function v = t_project_value ( m, n, x, c ) %*****************************************************************************80 % %% T_PROJECT_VALUE evaluates an expansion in Chebyshev polynomials T(n,x). % % Discussion: % % The projection is assumed to be based on the interval [-1,+1]. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 29 March 2012 % % Author: % % John Burkardt % % Parameters: % % Input, integer M, the number of evaluation points. % % Input, integer N, the highest order polynomial to compute. % % Input, real X(M,1), the evaluation points. % % Input, real C(N+1,1), the expansion coefficients. % % Output, real V(M,1), the value of the Chebyshev function. % % % Blasted X and C must be column vectors. % c = c(:); x = x(:); b1 = zeros(m,1); b0 = zeros(m,1); for j = n : -1 : 0 b2(1:m,1) = b1(1:m,1); b1(1:m,1) = b0(1:m,1); b0(1:m,1) = c(j+1) + 2.0 * x(1:m) .* b1(1:m,1) - b2(1:m,1); end v(1:m,1) = 0.5 * ( c(1) + b0(1:m,1) - b2(1:m,1) ); return end