一、CEC2009无约束多目标测试集

二、CEC2009无约束多目标测试集UF1-UF10Matlab代码

% cec09.m
% The Matlab version of the test instances for CEC 2009 Multiobjective
% Optimization Competition.
function fobj = cec09(name)switch namecase 'UF1'fobj = @UF1;case 'UF2'fobj = @UF2; case 'UF3'fobj = @UF3;  case 'UF4'fobj = @UF4;case 'UF5'fobj = @UF5; case 'UF6'fobj = @UF6;case 'UF7'fobj = @UF7;case 'UF8'fobj = @UF8; case 'UF9'fobj = @UF9; case 'UF10'fobj = @UF10;case 'CF1'fobj = @CF1;case 'CF2'fobj = @CF2; case 'CF3'fobj = @CF3;  case 'CF4'fobj = @CF4;case 'CF5'fobj = @CF5; case 'CF6'fobj = @CF6;case 'CF7'fobj = @CF7;case 'CF8'fobj = @CF8; case 'CF9'fobj = @CF9; case 'CF10'fobj = @CF10;           otherwisefobj = @UF1;end
end%% UF1
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF1(x)[dim, num]  = size(x);tmp         = zeros(dim,num);tmp(2:dim,:)= (x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]))).^2;tmp1        = sum(tmp(3:2:dim,:));  % odd indextmp2        = sum(tmp(2:2:dim,:));  % even indexy(1,:)      = x(1,:)             + 2.0*tmp1/size(3:2:dim,2);y(2,:)      = 1.0 - sqrt(x(1,:)) + 2.0*tmp2/size(2:2:dim,2);clear tmp;
end%% UF2
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF2(x)[dim, num]  = size(x);X1          = repmat(x(1,:),[dim-1,1]);A           = 6*pi*X1 + pi/dim*repmat((2:dim)',[1,num]);tmp         = zeros(dim,num);    tmp(2:dim,:)= (x(2:dim,:) - 0.3*X1.*(X1.*cos(4.0*A)+2.0).*cos(A)).^2;tmp1        = sum(tmp(3:2:dim,:));  % odd indextmp(2:dim,:)= (x(2:dim,:) - 0.3*X1.*(X1.*cos(4.0*A)+2.0).*sin(A)).^2;tmp2        = sum(tmp(2:2:dim,:));  % even indexy(1,:)      = x(1,:)             + 2.0*tmp1/size(3:2:dim,2);y(2,:)      = 1.0 - sqrt(x(1,:)) + 2.0*tmp2/size(2:2:dim,2);clear X1 A tmp;
end%% UF3
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF3(x)[dim, num]   = size(x);Y            = zeros(dim,num);Y(2:dim,:)   = x(2:dim,:) - repmat(x(1,:),[dim-1,1]).^(0.5+1.5*(repmat((2:dim)',[1,num])-2.0)/(dim-2.0));tmp1         = zeros(dim,num);tmp1(2:dim,:)= Y(2:dim,:).^2;tmp2         = zeros(dim,num);tmp2(2:dim,:)= cos(20.0*pi*Y(2:dim,:)./sqrt(repmat((2:dim)',[1,num])));tmp11        = 4.0*sum(tmp1(3:2:dim,:)) - 2.0*prod(tmp2(3:2:dim,:)) + 2.0;  % odd indextmp21        = 4.0*sum(tmp1(2:2:dim,:)) - 2.0*prod(tmp2(2:2:dim,:)) + 2.0;  % even indexy(1,:)       = x(1,:)             + 2.0*tmp11/size(3:2:dim,2);y(2,:)       = 1.0 - sqrt(x(1,:)) + 2.0*tmp21/size(2:2:dim,2);clear Y tmp1 tmp2;
end%% UF4
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF4(x)[dim, num]  = size(x);Y           = zeros(dim,num);Y(2:dim,:)  = x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));H           = zeros(dim,num);H(2:dim,:)  = abs(Y(2:dim,:))./(1.0+exp(2.0*abs(Y(2:dim,:))));tmp1        = sum(H(3:2:dim,:));  % odd indextmp2        = sum(H(2:2:dim,:));  % even indexy(1,:)      = x(1,:)          + 2.0*tmp1/size(3:2:dim,2);y(2,:)      = 1.0 - x(1,:).^2 + 2.0*tmp2/size(2:2:dim,2);clear Y H;
end%% UF5
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF5(x)N           = 10.0;E           = 0.1;[dim, num]  = size(x);Y           = zeros(dim,num);Y(2:dim,:)  = x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));H           = zeros(dim,num);H(2:dim,:)  = 2.0*Y(2:dim,:).^2 - cos(4.0*pi*Y(2:dim,:)) + 1.0;tmp1        = sum(H(3:2:dim,:));  % odd indextmp2        = sum(H(2:2:dim,:));  % even indextmp         = (0.5/N+E)*abs(sin(2.0*N*pi*x(1,:)));y(1,:)      = x(1,:)      + tmp + 2.0*tmp1/size(3:2:dim,2);y(2,:)      = 1.0 - x(1,:)+ tmp + 2.0*tmp2/size(2:2:dim,2);clear Y H;
end%% UF6
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF6(x)N            = 2.0;E            = 0.1;[dim, num]   = size(x);Y            = zeros(dim,num);Y(2:dim,:)  = x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));tmp1         = zeros(dim,num);tmp1(2:dim,:)= Y(2:dim,:).^2;tmp2         = zeros(dim,num);tmp2(2:dim,:)= cos(20.0*pi*Y(2:dim,:)./sqrt(repmat((2:dim)',[1,num])));tmp11        = 4.0*sum(tmp1(3:2:dim,:)) - 2.0*prod(tmp2(3:2:dim,:)) + 2.0;  % odd indextmp21        = 4.0*sum(tmp1(2:2:dim,:)) - 2.0*prod(tmp2(2:2:dim,:)) + 2.0;  % even indextmp          = max(0,(1.0/N+2.0*E)*sin(2.0*N*pi*x(1,:)));y(1,:)       = x(1,:)       + tmp + 2.0*tmp11/size(3:2:dim,2);y(2,:)       = 1.0 - x(1,:) + tmp + 2.0*tmp21/size(2:2:dim,2);clear Y tmp1 tmp2;
end%% UF7
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF7(x)[dim, num]  = size(x);Y           = zeros(dim,num);Y(2:dim,:)  = (x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]))).^2;tmp1        = sum(Y(3:2:dim,:));  % odd indextmp2        = sum(Y(2:2:dim,:));  % even indextmp         = (x(1,:)).^0.2;y(1,:)      = tmp       + 2.0*tmp1/size(3:2:dim,2);y(2,:)      = 1.0 - tmp + 2.0*tmp2/size(2:2:dim,2);clear Y;
end%% UF8
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF8(x)[dim, num]  = size(x);Y           = zeros(dim,num);Y(3:dim,:)  = (x(3:dim,:) - 2.0*repmat(x(2,:),[dim-2,1]).*sin(2.0*pi*repmat(x(1,:),[dim-2,1]) + pi/dim*repmat((3:dim)',[1,num]))).^2;tmp1        = sum(Y(4:3:dim,:));  % j-1 = 3*ktmp2        = sum(Y(5:3:dim,:));  % j-2 = 3*ktmp3        = sum(Y(3:3:dim,:));  % j-0 = 3*ky(1,:)      = cos(0.5*pi*x(1,:)).*cos(0.5*pi*x(2,:)) + 2.0*tmp1/size(4:3:dim,2);y(2,:)      = cos(0.5*pi*x(1,:)).*sin(0.5*pi*x(2,:)) + 2.0*tmp2/size(5:3:dim,2);y(3,:)      = sin(0.5*pi*x(1,:))                     + 2.0*tmp3/size(3:3:dim,2);clear Y;
end%% UF9
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF9(x)E           = 0.1;[dim, num]  = size(x);Y           = zeros(dim,num);Y(3:dim,:)  = (x(3:dim,:) - 2.0*repmat(x(2,:),[dim-2,1]).*sin(2.0*pi*repmat(x(1,:),[dim-2,1]) + pi/dim*repmat((3:dim)',[1,num]))).^2;tmp1        = sum(Y(4:3:dim,:));  % j-1 = 3*ktmp2        = sum(Y(5:3:dim,:));  % j-2 = 3*ktmp3        = sum(Y(3:3:dim,:));  % j-0 = 3*ktmp         = max(0,(1.0+E)*(1-4.0*(2.0*x(1,:)-1).^2));y(1,:)      = 0.5*(tmp+2*x(1,:)).*x(2,:)     + 2.0*tmp1/size(4:3:dim,2);y(2,:)      = 0.5*(tmp-2*x(1,:)+2.0).*x(2,:) + 2.0*tmp2/size(5:3:dim,2);y(3,:)      = 1-x(2,:)                       + 2.0*tmp3/size(3:3:dim,2);clear Y;
end%% UF10
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function y = UF10(x)[dim, num]  = size(x);Y           = zeros(dim,num);Y(3:dim,:)  = x(3:dim,:) - 2.0*repmat(x(2,:),[dim-2,1]).*sin(2.0*pi*repmat(x(1,:),[dim-2,1]) + pi/dim*repmat((3:dim)',[1,num]));H           = zeros(dim,num);H(3:dim,:)  = 4.0*Y(3:dim,:).^2 - cos(8.0*pi*Y(3:dim,:)) + 1.0;tmp1        = sum(H(4:3:dim,:));  % j-1 = 3*ktmp2        = sum(H(5:3:dim,:));  % j-2 = 3*ktmp3        = sum(H(3:3:dim,:));  % j-0 = 3*ky(1,:)      = cos(0.5*pi*x(1,:)).*cos(0.5*pi*x(2,:)) + 2.0*tmp1/size(4:3:dim,2);y(2,:)      = cos(0.5*pi*x(1,:)).*sin(0.5*pi*x(2,:)) + 2.0*tmp2/size(5:3:dim,2);y(3,:)      = sin(0.5*pi*x(1,:))                     + 2.0*tmp3/size(3:3:dim,2);clear Y H;
end%% CF1
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF1(x)a            = 1.0;N            = 10.0;[dim, num]   = size(x);Y            = zeros(dim,num);Y(2:dim,:)   = (x(2:dim,:) - repmat(x(1,:),[dim-1,1]).^(0.5+1.5*(repmat((2:dim)',[1,num])-2.0)/(dim-2.0))).^2;tmp1         = sum(Y(3:2:dim,:));% odd indextmp2         = sum(Y(2:2:dim,:));% even index y(1,:)       = x(1,:)       + 2.0*tmp1/size(3:2:dim,2);y(2,:)       = 1.0 - x(1,:) + 2.0*tmp2/size(2:2:dim,2);c(1,:)       = y(1,:) + y(2,:) - a*abs(sin(N*pi*(y(1,:)-y(2,:)+1.0))) - 1.0;clear Y;
end%% CF2
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF2(x)a           = 1.0;N           = 2.0;[dim, num]  = size(x);tmp         = zeros(dim,num);tmp(2:dim,:)= (x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]))).^2;tmp1        = sum(tmp(3:2:dim,:));  % odd indextmp(2:dim,:)= (x(2:dim,:) - cos(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]))).^2;tmp2        = sum(tmp(2:2:dim,:));  % even indexy(1,:)      = x(1,:)             + 2.0*tmp1/size(3:2:dim,2);y(2,:)      = 1.0 - sqrt(x(1,:)) + 2.0*tmp2/size(2:2:dim,2);t           = y(2,:) + sqrt(y(1,:)) - a*sin(N*pi*(sqrt(y(1,:))-y(2,:)+1.0)) - 1.0;c(1,:)      = sign(t).*abs(t)./(1.0+exp(4.0*abs(t)));clear tmp;
end%% CF3
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF3(x)a            = 1.0;N            = 2.0;[dim, num]   = size(x);Y            = zeros(dim,num);Y(2:dim,:)   = x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));tmp1         = zeros(dim,num);tmp1(2:dim,:)= Y(2:dim,:).^2;tmp2         = zeros(dim,num);tmp2(2:dim,:)= cos(20.0*pi*Y(2:dim,:)./sqrt(repmat((2:dim)',[1,num])));tmp11        = 4.0*sum(tmp1(3:2:dim,:)) - 2.0*prod(tmp2(3:2:dim,:)) + 2.0;  % odd indextmp21        = 4.0*sum(tmp1(2:2:dim,:)) - 2.0*prod(tmp2(2:2:dim,:)) + 2.0;  % even indexy(1,:)       = x(1,:)          + 2.0*tmp11/size(3:2:dim,2);y(2,:)       = 1.0 - x(1,:).^2 + 2.0*tmp21/size(2:2:dim,2);c(1,:)       = y(2,:) + y(1,:).^2 - a*sin(N*pi*(y(1,:).^2-y(2,:)+1.0)) - 1.0;   clear Y tmp1 tmp2;
end%% CF4
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF4(x)[dim, num]  = size(x);tmp         = zeros(dim,num);tmp(2:dim,:)= x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));tmp1        = sum(tmp(3:2:dim,:).^2);  % odd indextmp2        = sum(tmp(4:2:dim,:).^2);  % even indexindex1      = tmp(2,:) < (1.5-0.75*sqrt(2.0));index2      = tmp(2,:)>= (1.5-0.75*sqrt(2.0));tmp(2,index1) = abs(tmp(2,index1));tmp(2,index2) = 0.125 + (tmp(2,index2)-1.0).^2;y(1,:)      = x(1,:)                  + tmp1;y(2,:)      = 1.0 - x(1,:) + tmp(2,:) + tmp2;t           = x(2,:) - sin(6.0*pi*x(1,:)+2.0*pi/dim) - 0.5*x(1,:) + 0.25;c(1,:)      = sign(t).*abs(t)./(1.0+exp(4.0*abs(t)));clear tmp index1 index2;
end%% CF5
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF5(x)[dim, num]  = size(x);tmp         = zeros(dim,num);tmp(2:dim,:)= x(2:dim,:) - 0.8*repmat(x(1,:),[dim-1,1]).*cos(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));tmp1        = sum(2.0*tmp(3:2:dim,:).^2-cos(4.0*pi*tmp(3:2:dim,:))+1.0);  % odd indextmp(2:dim,:)= x(2:dim,:) - 0.8*repmat(x(1,:),[dim-1,1]).*sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));    tmp2        = sum(2.0*tmp(4:2:dim,:).^2-cos(4.0*pi*tmp(4:2:dim,:))+1.0);  % even indexindex1      = tmp(2,:) < (1.5-0.75*sqrt(2.0));index2      = tmp(2,:)>= (1.5-0.75*sqrt(2.0));tmp(2,index1) = abs(tmp(2,index1));tmp(2,index2) = 0.125 + (tmp(2,index2)-1.0).^2;y(1,:)      = x(1,:)                  + tmp1;y(2,:)      = 1.0 - x(1,:) + tmp(2,:) + tmp2;c(1,:)      = x(2,:) - 0.8*x(1,:).*sin(6.0*pi*x(1,:)+2.0*pi/dim) - 0.5*x(1,:) + 0.25;clear tmp;
end%% CF6
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF6(x)[dim, num]  = size(x);tmp         = zeros(dim,num);tmp(2:dim,:)= x(2:dim,:) - 0.8*repmat(x(1,:),[dim-1,1]).*cos(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));tmp1        = sum(tmp(3:2:dim,:).^2);  % odd indextmp(2:dim,:)= x(2:dim,:) - 0.8*repmat(x(1,:),[dim-1,1]).*sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));    tmp2        = sum(tmp(2:2:dim,:).^2);  % even indexy(1,:)      = x(1,:)            + tmp1;y(2,:)      = (1.0 - x(1,:)).^2 + tmp2;tmp         = 0.5*(1-x(1,:))-(1-x(1,:)).^2;c(1,:)      = x(2,:) - 0.8*x(1,:).*sin(6.0*pi*x(1,:)+2*pi/dim) - sign(tmp).*sqrt(abs(tmp));tmp         = 0.25*sqrt(1-x(1,:))-0.5*(1-x(1,:));c(2,:)      = x(4,:) - 0.8*x(1,:).*sin(6.0*pi*x(1,:)+4*pi/dim) - sign(tmp).*sqrt(abs(tmp));    clear tmp;
end%% CF7
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF7(x)[dim, num]  = size(x);tmp         = zeros(dim,num);tmp(2:dim,:)= x(2:dim,:) - cos(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));tmp1        = sum(2.0*tmp(3:2:dim,:).^2-cos(4.0*pi*tmp(3:2:dim,:))+1.0);  % odd indextmp(2:dim,:)= x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]));tmp2        = sum(2.0*tmp(6:2:dim,:).^2-cos(4.0*pi*tmp(6:2:dim,:))+1.0);  % even indextmp(2,:)    = tmp(2,:).^2;tmp(4,:)    = tmp(4,:).^2;y(1,:)      = x(1,:)                                  + tmp1;y(2,:)      = (1.0 - x(1,:)).^2 + tmp(2,:) + tmp(4,:) + tmp2;tmp         = 0.5*(1-x(1,:))-(1-x(1,:)).^2;c(1,:)      = x(2,:) - sin(6.0*pi*x(1,:)+2*pi/dim) - sign(tmp).*sqrt(abs(tmp));tmp         = 0.25*sqrt(1-x(1,:))-0.5*(1-x(1,:));c(2,:)      = x(4,:) - sin(6.0*pi*x(1,:)+4*pi/dim) - sign(tmp).*sqrt(abs(tmp));    clear tmp;
end%% CF8
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF8(x)N           = 2.0;a           = 4.0;[dim, num]  = size(x);Y           = zeros(dim,num);Y(3:dim,:)  = (x(3:dim,:) - 2.0*repmat(x(2,:),[dim-2,1]).*sin(2.0*pi*repmat(x(1,:),[dim-2,1]) + pi/dim*repmat((3:dim)',[1,num]))).^2;tmp1        = sum(Y(4:3:dim,:));  % j-1 = 3*ktmp2        = sum(Y(5:3:dim,:));  % j-2 = 3*ktmp3        = sum(Y(3:3:dim,:));  % j-0 = 3*ky(1,:)      = cos(0.5*pi*x(1,:)).*cos(0.5*pi*x(2,:)) + 2.0*tmp1/size(4:3:dim,2);y(2,:)      = cos(0.5*pi*x(1,:)).*sin(0.5*pi*x(2,:)) + 2.0*tmp2/size(5:3:dim,2);y(3,:)      = sin(0.5*pi*x(1,:))                     + 2.0*tmp3/size(3:3:dim,2);c(1,:)      = (y(1,:).^2+y(2,:).^2)./(1.0-y(3,:).^2) - a*abs(sin(N*pi*((y(1,:).^2-y(2,:).^2)./(1.0-y(3,:).^2)+1.0))) - 1.0;clear Y;
end%% CF9
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF9(x)N           = 2.0;a           = 3.0;[dim, num]  = size(x);Y           = zeros(dim,num);Y(3:dim,:)  = (x(3:dim,:) - 2.0*repmat(x(2,:),[dim-2,1]).*sin(2.0*pi*repmat(x(1,:),[dim-2,1]) + pi/dim*repmat((3:dim)',[1,num]))).^2;tmp1        = sum(Y(4:3:dim,:));  % j-1 = 3*ktmp2        = sum(Y(5:3:dim,:));  % j-2 = 3*ktmp3        = sum(Y(3:3:dim,:));  % j-0 = 3*ky(1,:)      = cos(0.5*pi*x(1,:)).*cos(0.5*pi*x(2,:)) + 2.0*tmp1/size(4:3:dim,2);y(2,:)      = cos(0.5*pi*x(1,:)).*sin(0.5*pi*x(2,:)) + 2.0*tmp2/size(5:3:dim,2);y(3,:)      = sin(0.5*pi*x(1,:))                     + 2.0*tmp3/size(3:3:dim,2);c(1,:)      = (y(1,:).^2+y(2,:).^2)./(1.0-y(3,:).^2) - a*sin(N*pi*((y(1,:).^2-y(2,:).^2)./(1.0-y(3,:).^2)+1.0)) - 1.0;clear Y;
end%% CF10
% x and y are columnwise, the imput x must be inside the search space and
% it could be a matrix
function [y,c] = CF10(x)a           = 1.0;N           = 2.0;[dim, num]  = size(x);Y           = zeros(dim,num);Y(3:dim,:)  = x(3:dim,:) - 2.0*repmat(x(2,:),[dim-2,1]).*sin(2.0*pi*repmat(x(1,:),[dim-2,1]) + pi/dim*repmat((3:dim)',[1,num]));H           = zeros(dim,num);H(3:dim,:)  = 4.0*Y(3:dim,:).^2 - cos(8.0*pi*Y(3:dim,:)) + 1.0;tmp1        = sum(H(4:3:dim,:));  % j-1 = 3*ktmp2        = sum(H(5:3:dim,:));  % j-2 = 3*ktmp3        = sum(H(3:3:dim,:));  % j-0 = 3*ky(1,:)      = cos(0.5*pi*x(1,:)).*cos(0.5*pi*x(2,:)) + 2.0*tmp1/size(4:3:dim,2);y(2,:)      = cos(0.5*pi*x(1,:)).*sin(0.5*pi*x(2,:)) + 2.0*tmp2/size(5:3:dim,2);y(3,:)      = sin(0.5*pi*x(1,:))                     + 2.0*tmp3/size(3:3:dim,2);c(1,:)      = (y(1,:).^2+y(2,:).^2)./(1.0-y(3,:).^2) - a*sin(N*pi*((y(1,:).^2-y(2,:).^2)./(1.0-y(3,:).^2)+1.0)) - 1.0;clear Y H;
end