Using the C++ Math Library

The M-File roots() Function

The C++ example_roots() function is a translation of the M-file roots() function. For purposes of comparison, roots.m is reproduced below. Not counting the comments or the main routine, the C++ code is only four lines longer than the M-code. Two of the extra lines are used for declaring variables and the other two for including header files.

MATLAB M-file code for roots():

function r = roots(c)
%ROOTSFind polynomial roots.
%   ROOTS(C) computes the roots of the polynomial whose
%   coefficients are the elements of the vector C. If C has N+1
%   components, the polynomial is C(1)*X^N + ... + C(N)*X +
%   C(N+1).
%
%   See also POLY.
%   J.N. Little 3-17-86
%   Copyright (c) 1984-97 by The MathWorks, Inc.
% ROOTS finds the eigenvalues of the associated companion matrix.

n = size(c);
if ~sum(n <= 1)
    error('Must be a vector.')
end
n = max(n);
c = c(:).';    % Make sure it's a row vector

% Strip leading zeros and throw away.  Strip trailing zeros,
% but remember them as roots at zero.
inz = find(abs(c));
nnz = max(size(inz));
if nnz ~= 0
    c = c(inz(1):inz(nnz));
    r = zeros(n-inz(nnz),1);
else
    r = [];
end

% Polynomial roots via a companion matrix
n = max(size(c));
a = diag(ones(1,n-2),-1);
if n > 1
    a(1,:) = -c(2:n) ./ c(1);
end
r = [r;eig(a)];

Example Program: Rewriting roots.m in C++ (ex8.cpp)

The C++ roots() Function