function value = p23_f ( dim_num, point_num, x ) %*****************************************************************************80 % %% P23_F evaluates the integrand for problem 23. % % Dimension: % % DIM_NUM is arbitrary. % % Region: % % The interior of the unit simplex, for which all X's are nonnegative, % and sum ( X(1:N) ) <= 1. % % Integral Parameters: % % C defaults to 1.0. % Call P23_R8 to get or set this value. % % E(1:DIM_NUM) defaults to (/ 2, 2, ..., 2 /). % Call P23_I4VEC to get or set this value. % % Integrand: % % F(X) = C * X1^E1 * X2^E2 * ... * Xn^En % % C is real, all exponents E are nonnegative integers. % % Exact Integral: % % C * Gamma(E1+1) * Gamma(E2+1) * ... * Gamma(En+1) / Gamma(E1+E2+...+En+1) % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 02 June 2007 % % Author: % % John Burkardt % % Reference: % % Philip Davis, Philip Rabinowitz, % Methods of Numerical Integration, % Second Edition, % Dover, 2007, % ISBN: 0486453391, % LC: QA299.3.D28. % % Parameters: % % Input, integer DIM_NUM, the dimension of the argument. % % Input, integer POINT_NUM, the number of points. % % Input, real X(DIM_NUM,POINT_NUM), the evaluation points. % % Output, real VALUE(POINT_NUM), the integrand values. % c = 0.0; c = p23_r8 ( 'G', 'C', c ); e = []; e = p23_i4vec ( 'G', 'E', dim_num, e ); value(1:point_num) = c; for point = 1 : point_num for dim = 1 : dim_num value(point) = value * x(dim,point)^e(dim); end end p23_i4 ( 'I', '#', point_num ); return end