function value = p30_f ( dim_num, point_num, x ) %*****************************************************************************80 % %% P30_F evaluates the integrand for problem 30. % % Dimension: % % N arbitrary. % % Region: % % 0 <= X(1:DIM_NUM) <= 1 % % Integral Parameters: % % The integral depends on vectors C(1:N) and Z(1:N). % % The reference suggests choosing C at random in [0,1] % and then multiplying by the normalizing factor sqrt(140/N**(3/2)). % % C(1:N) defaults to 1/N. % Z(1:N) defaults to 0.5. % % To get or set C or Z, call P30_R8VEC. % % Integrand: % % exp ( - sum ( c(1:n)**2 * ( x(1:n) - z(1:n) )**2 ) % % Exact Integral: % % product % ( sqrt ( pi ) % * ( erf ( c(1:n) * ( 1 - z(1:n) ) ) % + erf ( c(1:n) * z(1:n) ) ) % / ( 2 * c(1:n) ) % ) % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 02 June 2007 % % Author: % % John Burkardt % % Reference: % % Alan Genz, % [Integral #4] % A Package for Testing Multiple Integration Subroutines, % in Numerical Integration: Recent Developments, Software % and Applications, % edited by Patrick Keast and Graeme Fairweather, % D Reidel, 1987, pages 337-340, % LC: QA299.3.N38. % % Thomas Patterson, % [Integral #9], % 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 = p30_r8vec ( 'G', 'C', dim_num, c ); z = []; z = p30_r8vec ( 'G', 'Z', dim_num, z ); value(1:point_num) = 0.0; for point = 1 : point_num value(point) = exp ( ... - sum ( c(1:dim_num)'.^2 .* ( x(1:dim_num,point) - z(1:dim_num)' ).^2 ) ); end p30_i4 ( 'I', '#', point_num ); return end