function value = p32_f ( dim_num, point_num, x ) %*****************************************************************************80 % %% P32_F evaluates the integrand for problem 32. % % 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)). % % The default value of C(1:N) is (1/2)^(1/N). % % The default value of Z(1:N) is (1/2)^(1/N). % % Integrand: % % exp ( c(1:n)*x(1:n) ) if all x(1:n) <= z(1:n) % 0 otherwise % % Exact Integral: % % product ( g(1:n)(x,z,a,b,c) ) % % where g(i)(x,z,a,b,c) = % % 0 if z(i) <= a(i) % ( e^(c(i)*z(i) ) - e^(c(i)*a(i)) ) / c(i) if a(i) <= z(i) <= b(i) % ( e^(c(i)*b(i) ) - e^(c(i)*a(i)) ) / c(i) if b(i) <= z(i) % % with obvious modifications when c(i) = 0. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 02 June 2007 % % Author: % % John Burkardt % % Reference: % % Alan Genz, % [Integral #6] % 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. % % 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 = p32_r8vec ( 'G', 'C', dim_num, c ); z = []; z = p32_r8vec ( 'G', 'Z', dim_num, z ); value(1:point_num) = 0.0; for point = 1 : point_num if ( all ( x(1:dim_num,point) <= z(1:dim_num)' ) ) value(point) = exp ( c(1:dim_num) * x(1:dim_num,point) ); else value(point) = 0.0; end end p32_i4 ( 'I', '#', point_num ); return end