function quadrule_test11 ( ) %*****************************************************************************80 % %% TEST11 tests FEJER2_RULE_COMPUTE. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 03 March 2007 % % Author: % % John Burkardt % order_max = 16; fprintf ( 1, '\n' ); fprintf ( 1, 'TEST11\n' ); fprintf ( 1, ' FEJER2_RULE_COMPUTE computes a Fejer Type 2 rule;\n' ); fprintf ( 1, '\n' ); fprintf ( 1, ' The integration interval is [-1,1].\n' ); fprintf ( 1, ' Quadrature order will vary.\n' ); fprintf ( 1, ' Integrand will vary.\n' ); fprintf ( 1, '\n' ); fprintf ( 1, ' Order F1 F2 F3\n' ); fprintf ( 1, '\n' ); for order = 1 : order_max [ xtab, weight ] = fejer2_rule_compute ( order ); result(1) = 0.0; for i = 1 : order result(1) = result(1) + weight(i) * f1 ( xtab(i) ); end result(2) = 0.0; for i = 1 : order result(2) = result(2) + weight(i) * f2 ( xtab(i) ); end result(3) = 0.0; for i = 1 : order result(3) = result(3) + weight(i) * f3 ( xtab(i) ); end fprintf ( 1, ' %6d %14f %14f %14f\n', order, result(1:3) ); end fprintf ( 1, '\n' ); result(1) = 46.0 * sinh ( 1.0 ) / 25.0 - 2.0 * sin ( 1.0 ); result(2) = 1.5822329637296729331; result(3) = ( sqrt ( 2.0 ) + 3.0 * sqrt ( 6.0 ) ) / 6.0; fprintf ( 1, ' Exact %14f %14f %14f\n', result(1:3) ); return end