function [B,i] = ddom4 (A,tol)
%
%DDOM4
%
%     [B, i] = ddom4 (A, tol)
%
% DDOM4 returns a diagonally dominant matrix B by modifying the
% diagonal of A.  If row i violates diagonal dominance, then A(i,i) is
% modified by setting it so that its absolute value is (1+tol)*f, where
% f is the sum of the absolute values of the off-diagonal entries in row i
% (assuming f is large enough).  If f is smaller than tol, then the absolute
% value of A(i,i) is set to (1+tol)*tol.  The sign of A(i,i) is preserved.
% The input argument tol is optional; if not present, a default value of
% 100*eps is used.  The outputs are B (the modified matrix) and a vector i
% that contains a list of the row indices of the rows that violated
% diagonal dominance.
%
% MATLAB Primer, 6th Edition
% Kermit Sigmon and Timothy A. Davis
% Section 7.6, page 38.

d = diag (A) ;
a = abs (d) ;
f = sum (abs (A), 2) - a ;
i = find (f >= a) ;
[m n] = size (A) ;
k = i + (i-1)*m ;
if (nargin == 1)
    tol = 100 * eps ;
end
s = 2 * (d (i) >= 0) - 1 ;
A (k) = (1+tol) * s .* max (f (i), tol) ;

B = A ;