Please assist to resolve "magaa and mag2a" codes problems; probably FUN and fsolve, not properly sets. The mag2 has to generate 12 (Qy-variable) questions by for-end. Thanks

Question

Eng. FM 2024-4-26

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2112006-please-assist-to-resolve-magaa-and-mag2a-codes-problems-probably-fun-and-fsolve-not-properly-set

评论： Eng. FM 2024-4-27

I have two file execution files, MAGa is main and mag2a is responsible for produce and generate 12 non-linear equations, and probably could goes to 100. The MAGa file has to call mag2a and produce the output in table format. I have failed to known what is main problem, include set up FUN in mag2 file and solver (non-linear) I has proposed. See the attached files and executed output; appreciate your assistance

FILE MAGa and mag2a

MAGa

function [Qy, FUN] = MAGa(Qy0)
tic,    n=12; pipes=n;  dia=n; LP=4; cCc=7;    HLD=-0; ee=0.04; vs=1.00001*10^-6;                   format shortEng
        D=[1.120, 0.059, 0.019, 0.033, 0.060, 0.052, 0.023, 0.029, 0.017, 0.018, 0.058, 0.150];     L=[50, 50, 40, 50, 40, 50, 60, 60, 50, 50, 60, 40];                             
 
FUN =  @mag2a;          %
    
   options = optimoptions('fsolve','Display','iter',MaxIterations=10000000, MaxFunctionEvaluations=10000000, Algorithm='levenberg-marquardt');
   %  Qy0(1:12,1)=0.30;               
   
[Qy]=fsolve(FUN, Qy0, options);    
                                             Len=L(1,:)'; Dia=D(1,:)'; vel=4*Qy(:,1)./(3.14.*Dia(:,1).^2);   Re=4.*Qy(:,1)./(3.14*vs.*Dia(:,1)); 
                                             fy11=-2*log10(ee./(3.7.*Dia(:,1))+2.51*3.14*vs.*Dia(:,1)./(4.*Qy(:,1)*0.0001.^0.5)); fy1=-2*log10(ee./(3.7.*Dia(:,1))+2.51*3.14*vs.*Dia(:,1)./(4.*Qy(:,1)).*fy11.^0.5); fy=-2*log10(ee./(3.7.*Dia(:,1))+2.51*3.14*vs.*Dia(:,1)./(4.*Qy(:,1)).*fy1.^0.5);  f=-2*log10(ee./(3.7.*Dia(:,1))+2.51*3.14*vs.*Dia(:,1)./(4.*Qy(:,1)).*fy.^0.5); ff=(1./f).^2;
                                             Data1=zeros(n,cCc);   Data1(:,1)=Len(:,1); Data1(:,2)=Dia(:,1); Data1(:,3)=Qy(:,1);   Data1(:,4)=vel(:,1); Data1(:,5)=ff(:,1);  Data1(:,6)=Re(:,1); % Data1, 
StrNum={'string','double','double','double','double','double','double','double'};           subTitl={'Pipes [x-z]', 'Length [m]', 'Diameter [m]', 'Flow rate [m3/s]', 'Velocity [m/s]', 'Friction, f', 'Reynold No.', 'Headlosses [m]'};	%
tz=table('size', [n, cCc+1], 'variabletypes',StrNum, 'variablenames', subTitl);             Pipexz=["1P(N1-N2)","2P(N1-N2)","3P(N1-N2)","4P(N1-N2)","5P(N1-N2)","6P(N1-N2)","7P(N1-N2)","8P(N1-N2)","9P(N1-N2)","10P(N1-N2)","11P(N1-N2)","12P(N1-N2)"];
                                                                                            tz{:,1}=Pipexz';  tz{:,2:cCc+1}=Data1(:,1:cCc),                   toc                           % MIDsrt=sortrows(tz,sn);  MIDfn=MIDsrt;  MIDfn(:,end)=[ ];     
end

mag2a

function [FUN] = mag2a(D,L,LP,n,ee,vs,matr,HLD)
           matr=[1,0,0,0,1,-1,0,0,0,0,0,-1; 0,1,1,-1,-1,0,0,0,0,0,0,0; 0,0,0,1,0,0,1,-1,-1,0,0,0; 0,0,0,0,0,1,0,1,0,-1,-1,0]; LP=4; n=12;
 fprintf('FUN=@(Qy)[');                        
            for j=1:LP, j;      
              if (j<=4-0) 
                  for k=1:n, k;     
                         if sum(matr(j,1:k))~=sum(matr(j,:))&&matr(j,k)~=0 fprintf('%d*(Qy(%d)*abs(Qy(%d)*8*L(1,%d)*1./(9.81*3.14.^2*D(1,%d).^5)*(-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...\n',matr(j,k),k,k,k,k,k,k,k,k,k,k,k,k,k), end
                         if sum(matr(j,1:k))==sum(matr(j,:))&&matr(j,k)~=0 fprintf('%d*(Qy(%d)*abs(Qy(%d)*8*L(1,%d)*1./(9.81*3.14.^2*D(1,%d).^5)*(-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2;\n',matr(j,k),k,k,k,k,k,k,k,k,k,k,k,k,k),
                         end, end, end
            end
            fprintf('Qy(1)-Qy(2)-Qy(5)-0.03; Qy(2)-Qy(3)-0.04; Qy(3)+Qy(4)-Qy(7)-0.03; Qy(6)+Qy(5)-Qy(4)-Qy(8)-0.05; Qy(7)+Qy(9)-0.04; Qy(8)+Qy(10)-Qy(9)-0.03; Qy(11)-Qy(10)-0.04; Qy(12)-Qy(6)-Qy(11)-0.04];\n');                                                                   % 1/(Qy(7)).^0.5+4*log(ee./(3.7*D(1,1))+2.54*3.14*D(1,1)*vs./(4*Qy(1)*(Qy(7)).^0.5));...
end

OUTPUT OF EXECUTION (OUTPUTS)

Qy0(1:12,1)=0.30; MAGa(Qy0)

FUN=@(Qy)[1*(Qy(1)*abs(Qy(1)*8*L(1,1)*1./(9.81*3.14.^2*D(1,1).^5)*(-2*log10(ee./(3.7.*D(1,1))+2.51*3.14*vs.*D(1,1)./(4.*Qy(1,1)*((-2*log10(ee./(3.7.*D(1,1))+2.51*3.14*vs.*D(1,1)./(4.*Qy(1,1)*((-2*log10(ee./(3.7.*D(1,1))+2.51*3.14*vs.*D(1,1)./(4.*Qy(1,1)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

1*(Qy(5)*abs(Qy(5)*8*L(1,5)*1./(9.81*3.14.^2*D(1,5).^5)*(-2*log10(ee./(3.7.*D(1,5))+2.51*3.14*vs.*D(1,5)./(4.*Qy(1,5)*((-2*log10(ee./(3.7.*D(1,5))+2.51*3.14*vs.*D(1,5)./(4.*Qy(1,5)*((-2*log10(ee./(3.7.*D(1,5))+2.51*3.14*vs.*D(1,5)./(4.*Qy(1,5)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

-1*(Qy(6)*abs(Qy(6)*8*L(1,6)*1./(9.81*3.14.^2*D(1,6).^5)*(-2*log10(ee./(3.7.*D(1,6))+2.51*3.14*vs.*D(1,6)./(4.*Qy(1,6)*((-2*log10(ee./(3.7.*D(1,6))+2.51*3.14*vs.*D(1,6)./(4.*Qy(1,6)*((-2*log10(ee./(3.7.*D(1,6))+2.51*3.14*vs.*D(1,6)./(4.*Qy(1,6)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

-1*(Qy(12)*abs(Qy(12)*8*L(1,12)*1./(9.81*3.14.^2*D(1,12).^5)*(-2*log10(ee./(3.7.*D(1,12))+2.51*3.14*vs.*D(1,12)./(4.*Qy(1,12)*((-2*log10(ee./(3.7.*D(1,12))+2.51*3.14*vs.*D(1,12)./(4.*Qy(1,12)*((-2*log10(ee./(3.7.*D(1,12))+2.51*3.14*vs.*D(1,12)./(4.*Qy(1,12)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2;

1*(Qy(2)*abs(Qy(2)*8*L(1,2)*1./(9.81*3.14.^2*D(1,2).^5)*(-2*log10(ee./(3.7.*D(1,2))+2.51*3.14*vs.*D(1,2)./(4.*Qy(1,2)*((-2*log10(ee./(3.7.*D(1,2))+2.51*3.14*vs.*D(1,2)./(4.*Qy(1,2)*((-2*log10(ee./(3.7.*D(1,2))+2.51*3.14*vs.*D(1,2)./(4.*Qy(1,2)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

1*(Qy(3)*abs(Qy(3)*8*L(1,3)*1./(9.81*3.14.^2*D(1,3).^5)*(-2*log10(ee./(3.7.*D(1,3))+2.51*3.14*vs.*D(1,3)./(4.*Qy(1,3)*((-2*log10(ee./(3.7.*D(1,3))+2.51*3.14*vs.*D(1,3)./(4.*Qy(1,3)*((-2*log10(ee./(3.7.*D(1,3))+2.51*3.14*vs.*D(1,3)./(4.*Qy(1,3)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

-1*(Qy(4)*abs(Qy(4)*8*L(1,4)*1./(9.81*3.14.^2*D(1,4).^5)*(-2*log10(ee./(3.7.*D(1,4))+2.51*3.14*vs.*D(1,4)./(4.*Qy(1,4)*((-2*log10(ee./(3.7.*D(1,4))+2.51*3.14*vs.*D(1,4)./(4.*Qy(1,4)*((-2*log10(ee./(3.7.*D(1,4))+2.51*3.14*vs.*D(1,4)./(4.*Qy(1,4)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

-1*(Qy(5)*abs(Qy(5)*8*L(1,5)*1./(9.81*3.14.^2*D(1,5).^5)*(-2*log10(ee./(3.7.*D(1,5))+2.51*3.14*vs.*D(1,5)./(4.*Qy(1,5)*((-2*log10(ee./(3.7.*D(1,5))+2.51*3.14*vs.*D(1,5)./(4.*Qy(1,5)*((-2*log10(ee./(3.7.*D(1,5))+2.51*3.14*vs.*D(1,5)./(4.*Qy(1,5)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2;

1*(Qy(4)*abs(Qy(4)*8*L(1,4)*1./(9.81*3.14.^2*D(1,4).^5)*(-2*log10(ee./(3.7.*D(1,4))+2.51*3.14*vs.*D(1,4)./(4.*Qy(1,4)*((-2*log10(ee./(3.7.*D(1,4))+2.51*3.14*vs.*D(1,4)./(4.*Qy(1,4)*((-2*log10(ee./(3.7.*D(1,4))+2.51*3.14*vs.*D(1,4)./(4.*Qy(1,4)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

1*(Qy(7)*abs(Qy(7)*8*L(1,7)*1./(9.81*3.14.^2*D(1,7).^5)*(-2*log10(ee./(3.7.*D(1,7))+2.51*3.14*vs.*D(1,7)./(4.*Qy(1,7)*((-2*log10(ee./(3.7.*D(1,7))+2.51*3.14*vs.*D(1,7)./(4.*Qy(1,7)*((-2*log10(ee./(3.7.*D(1,7))+2.51*3.14*vs.*D(1,7)./(4.*Qy(1,7)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

-1*(Qy(8)*abs(Qy(8)*8*L(1,8)*1./(9.81*3.14.^2*D(1,8).^5)*(-2*log10(ee./(3.7.*D(1,8))+2.51*3.14*vs.*D(1,8)./(4.*Qy(1,8)*((-2*log10(ee./(3.7.*D(1,8))+2.51*3.14*vs.*D(1,8)./(4.*Qy(1,8)*((-2*log10(ee./(3.7.*D(1,8))+2.51*3.14*vs.*D(1,8)./(4.*Qy(1,8)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

-1*(Qy(9)*abs(Qy(9)*8*L(1,9)*1./(9.81*3.14.^2*D(1,9).^5)*(-2*log10(ee./(3.7.*D(1,9))+2.51*3.14*vs.*D(1,9)./(4.*Qy(1,9)*((-2*log10(ee./(3.7.*D(1,9))+2.51*3.14*vs.*D(1,9)./(4.*Qy(1,9)*((-2*log10(ee./(3.7.*D(1,9))+2.51*3.14*vs.*D(1,9)./(4.*Qy(1,9)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2;

1*(Qy(6)*abs(Qy(6)*8*L(1,6)*1./(9.81*3.14.^2*D(1,6).^5)*(-2*log10(ee./(3.7.*D(1,6))+2.51*3.14*vs.*D(1,6)./(4.*Qy(1,6)*((-2*log10(ee./(3.7.*D(1,6))+2.51*3.14*vs.*D(1,6)./(4.*Qy(1,6)*((-2*log10(ee./(3.7.*D(1,6))+2.51*3.14*vs.*D(1,6)./(4.*Qy(1,6)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

1*(Qy(8)*abs(Qy(8)*8*L(1,8)*1./(9.81*3.14.^2*D(1,8).^5)*(-2*log10(ee./(3.7.*D(1,8))+2.51*3.14*vs.*D(1,8)./(4.*Qy(1,8)*((-2*log10(ee./(3.7.*D(1,8))+2.51*3.14*vs.*D(1,8)./(4.*Qy(1,8)*((-2*log10(ee./(3.7.*D(1,8))+2.51*3.14*vs.*D(1,8)./(4.*Qy(1,8)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

-1*(Qy(10)*abs(Qy(10)*8*L(1,10)*1./(9.81*3.14.^2*D(1,10).^5)*(-2*log10(ee./(3.7.*D(1,10))+2.51*3.14*vs.*D(1,10)./(4.*Qy(1,10)*((-2*log10(ee./(3.7.*D(1,10))+2.51*3.14*vs.*D(1,10)./(4.*Qy(1,10)*((-2*log10(ee./(3.7.*D(1,10))+2.51*3.14*vs.*D(1,10)./(4.*Qy(1,10)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+...

-1*(Qy(11)*abs(Qy(11)*8*L(1,11)*1./(9.81*3.14.^2*D(1,11).^5)*(-2*log10(ee./(3.7.*D(1,11))+2.51*3.14*vs.*D(1,11)./(4.*Qy(1,11)*((-2*log10(ee./(3.7.*D(1,11))+2.51*3.14*vs.*D(1,11)./(4.*Qy(1,11)*((-2*log10(ee./(3.7.*D(1,11))+2.51*3.14*vs.*D(1,11)./(4.*Qy(1,11)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2;

Qy(1)-Qy(2)-Qy(5)-0.03; Qy(2)-Qy(3)-0.04; Qy(3)+Qy(4)-Qy(7)-0.03; Qy(6)+Qy(5)-Qy(4)-Qy(8)-0.05; Qy(7)+Qy(9)-0.04; Qy(8)+Qy(10)-Qy(9)-0.03; Qy(11)-Qy(10)-0.04; Qy(12)-Qy(6)-Qy(11)-0.04];

Output argument "FUN" (and possibly others) not assigned a value in the execution with "mag2a" function.

Error in fsolve (line 270)

fuser = feval(funfcn{3},x,varargin{:});

Error in MAGa (line 8)

[Qy]=fsolve(FUN, Qy0, options);

Caused by:

Failure in initial objective function evaluation. FSOLVE cannot continue.

>>

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Answer 1

Walter Roberson 2024-4-26

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2112006-please-assist-to-resolve-magaa-and-mag2a-codes-problems-probably-fun-and-fsolve-not-properly-set#answer_1448356

编辑：Walter Roberson 2024-4-26

在 MATLAB Online 中打开

function [Qy, FUN] = MAGa(Qy0)
tic,    n=12; pipes=n;  dia=n; LP=4; cCc=7;    HLD=-0; ee=0.04; vs=1.00001*10^-6;                   format shortEng
        D=[1.120, 0.059, 0.019, 0.033, 0.060, 0.052, 0.023, 0.029, 0.017, 0.018, 0.058, 0.150];     L=[50, 50, 40, 50, 40, 50, 60, 60, 50, 50, 60, 40];                             
FUN = '';
eval(mag2a(D,L,LP,n,ee,vs,matr,HLD));   %assigns to FUN
    
options = optimoptions('fsolve','Display','iter',MaxIterations=10000000, MaxFunctionEvaluations=10000000, Algorithm='levenberg-marquardt');
   %  Qy0(1:12,1)=0.30;               
   
[Qy]=fsolve(FUN, Qy0, options);    
                                             Len=L(1,:)'; Dia=D(1,:)'; vel=4*Qy(:,1)./(3.14.*Dia(:,1).^2);   Re=4.*Qy(:,1)./(3.14*vs.*Dia(:,1)); 
                                             fy11=-2*log10(ee./(3.7.*Dia(:,1))+2.51*3.14*vs.*Dia(:,1)./(4.*Qy(:,1)*0.0001.^0.5)); fy1=-2*log10(ee./(3.7.*Dia(:,1))+2.51*3.14*vs.*Dia(:,1)./(4.*Qy(:,1)).*fy11.^0.5); fy=-2*log10(ee./(3.7.*Dia(:,1))+2.51*3.14*vs.*Dia(:,1)./(4.*Qy(:,1)).*fy1.^0.5);  f=-2*log10(ee./(3.7.*Dia(:,1))+2.51*3.14*vs.*Dia(:,1)./(4.*Qy(:,1)).*fy.^0.5); ff=(1./f).^2;
                                             Data1=zeros(n,cCc);   Data1(:,1)=Len(:,1); Data1(:,2)=Dia(:,1); Data1(:,3)=Qy(:,1);   Data1(:,4)=vel(:,1); Data1(:,5)=ff(:,1);  Data1(:,6)=Re(:,1); % Data1, 
StrNum={'string','double','double','double','double','double','double','double'};           subTitl={'Pipes [x-z]', 'Length [m]', 'Diameter [m]', 'Flow rate [m3/s]', 'Velocity [m/s]', 'Friction, f', 'Reynold No.', 'Headlosses [m]'};	%
tz=table('size', [n, cCc+1], 'variabletypes',StrNum, 'variablenames', subTitl);             Pipexz=["1P(N1-N2)","2P(N1-N2)","3P(N1-N2)","4P(N1-N2)","5P(N1-N2)","6P(N1-N2)","7P(N1-N2)","8P(N1-N2)","9P(N1-N2)","10P(N1-N2)","11P(N1-N2)","12P(N1-N2)"];
                                                                                            tz{:,1}=Pipexz';  tz{:,2:cCc+1}=Data1(:,1:cCc),                   toc                           % MIDsrt=sortrows(tz,sn);  MIDfn=MIDsrt;  MIDfn(:,end)=[ ];     
end
function [FUN] = mag2a(D,L,LP,n,ee,vs,matr,HLD)
           matr=[1,0,0,0,1,-1,0,0,0,0,0,-1; 0,1,1,-1,-1,0,0,0,0,0,0,0; 0,0,0,1,0,0,1,-1,-1,0,0,0; 0,0,0,0,0,1,0,1,0,-1,-1,0]; LP=4; n=12;
 FUN = 'FUN=@(Qy)[';
            for j=1:LP;      
              if (j<=4-0) 
                  for k=1:n, k;     
                         if sum(matr(j,1:k))~=sum(matr(j,:))&&matr(j,k)~=0 FUN = [FUN, sprintf('%d*(Qy(%d)*abs(Qy(%d)*8*L(1,%d)*1./(9.81*3.14.^2*D(1,%d).^5)*(-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+',matr(j,k),k,k,k,k,k,k,k,k,k,k,k,k,k)]; end
                         if sum(matr(j,1:k))==sum(matr(j,:))&&matr(j,k)~=0 FUN = [FUN, sprintf('%d*(Qy(%d)*abs(Qy(%d)*8*L(1,%d)*1./(9.81*3.14.^2*D(1,%d).^5)*(-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2',matr(j,k),k,k,k,k,k,k,k,k,k,k,k,k,k)]; end
                  end
              end
            end
            FUN = [FUN, 'Qy(1)-Qy(2)-Qy(5)-0.03; Qy(2)-Qy(3)-0.04; Qy(3)+Qy(4)-Qy(7)-0.03; Qy(6)+Qy(5)-Qy(4)-Qy(8)-0.05; Qy(7)+Qy(9)-0.04; Qy(8)+Qy(10)-Qy(9)-0.03; Qy(11)-Qy(10)-0.04; Qy(12)-Qy(6)-Qy(11)-0.04];'];                                                                   % 1/(Qy(7)).^0.5+4*log(ee./(3.7*D(1,1))+2.54*3.14*D(1,1)*vs./(4*Qy(1)*(Qy(7)).^0.5));...
end

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Walter Roberson 2024-4-26

在 MATLAB Online 中打开

if sum(matr(j,1:k))~=sum(matr(j,:))&&matr(j,k)~=0 FUN = [FUN, sprintf('%d*(Qy(%d)*abs(Qy(%d)*8*L(1,%d)*1./(9.81*3.14.^2*D(1,%d).^5)*(-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*((-2*log10(ee./(3.7.*D(1,%d))+2.51*3.14*vs.*D(1,%d)./(4.*Qy(1,%d)*(0.0001).^0.5)))).^0.5)))).^0.5))).^-2+',matr(j,k),k,k,k,k,k,k,k,k,k,k,k,k,k)]; end
%                                                                         1  2  1    2  3  2    3    2    3              4    3   2 3        4    5      6    54                5    4  5     6    5 67        8    9      A    98                9    8  9     A    9 AB        C    D      E    DC                D    C  D     E    D E      D     CBA9     8765     432

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