Inner matrix dimensions must agree

Hi,

when I execute the following code, I get the error message "Inner matrix dimensions must agree".

The error is in line 31, which performs the multiplication of three real matrix of the same size.

this is what I can't understand.

i would like you to help me understand what is the problem.

thank you!

    
de=ones(5,1); u=ones(22); %dde=zeros(5,1);
   Cz=0.001; %vertical deflection rate of the tyre  
   Cs=50000;
   epsilon=0.015;
   I=2.1;
   Iz=1627;
   R=0.35;
   Ca=30000;
   m=1298.9;
   lf=1; 
   lr=1.454;
   br=1.436;
   bf=br;
   mu=0.9;
   g=9.81;
   cons=m/(lr+lf);
   h=0.5;
   C=[0 m*u(22) 0 0 0;-m*u(22) 0 0 0 0;0 0 0 0 0;0 0 0 cos(u(21)) -sin(u(21));0 0 0 sin(u(21)) cos(u(21))];
   M=[m 0 0 0 0;0 m 0 0 0;0 0 Iz 0 0;0 0 0 1 0;0 0 0 0 1];
   
   u1=(de(2)+lf*de(3))/(de(1)+0.5*bf*de(3));
   u2=(de(2)+lf*de(3))/(de(1)-0.5*bf*de(3));
   u3=(de(2)-lr*de(3))/(de(1)+0.5*br*de(3));    %% les ui représentent les rapports permettant de calculer les angles de dérives de chaque roue%%
   u4=(de(2)-lr*de(3))/(de(1)-0.5*br*de(3));
   U=[u1 u2 u3 u4];
   
   
                          %------vertical load----------
                                   
       dde=(-de*C)\M; % here: Inner matrix dimensions must agree !
       
       Fz1= cons*(0.5*g*lr-0.5*dde(1)*h-lr*h*dde(2)/bf);
       Fz2= cons*(0.5*g*lr-0.5*dde(1)*h+lr*h*dde(2)/bf);
       Fz3= cons*(0.5*g*lr+0.5*dde(1)*h-lr*h*dde(2)/bf); 
       Fz4= cons*(0.5*g*lr+0.5*dde(1)*h+lr*h*dde(2)/bf);                        
       Fz=[Fz1 Fz2 Fz3 Fz4]';
  
            %%% velocity component in the wheel plane : is the longitunal velocity
       v1=(de(1)+0.5*bf*de(3))*cos(u(1))+(de(2)+lf*de(3))*sin(u(1));
       v2=(de(1)-0.5*bf*de(3))*cos(u(2))+(de(2)+lf*de(3))*sin(u(2));
       v3=(de(1)+0.5*br*de(3))*cos(u(3))+(de(2)-lr*de(3))*sin(u(3));
       v4=(de(1)-0.5*br*de(3))*cos(u(4))+(de(2)-lr*de(3))*sin(u(4));
       V=[v1 v2 v3 v4]';
       
   lamda=zeros(4,1);f=length(lamda);
   omega=zeros(4,1);
   alph=zeros(4,1);
   Re=zeros(4,1);
   S=zeros(4,1);
   dz=zeros(4,1);
   Fs=zeros(4,1);
   Ft=zeros(4,1);
  for i=1:4
      dz(i)=-Cz*Fz(i)+ 0.33*R;
      Re(i)=R-dz(i)./3;
      omega(i)=(-R*u(i+16)+u(i+4))/I;
      S(i)=1+omega(i)*Re(i)./V(i);
      alph(i)=atan(U(i))-u(i);
      lamda(i)= mu*Fz(i).*(1-S(i))*(1-epsilon*V(i).*sqrt((S(i))^2 + (tan(alph(i)))^2))./(2*sqrt((Cs^2)*(S(i))^2 + (Ca^2)*(tan(alph(i))^2)));
      if lamda(i)<1
         f(i)=lamda(i)*(2-lamda(i));
         Fs(i)=Ca*f(i).*tan(alph(i))./(1-S(i));
         Ft(i)=Cs*f(i).*S(i)./(1-S(i));
      elseif lamda(i)>1
          f(i)=1;
          Fs(i)=Ca*f(i).*tan(alph(i))./(1-S(i));
          Ft(i)=Cs*f(i).*S(i)./(1-S(i));
      end
  end

[Murugan C]

in 31 line, de has 5x1 size , because of that only you got error like index matrix dimension must agree.

To avoid this error, make de as same of C and M or de should be scalar like

de = ones(5,5); % or
de = 1;

[Robert Collins]

Reducing the code to a minimal working example gives:

de=ones(5,1);
u=ones(22);
Iz=1627;
m=1298.9;
mu=0.9;

C=[0 m*u(22) 0 0 0;-m*u(22) 0 0 0 0;0 0 0 0 0;0 0 0 cos(u(21)) -sin(u(21));0 0 0 sin(u(21)) cos(u(21))];
M=[m 0 0 0 0;0 m 0 0 0;0 0 Iz 0 0;0 0 0 1 0;0 0 0 0 1];
                                  
dde=(-de'*C)\M; % here: Inner matrix dimensions must agree !

Then looking at the dimensions of de, C, and M should indicate where the mistake is. de is a 5 element vector, while C and M are 5x5 matrices. This explains the error message.

[Murugan C]

now also you will get error.

dde=(-de'*C)\M; % here: Inner matrix dimensions must agree !

K>> dde=(-de'*C)\M;
Error using  \ 
Matrix dimensions must agree.

[Valéry Ebogo]

dde=(-de'*C)\M;
Error using  \
% The problem is solved by changing \ by /.

Thank you!

Answer 1

[Valéry Ebogo]

I realized the mistake!

in fact, d is a vector 5x1, the product de*C is correct if the number of columns of de is equal to the number of rows of C. it is thus necessary here to take the transpose of de for this product to be correct.

We thus obtain a vector de'*C which has the same number of columns as M, which leads us to change \ by /(Matrix right division), better adapted in our case.

ie

dde=(-de'*C)/M;