function value = p17_f ( dim_num, point_num, x ) %*****************************************************************************80 % %% P17_F evaluates the integrand for problem 17. % % Discussion: % % This integrand can be regarded as the square of the L2 % norm of X - Z. % % This integrand has the advantage of symmetry under rotation % about Z. Thus, it is possible to test whether a particular % quadrature rule has an occasional advantage because it % "lines up" with the X and Y coordinate axes and hence can % integrate some separable integrals very well. % % Dimension: % % DIM_NUM arbitrary. % % Region: % % 0 <= X(1:DIM_NUM) <= 1 % % Integral Parameters: % % There is a basis point Z associated with the integrand. % Z(1:DIM_NUM) defaults to ( 0.5, 0.5, ..., 0.5 ). % The user can set, get, or randomize this value by calling % P17_R8VEC. % % Integrand: % % sum ( ( x(1:dim_num) - z(1:dim_num) )**2 ) % % Exact Integral: % % The integral may be broken into the sum of weighted % one dimensional integrals. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 02 June 2007 % % Author: % % John Burkardt % % 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. % z = []; z = p17_r8vec ( 'G', 'Z', dim_num, z ); value(1:point_num) = 0.0; for point = 1 : point_num value(point) = sum ( ( x(1:dim_num,point) - z(1:dim_num)' ).^2 ); end p17_i4 ( 'I', '#', point_num ); return end