function [ x, w ] = clenshaw_curtis_set ( order ) %*****************************************************************************80 % %% CLENSHAW_CURTIS_SET sets a Clenshaw-Curtis quadrature rule. % % Discussion: % % The integration interval is [ -1, 1 ]. % % The integral to approximate: % % Integral ( -1 <= X <= 1 ) F(X) dX % % The quadrature rule: % % Sum ( 1 <= I <= ORDER ) W(I) * F ( X(I) ) % % The abscissas for the rule of order ORDER can be regarded % as the cosines of equally spaced angles between 180 and 0 degrees: % % X(I) = cos ( ( I - 1 ) * PI / ( ORDER - 1 ) ) % % except for the basic case ORDER = 1, when % % X(1) = 0. % % A Clenshaw-Curtis rule that uses ORDER points will integrate % exactly all polynomials of degrees 0 through ORDER-1. If ORDER % is odd, then by symmetry the polynomial of degree ORDER will % also be integrated exactly. % % If the value of ORDER is increased in a sensible way, then % the new set of abscissas will include the old ones. One such % sequence would be ORDER(K) = 2*K+1 for K = 0, 1, 2, ... % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 14 May 2007 % % Author: % % John Burkardt % % Reference: % % Charles Clenshaw, Alan Curtis, % A Method for Numerical Integration on an Automatic Computer, % Numerische Mathematik, % Volume 2, Number 1, December 1960, pages 197-205. % % Parameters: % % Input, integer ORDER, the order of the rule. % ORDER must be between 1 and 17, 33, 65 or 129. % % Output, real X(ORDER), the abscissas of the rule. % % Output, real W(ORDER), the weights of the rule. % The weights are symmetric and sum to 2. % if ( order == 1 ) x(1) = 0.00000000000000000000; w(1) = 2.00000000000000000000; elseif ( order == 2 ) x(1) = -1.00000000000000000000; x(2) = 1.00000000000000000000; w(1) = 1.00000000000000000000; w(2) = 1.00000000000000000000; elseif ( order == 3 ) x(1) = -1.00000000000000000000; x(2) = 0.00000000000000000000; x(3) = 1.00000000000000000000; w(1) = 0.33333333333333333333; w(2) = 1.33333333333333333333; w(3) = 0.33333333333333333333; elseif ( order == 4 ) x(1) = -1.00000000000000000000; x(2) = -0.50000000000000000000; x(3) = 0.50000000000000000000; x(4) = 1.00000000000000000000; w(1) = 0.11111111111111111111; w(2) = 0.88888888888888888889; w(3) = 0.88888888888888888889; w(4) = 0.11111111111111111111; elseif ( order == 5 ) x(1) = -1.00000000000000000000; x(2) = -0.70710678118654752440; x(3) = 0.00000000000000000000; x(4) = 0.70710678118654752440; x(5) = 1.00000000000000000000; w(1) = 0.06666666666666666667; w(2) = 0.53333333333333333333; w(3) = 0.80000000000000000000; w(4) = 0.53333333333333333333; w(5) = 0.06666666666666666667; elseif ( order == 6 ) x(1) = -1.00000000000000000000; x(2) = -0.80901699437494742410; x(3) = -0.30901699437494742410; x(4) = 0.30901699437494742410; x(5) = 0.80901699437493732410; x(6) = 1.00000000000000000000; w(1) = 0.04000000000000000000; w(2) = 0.36074304120001121619; w(3) = 0.59925695879998878381; w(4) = 0.59925695879998878381; w(5) = 0.36074304120001121619; w(6) = 0.04000000000000000000; elseif ( order == 7 ) x(1) = -1.00000000000000000000; x(2) = -0.86602540378443864676; x(3) = -0.50000000000000000000; x(4) = 0.00000000000000000000; x(5) = 0.50000000000000000000; x(6) = 0.86602540378443864676; x(7) = 1.00000000000000000000; w(1) = 0.02857142857142857143; w(2) = 0.25396825396825396825; w(3) = 0.45714285714285714286; w(4) = 0.52063492063492063492; w(5) = 0.45714285714285714286; w(6) = 0.25396825396825396825; w(7) = 0.02857142857142857143; elseif ( order == 8 ) x(1) = -1.00000000000000000000; x(2) = -0.90096886790241912624; x(3) = -0.62348980185873353053; x(4) = -0.22252093395631440429; x(5) = 0.22252093395631440429; x(6) = 0.62348980185873353053; x(7) = 0.90096886790241910624; x(8) = 1.00000000000000000000; w(1) = 0.02040816326530612245; w(2) = 0.19014100721820835178; w(3) = 0.35224242371815911533; w(4) = 0.43720840579832641044; w(5) = 0.43720840579832641044; w(6) = 0.35224242371815911533; w(7) = 0.19014100721820835178; w(8) = 0.02040816326530612245; elseif ( order == 9 ) x(1) = -1.00000000000000000000; x(2) = -0.92387953251128675613; x(3) = -0.70710678118654752440; x(4) = -0.38268343236508977173; x(5) = 0.00000000000000000000; x(6) = 0.38268343236508977173; x(7) = 0.70710678118654752440; x(8) = 0.92387953251128675613; x(9) = 1.00000000000000000000; w(1) = 0.01587301587301587302; w(2) = 0.14621864921601815501; w(3) = 0.27936507936507936508; w(4) = 0.36171785872048978150; w(5) = 0.39365079365079365079; w(6) = 0.36171785872048978150; w(7) = 0.27936507936507936508; w(8) = 0.14621864921601815501; w(9) = 0.01587301587301587302; elseif ( order == 10 ) x(1) = -1.00000000000000000000; x(2) = -0.93969262078590838405; x(3) = -0.76604444311897903520; x(4) = -0.50000000000000000000; x(5) = -0.17364817766693034885; x(6) = 0.17364817766693034885; x(7) = 0.50000000000000000000; x(8) = 0.76604444311897903520; x(9) = 0.93969262078590838405; x(10) = 1.00000000000000000000; w(1) = 0.01234567901234567901; w(2) = 0.11656745657203712296; w(3) = 0.22528432333810440813; w(4) = 0.30194003527336860670; w(5) = 0.34386250580414418320; w(6) = 0.34386250580414418320; w(7) = 0.30194003527336860670; w(8) = 0.22528432333810440813; w(9) = 0.11656745657203712296; w(10) = 0.01234567901234567901; elseif ( order == 11 ) x(1) = -1.00000000000000000000; x(2) = -0.95105651629515357212; x(3) = -0.80901699437494742410; x(4) = -0.58778525229247312917; x(5) = -0.30901699437494742410; x(6) = 0.00000000000000000000; x(7) = 0.30901699437494742410; x(8) = 0.58778525229247312917; x(9) = 0.80901699437494742410; x(10) = 0.95105651629515357212; x(11) = 1.00000000000000000000; w(1) = 0.01010101010101010101; w(2) = 0.09457905488370156116; w(3) = 0.18563521442424776529; w(4) = 0.25358833328368660623; w(5) = 0.29921327042423708320; w(6) = 0.31376623376623376623; w(7) = 0.29921327042423708320; w(8) = 0.25358833328368660623; w(9) = 0.18563521442424776529; w(10) = 0.09457905488370156116; w(11) = 0.01010101010101010101; elseif ( order == 12 ) x(1) = -1.00000000000000000000; x(2) = -0.95949297361449738989; x(3) = -0.84125353283118116886; x(4) = -0.65486073394528506406; x(5) = -0.41541501300188642553; x(6) = -0.14231483827328514044; x(7) = 0.14231483827328514044; x(8) = 0.41541501300188642553; x(9) = 0.65486073394528506406; x(10) = 0.84125353283118116886; x(11) = 0.95949297361449738989; x(12) = 1.00000000000000000000; w(1) = 0.00826446280991735537; w(2) = 0.07856015374620000543; w(3) = 0.15504045508256136552; w(4) = 0.21556254600086858099; w(5) = 0.25991734106691617602; w(6) = 0.28265504129353651666; w(7) = 0.28265504129353651666; w(8) = 0.25991734106691617602; w(9) = 0.21556254600086858099; w(10) = 0.15504045508256136552; w(11) = 0.07856015374620000543; w(12) = 0.00826446280991735537; elseif ( order == 13 ) x(1) = -1.00000000000000000000; x(2) = -0.96592582628906828675; x(3) = -0.86602540378443864676; x(4) = -0.70710678118654752440; x(5) = -0.50000000000000000000; x(6) = -0.25881904510252076235; x(7) = 0.00000000000000000000; x(8) = 0.25881904510252076235; x(9) = 0.50000000000000000000; x(10) = 0.70710678118654752440; x(11) = 0.86602540378443864676; x(12) = 0.96592582628906828675; x(13) = 1.00000000000000000000; w(1) = 0.00699300699300699301; w(2) = 0.06605742495207439452; w(3) = 0.13154253154253154253; w(4) = 0.18476338476338476338; w(5) = 0.22697302697302697303; w(6) = 0.25267569378104433860; w(7) = 0.26198986198986198986; w(8) = 0.25267569378104433860; w(9) = 0.22697302697302697303; w(10) = 0.18476338476338476338; w(11) = 0.13154253154253154253; w(12) = 0.06605742495207439452; w(13) = 0.00699300699300699301; elseif ( order == 14 ) x(1) = -1.00000000000000000000; x(2) = -0.97094181742605202716; x(3) = -0.88545602565320989590; x(4) = -0.74851074817110109863; x(5) = -0.56806474673115580251; x(6) = -0.35460488704253562597; x(7) = -0.12053668025532305335; x(8) = 0.12053668025532305335; x(9) = 0.35460488704253562597; x(10) = 0.56806474673115580251; x(11) = 0.74851074817110109863; x(12) = 0.88545602565320989590; x(13) = 0.97094181742605202716; x(14) = 1.00000000000000000000; w(1) = 0.00591715976331360947; w(2) = 0.05646531376341444627; w(3) = 0.11276867248985655881; w(4) = 0.16003802611671868523; w(5) = 0.19899241036578321848; w(6) = 0.22590304977856444935; w(7) = 0.23991536772234903239; w(8) = 0.23991536772234903239; w(9) = 0.22590304977856444935; w(10) = 0.19899241036578321848; w(11) = 0.16003802611671868523; w(12) = 0.11276867248985655881; w(13) = 0.05646531376341444627; w(14) = 0.00591715976331360947; elseif ( order == 15 ) x(1) = -1.00000000000000000000; x(2) = -0.97492791218182360702; x(3) = -0.90096886790241912624; x(4) = -0.78183148246802980871; x(5) = -0.62348980185873353053; x(6) = -0.43388373911755812048; x(7) = -0.22252093395631440429; x(8) = 0.00000000000000000000; x(9) = 0.22252093395631440429; x(10) = 0.43388373911755812048; x(11) = 0.62348980185873353053; x(12) = 0.78183148246802980871; x(13) = 0.90096886790241912624; x(14) = 0.97492791218182360702; x(15) = 1.00000000000000000000; w(1) = 0.00512820512820512821; w(2) = 0.04869938729508823855; w(3) = 0.09782039167605215913; w(4) = 0.13966507849560431803; w(5) = 0.17560578900106674677; w(6) = 0.20205146748238357364; w(7) = 0.21888151163057340180; w(8) = 0.22429633858205286777; w(9) = 0.21888151163057340180; w(10) = 0.20205146748238357364; w(11) = 0.17560578900106674677; w(12) = 0.13966507849560431803; w(13) = 0.09782039167605215913; w(14) = 0.04869938729508823855; w(15) = 0.00512820512820512821; elseif ( order == 16 ) x(1) = -1.00000000000000000000; x(2) = -0.97814760073380563793; x(3) = -0.91354545764260089550; x(4) = -0.80901699437494742410; x(5) = -0.66913060635885821383; x(6) = -0.50000000000000000000; x(7) = -0.30901699437494742410; x(8) = -0.10452846326765347140; x(9) = 0.10452846326765347140; x(10) = 0.30901699437494742410; x(11) = 0.50000000000000000000; x(12) = 0.66913060635885821383; x(13) = 0.80901699437494742410; x(14) = 0.91354545764260089550; x(15) = 0.97814760073380563793; x(16) = 1.00000000000000000000; w(1) = 0.00444444444444444444; w(2) = 0.04251476624752508988; w(3) = 0.08553884025933288291; w(4) = 0.12294010082849361533; w(5) = 0.15573317603967369176; w(6) = 0.18132978132978132978; w(7) = 0.19921478132638853955; w(8) = 0.20828410952436040635; w(9) = 0.20828410952436040635; w(10) = 0.19921478132638853955; w(11) = 0.18132978132978132978; w(12) = 0.15573317603967369176; w(13) = 0.12294010082849361533; w(14) = 0.08553884025933288291; w(15) = 0.04251476624752508988; w(16) = 0.00444444444444444444; elseif ( order == 17 ) x(1) = -1.00000000000000000000; x(2) = -0.98078528040323044913; x(3) = -0.92387953251128675613; x(4) = -0.83146961230254523708; x(5) = -0.70710678118654752440; x(6) = -0.55557023301960222474; x(7) = -0.38268343236508977173; x(8) = -0.19509032201612826785; x(9) = 0.00000000000000000000; x(10) = 0.19509032201612826785; x(11) = 0.38268343236508977173; x(12) = 0.55557023301960222474; x(13) = 0.70710678118654752440; x(14) = 0.83146961230254523708; x(15) = 0.92387953251128675613; x(16) = 0.98078528040323044913; x(17) = 1.00000000000000000000; w(1) = 0.00392156862745098039; w(2) = 0.03736870283720561032; w(3) = 0.07548233154315183441; w(4) = 0.10890555258189093044; w(5) = 0.13895646836823307412; w(6) = 0.16317266428170330256; w(7) = 0.18147378423649335700; w(8) = 0.19251386461292564687; w(9) = 0.19641012582189052777; w(10) = 0.19251386461292564687; w(11) = 0.18147378423649335700; w(12) = 0.16317266428170330256; w(13) = 0.13895646836823307412; w(14) = 0.10890555258189093044; w(15) = 0.07548233154315183441; w(16) = 0.03736870283720561032; w(17) = 0.00392156862745098039; elseif ( order == 33 ) x(1) = -1.00000000000000000000; x(2) = -0.99518472667219688624; x(3) = -0.98078528040323044913; x(4) = -0.95694033573220886494; x(5) = -0.92387953251128675613; x(6) = -0.88192126434835502971; x(7) = -0.83146961230254523708; x(8) = -0.77301045336273696081; x(9) = -0.70710678118654752440; x(10) = -0.63439328416364549822; x(11) = -0.55557023301960222474; x(12) = -0.47139673682599764856; x(13) = -0.38268343236508977173; x(14) = -0.29028467725446236764; x(15) = -0.19509032201612826785; x(16) = -0.098017140329560601994; x(17) = 0.000000000000000000000; x(18) = 0.098017140329560601994; x(19) = 0.19509032201612826785; x(20) = 0.29028467725446236764; x(21) = 0.38268343236508977173; x(22) = 0.47139673682599764856; x(23) = 0.55557023301960222474; x(24) = 0.63439328416364549822; x(25) = 0.70710678118654752440; x(26) = 0.77301045336273696081; x(27) = 0.83146961230254523708; x(28) = 0.88192126434835502971; x(29) = 0.92387953251128675613; x(30) = 0.95694033573220886494; x(31) = 0.98078528040323044913; x(32) = 0.99518472667219688624; x(33) = 1.00000000000000000000; w(1) = 0.00097751710654936461; w(2) = 0.00939319796295501470; w(3) = 0.01923424513268114918; w(4) = 0.02845791667723369009; w(5) = 0.03759434191404720602; w(6) = 0.04626276283775174949; w(7) = 0.05455501630398031044; w(8) = 0.06227210954529400455; w(9) = 0.06942757563043545090; w(10) = 0.07588380044138847048; w(11) = 0.08163481765493851023; w(12) = 0.08657753844182743544; w(13) = 0.09070611286772099874; w(14) = 0.09394324443876873573; w(15) = 0.09629232594548817919; w(16) = 0.09769818820805558182; w(17) = 0.09817857778176829677; w(18) = 0.09769818820805558182; w(19) = 0.09629232594548817919; w(20) = 0.09394324443876873573; w(21) = 0.09070611286772099874; w(22) = 0.08657753844182743544; w(23) = 0.08163481765493851023; w(24) = 0.07588380044138847048; w(25) = 0.06942757563043545090; w(26) = 0.06227210954529400455; w(27) = 0.05455501630398031044; w(28) = 0.04626276283775174949; w(29) = 0.03759434191404720602; w(30) = 0.02845791667723369009; w(31) = 0.01923424513268114918; w(32) = 0.00939319796295501470; w(33) = 0.00097751710654936461; elseif ( order == 65 ) x(1) = -1.00000000000000000000; x(2) = -0.99879545620517239271; x(3) = -0.99518472667219688624; x(4) = -0.98917650996478097345; x(5) = -0.98078528040323044913; x(6) = -0.97003125319454399260; x(7) = -0.95694033573220886494; x(8) = -0.94154406518302077841; x(9) = -0.92387953251128675613; x(10) = -0.90398929312344333159; x(11) = -0.88192126434835502971; x(12) = -0.85772861000027206990; x(13) = -0.83146961230254523708; x(14) = -0.80320753148064490981; x(15) = -0.77301045336273696081; x(16) = -0.74095112535495909118; x(17) = -0.70710678118654752440; x(18) = -0.67155895484701840063; x(19) = -0.63439328416364549822; x(20) = -0.59569930449243334347; x(21) = -0.55557023301960222474; x(22) = -0.51410274419322172659; x(23) = -0.47139673682599764856; x(24) = -0.42755509343028209432; x(25) = -0.38268343236508977173; x(26) = -0.33688985339222005069; x(27) = -0.29028467725446236764; x(28) = -0.24298017990326388995; x(29) = -0.19509032201612826785; x(30) = -0.14673047445536175166; x(31) = -0.098017140329560601994; x(32) = -0.049067674327418014255; x(33) = 0.000000000000000000000; x(34) = 0.049067674327418014255; x(35) = 0.098017140329560601994; x(36) = 0.14673047445536175166; x(37) = 0.19509032201612826785; x(38) = 0.24298017990326388995; x(39) = 0.29028467725446236764; x(40) = 0.33688985339222005069; x(41) = 0.38268343236508977173; x(42) = 0.42755509343028209432; x(43) = 0.47139673682599764856; x(44) = 0.51410274419322172659; x(45) = 0.55557023301960222474; x(46) = 0.59569930449243334347; x(47) = 0.63439328416364549822; x(48) = 0.67155895484701840063; x(49) = 0.70710678118654752440; x(50) = 0.74095112535495909118; x(51) = 0.77301045336273696081; x(52) = 0.80320753148064490981; x(53) = 0.83146961230254523708; x(54) = 0.85772861000027206990; x(55) = 0.88192126434835502971; x(56) = 0.90398929312344333159; x(57) = 0.92387953251128675613; x(58) = 0.94154406518302077841; x(59) = 0.95694033573220886494; x(60) = 0.97003125319454399260; x(61) = 0.98078528040323044913; x(62) = 0.98917650996478097345; x(63) = 0.99518472667219688624; x(64) = 0.99879545620517239271; x(65) = 1.00000000000000000000; w(1) = 0.00024420024420024420; w(2) = 0.00235149067531170332; w(3) = 0.00483146544879091264; w(4) = 0.00719269316173611402; w(5) = 0.00958233879528379039; w(6) = 0.01192339471421277160; w(7) = 0.01425206043235199679; w(8) = 0.01653498765728958965; w(9) = 0.01878652974179578354; w(10) = 0.02098627442973743378; w(11) = 0.02314069493435819848; w(12) = 0.02523506498175476590; w(13) = 0.02727225714146838686; w(14) = 0.02924065319746833770; w(15) = 0.03114129710406762447; w(16) = 0.03296454656997632997; w(17) = 0.03471049818092511427; w(18) = 0.03637092028663918309; w(19) = 0.03794545992128481711; w(20) = 0.03942698871295609976; w(21) = 0.04081501340035783384; w(22) = 0.04210333111141810203; w(23) = 0.04329151496169082935; w(24) = 0.04437417923925731580; w(25) = 0.04535110955166067221; w(26) = 0.04621766751092557684; w(27) = 0.04697395904661414870; w(28) = 0.04761604458525019296; w(29) = 0.04814443257251220341; w(30) = 0.04855584485714105274; w(31) = 0.04885125664306609371; w(32) = 0.04902801843102555294; w(33) = 0.04908762351494245585; w(34) = 0.04902801843102555294; w(35) = 0.04885125664306609371; w(36) = 0.04855584485714105274; w(37) = 0.04814443257251220341; w(38) = 0.04761604458525019296; w(39) = 0.04697395904661414870; w(40) = 0.04621766751092557684; w(41) = 0.04535110955166067221; w(42) = 0.04437417923925731580; w(43) = 0.04329151496169082935; w(44) = 0.04210333111141810203; w(45) = 0.04081501340035783384; w(46) = 0.03942698871295609976; w(47) = 0.03794545992128481711; w(48) = 0.03637092028663918309; w(49) = 0.03471049818092511427; w(50) = 0.03296454656997632997; w(51) = 0.03114129710406762447; w(52) = 0.02924065319746833770; w(53) = 0.02727225714146838686; w(54) = 0.02523506498175476590; w(55) = 0.02314069493435819848; w(56) = 0.02098627442973743378; w(57) = 0.01878652974179578354; w(58) = 0.01653498765728958965; w(59) = 0.01425206043235199679; w(60) = 0.01192339471421277160; w(61) = 0.00958233879528379039; w(62) = 0.00719269316173611402; w(63) = 0.00483146544879091264; w(64) = 0.00235149067531170332; w(65) = 0.00024420024420024420; elseif ( order == 129 ) x(1) = -1.00000000000000000000; x(2) = -0.99969881869620422012; x(3) = -0.99879545620517239271; x(4) = -0.99729045667869021614; x(5) = -0.99518472667219688624; x(6) = -0.99247953459870999816; x(7) = -0.98917650996478097345; x(8) = -0.98527764238894124477; x(9) = -0.98078528040323044913; x(10) = -0.97570213003852854446; x(11) = -0.97003125319454399260; x(12) = -0.96377606579543986669; x(13) = -0.95694033573220886494; x(14) = -0.94952818059303666720; x(15) = -0.94154406518302077841; x(16) = -0.93299279883473888771; x(17) = -0.92387953251128675613; x(18) = -0.91420975570353065464; x(19) = -0.90398929312344333159; x(20) = -0.89322430119551532034; x(21) = -0.88192126434835502971; x(22) = -0.87008699110871141865; x(23) = -0.85772861000027206990; x(24) = -0.84485356524970707326; x(25) = -0.83146961230254523708; x(26) = -0.81758481315158369650; x(27) = -0.80320753148064490981; x(28) = -0.78834642762660626201; x(29) = -0.77301045336273696081; x(30) = -0.75720884650648454758; x(31) = -0.74095112535495909118; x(32) = -0.72424708295146692094; x(33) = -0.70710678118654752440; x(34) = -0.68954054473706692462; x(35) = -0.67155895484701840063; x(36) = -0.65317284295377676408; x(37) = -0.63439328416364549822; x(38) = -0.61523159058062684548; x(39) = -0.59569930449243334347; x(40) = -0.57580819141784530075; x(41) = -0.55557023301960222474; x(42) = -0.53499761988709721066; x(43) = -0.51410274419322172659; x(44) = -0.49289819222978403687; x(45) = -0.47139673682599764856; x(46) = -0.44961132965460660005; x(47) = -0.42755509343028209432; x(48) = -0.40524131400498987091; x(49) = -0.38268343236508977173; x(50) = -0.35989503653498814878; x(51) = -0.33688985339222005069; x(52) = -0.31368174039889147666; x(53) = -0.29028467725446236764; x(54) = -0.26671275747489838633; x(55) = -0.24298017990326388995; x(56) = -0.21910124015686979723; x(57) = -0.19509032201612826785; x(58) = -0.17096188876030122636; x(59) = -0.14673047445536175166; x(60) = -0.12241067519921619850; x(61) = -0.098017140329560601994; x(62) = -0.073564563599667423529; x(63) = -0.049067674327418014255; x(64) = -0.024541228522912288032; x(65) = 0.00000000000000000000; x(66) = 0.024541228522912288032; x(67) = 0.049067674327418014255; x(68) = 0.073564563599667423529; x(69) = 0.098017140329560601994; x(70) = 0.12241067519921619850; x(71) = 0.14673047445536175166; x(72) = 0.17096188876030122636; x(73) = 0.19509032201612826785; x(74) = 0.21910124015686979723; x(75) = 0.24298017990326388995; x(76) = 0.26671275747489838633; x(77) = 0.29028467725446236764; x(78) = 0.31368174039889147666; x(79) = 0.33688985339222005069; x(80) = 0.35989503653498814878; x(81) = 0.38268343236508977173; x(82) = 0.40524131400498987091; x(83) = 0.42755509343028209432; x(84) = 0.44961132965460660005; x(85) = 0.47139673682599764856; x(86) = 0.49289819222978403687; x(87) = 0.51410274419322172659; x(88) = 0.53499761988709721066; x(89) = 0.55557023301960222474; x(90) = 0.57580819141784530075; x(91) = 0.59569930449243334347; x(92) = 0.61523159058062684548; x(93) = 0.63439328416364549822; x(94) = 0.65317284295377676408; x(95) = 0.67155895484701840063; x(96) = 0.68954054473706692462; x(97) = 0.70710678118654752440; x(98) = 0.72424708295146692094; x(99) = 0.74095112535495909118; x(100) = 0.75720884650648454758; x(101) = 0.77301045336273696081; x(102) = 0.78834642762660626201; x(103) = 0.80320753148064490981; x(104) = 0.81758481315158369650; x(105) = 0.83146961230254523708; x(106) = 0.84485356524970707326; x(107) = 0.85772861000027206990; x(108) = 0.87008699110871141865; x(109) = 0.88192126434835502971; x(110) = 0.89322430119551532034; x(111) = 0.90398929312344333159; x(112) = 0.91420975570353065464; x(113) = 0.92387953251128675613; x(114) = 0.93299279883473888771; x(115) = 0.94154406518302077841; x(116) = 0.94952818059303666720; x(117) = 0.95694033573220886494; x(118) = 0.96377606579543986669; x(119) = 0.97003125319454399260; x(120) = 0.97570213003852854446; x(121) = 0.98078528040323044913; x(122) = 0.98527764238894124477; x(123) = 0.98917650996478097345; x(124) = 0.99247953459870999816; x(125) = 0.99518472667219688624; x(126) = 0.99729045667869021614; x(127) = 0.99879545620517239271; x(128) = 0.99969881869620422012; x(129) = 1.00000000000000000000; w(1) = 0.00006103888176768602; w(2) = 0.00058807215382869754; w(3) = 0.00120930061875273991; w(4) = 0.00180308126695362360; w(5) = 0.00240715327877140915; w(6) = 0.00300345869904497128; w(7) = 0.00360197835812614147; w(8) = 0.00419553798718534675; w(9) = 0.00478862143341336763; w(10) = 0.00537724746840184621; w(11) = 0.00596388034730799521; w(12) = 0.00654590843862298928; w(13) = 0.00712483332325489785; w(14) = 0.00769875778896082811; w(15) = 0.00826865154203087108; w(16) = 0.00883303867470133581; w(17) = 0.00939256583934814871; w(18) = 0.00994602784923457905; w(19) = 0.01049386202576892125; w(20) = 0.01103504877427254184; w(21) = 0.01156988348290849967; w(22) = 0.01209748052807164113; w(23) = 0.01261803597977743271; w(24) = 0.01313076516693974630; w(25) = 0.01363579321293772047; w(26) = 0.01413241437853094133; w(27) = 0.01462070254634350205; w(28) = 0.01510001572479266783; w(29) = 0.01557039073899425960; w(30) = 0.01603123858745057916; w(31) = 0.01648256956220377909; w(32) = 0.01692383985846499368; w(33) = 0.01735504125411394958; w(34) = 0.01777566938875279997; w(35) = 0.01818570377926339481; w(36) = 0.01858467519566908661; w(37) = 0.01897255587067948426; w(38) = 0.01934890842392451844; w(39) = 0.01971370183700155725; w(40) = 0.02006652805198357604; w(41) = 0.02040735612003867863; w(42) = 0.02073580533490147816; w(43) = 0.02105184759002011131; w(44) = 0.02135512797425970725; w(45) = 0.02164562356712882440; w(46) = 0.02192300400598756892; w(47) = 0.02218725355897195088; w(48) = 0.02243806539722630184; w(49) = 0.02267543270456671718; w(50) = 0.02289907134390605882; w(51) = 0.02310898491627407168; w(52) = 0.02330491126131143273; w(53) = 0.02348686571193163505; w(54) = 0.02365460746057766523; w(55) = 0.02380816473024258975; w(56) = 0.02394731750476901502; w(57) = 0.02407210792327850000; w(58) = 0.02418233623893147567; w(59) = 0.02427805942075745923; w(60) = 0.02435909748927643184; w(61) = 0.02442552306156708690; w(62) = 0.02447717542743444284; w(63) = 0.02451414358881568292; w(64) = 0.02453628559651495473; w(65) = 0.02454370750551418263; w(66) = 0.02453628559651495473; w(67) = 0.02451414358881568292; w(68) = 0.02447717542743444284; w(69) = 0.02442552306156708690; w(70) = 0.02435909748927643184; w(71) = 0.02427805942075745923; w(72) = 0.02418233623893147567; w(73) = 0.02407210792327850000; w(74) = 0.02394731750476901502; w(75) = 0.02380816473024258975; w(76) = 0.02365460746057766523; w(77) = 0.02348686571193163505; w(78) = 0.02330491126131143273; w(79) = 0.02310898491627407168; w(80) = 0.02289907134390605882; w(81) = 0.02267543270456671718; w(82) = 0.02243806539722630184; w(83) = 0.02218725355897195088; w(84) = 0.02192300400598756892; w(85) = 0.02164562356712882440; w(86) = 0.02135512797425970725; w(87) = 0.02105184759002011131; w(88) = 0.02073580533490147816; w(89) = 0.02040735612003867863; w(90) = 0.02006652805198357604; w(91) = 0.01971370183700155725; w(92) = 0.01934890842392451844; w(93) = 0.01897255587067948426; w(94) = 0.01858467519566908661; w(95) = 0.01818570377926339481; w(96) = 0.01777566938875279997; w(97) = 0.01735504125411394958; w(98) = 0.01692383985846499368; w(99) = 0.01648256956220377909; w(100) = 0.01603123858745057916; w(101) = 0.01557039073899425960; w(102) = 0.01510001572479266783; w(103) = 0.01462070254634350205; w(104) = 0.01413241437853094133; w(105) = 0.01363579321293772047; w(106) = 0.01313076516693974630; w(107) = 0.01261803597977743271; w(108) = 0.01209748052807164113; w(109) = 0.01156988348290849967; w(110) = 0.01103504877427254184; w(111) = 0.01049386202576892125; w(112) = 0.00994602784923457905; w(113) = 0.00939256583934814871; w(114) = 0.00883303867470133581; w(115) = 0.00826865154203087108; w(116) = 0.00769875778896082811; w(117) = 0.00712483332325489785; w(118) = 0.00654590843862298928; w(119) = 0.00596388034730799521; w(120) = 0.00537724746840184621; w(121) = 0.00478862143341336763; w(122) = 0.00419553798718534675; w(123) = 0.00360197835812614147; w(124) = 0.00300345869904497128; w(125) = 0.00240715327877140915; w(126) = 0.00180308126695362360; w(127) = 0.00120930061875273991; w(128) = 0.00058807215382869754; w(129) = 0.00006103888176768602; else fprintf ( 1, '\n' ); fprintf ( 1, 'CLENSHAW_CURTIS_SET - Fatal error!\n' ); fprintf ( 1, ' Illegal value of ORDER = %d\n', order ); fprintf ( 1, ' Legal values are 1 to 17, 33, 65 or 129.\n' ); error ( 'CLENSHAW_CURTIS_SET - Fatal error!' ); end return end