function value = p26_f ( dim_num, point_num, x ) %*****************************************************************************80 % %% P26_F evaluates the integrand for problem 26. % % Discussion: % % The integrand is similar to that for the Patterson integral #7, % except for a normalization of the constants, and a (random) constant % factor in the integrand. % % Dimension: % % N arbitrary. % % Region: % % 0 <= X(1:DIM_NUM) <= 1 % % Integral Parameters: % % The integral depends on a parameter vector C(1:N). % % The reference suggests choosing C at random in [0,1]. % C(1:N) defaults to 1/N. % % To get or set C, call P26_R8VEC. % % Integrand: % % product ( c(1:dim_num) * ( exp ( - c(1:dim_num) * x(1:dim_num) ) ) ) % = product ( c(1:dim_num) ) * exp ( - sum ( c(1:dim_num) * x(1:dim_num) ) ) % % Exact Integral: % % product ( 1 - exp ( c(1:n) ) ) % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 02 June 2007 % % Author: % % John Burkardt % % Reference: % % Thomas Patterson, % [Integral #1], % On the Construction of a Practical Ermakov-Zolotukhin % Multiple Integrator, % in Numerical Integration: Recent Developments, Software % and Applications, % edited by Patrick Keast and Graeme Fairweather, % D. Reidel, 1987, pages 269-290, % LC: QA299.3.N38 % % 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 = []; c = p26_r8vec ( 'G', 'C', dim_num, c ); value(1:point_num) = 0.0; for point = 1 : point_num value(point) = prod ( c(1:dim_num) ) ... * exp ( - c(1:dim_num) * x(1:dim_num,point) ); end p26_i4 ( 'I', '#', point_num ); return end