %
0015 % $ Remarks $
0016 %   - If the matrix is singular, inf or -inf would be return.
0017 %
0018 % $ History $
0019 %   - Created by Dahua Lin on Dec 28th, 2005
0020 %
0021 
0022 %% parse and verify input arguments
0023 if ndims(A) ~= 2
0024     error('sltoolbox:invalidarg', 'A should be a 2D matrix');
0025 end
0026 d = size(A, 1);
0027 if size(A, 2) ~= d
0028     error('sltoolbox:invalidarg', 'A shoule be a square matrix');
0029 end
0030 
0031 %% compute
0032 
0033 % triangular decomposition
0034 [L, U] = lu(A);
0035 diagU = diag(U);
0036 slignorevars(L);
0037 clear L U;
0038 
0039 % sign controlling
0040 neg_u_entries = find(diagU < 0);
0041 if ~isempty(neg_u_entries)
0042     diagU(neg_u_entries) = -diagU(neg_u_entries);
0043 end
0044 
0045 % log-product
0046 wid = 'MATLAB:log:logOfZero';
0047 st = warning('query', wid);
0048 st = st.state;
0049 
0050 warning('off', wid);
0051 r = sum(log(diagU));
0052 warning(st, wid);
0053 
0054 
0055 
0056

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