Error Using * (inner matrix dimensions must agree)

I need to multiply 2 vectors x(:,1) and x(:,4) that are the solutions of an ode45 I previously used, but I get this error. I understand the reason but I can't find a solution to make it work... Below is my script:

clear
clc
close all

%%%dedomena
AU=15000; %kJ/(hm^2)
k0=5E+10; %1/h
ER=9020; %K
dh1=-92.820; %%%kJ/kmol
dh2=-424.2;
dh3=-241.0;
cp1=125; %%%kJ/(kmol*K)
cp2=250;
cp3=75;
d1=14.384; %%%kJ/m^3
d2=13.668;
d3=55.382;
Tref=298; %K

options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4 1e-5 1e-5]);
[t,x]=ode45(@rigid1,[0 120],[10 0 20 333],options);
subplot(3,2,1)
plot(t,x(:,1),'-',t,x(:,2),'-.',t,x(:,3),'.')
title('Molarities')

V=x(:,1)/d1+x(:,2)/d2+x(:,3)/d3;
subplot(3,2,2)
plot(V,'g-')
title('Volume')

CA=x(:,1)/V(:,1);
subplot(3,2,3)
plot(CA(:,1),'b.')
title('C_A')

r=(k0)*exp(-ER/x(:,4))*x(:,1);
subplot(3,2,5)
plot(r,'b-')
title('r')

subplot(3,2,6)
plot(t,x(:,4),'r-.')
title('Temperature')

H=x(:,1)*(dh1+cp1*(x(:,4)-Tref))+x(:,2)*(dh2+cp2*(x(:,4)-Tref))+x(:,3)*(dh3+cp3*(x(:,4)-Tref));
subplot(2,2,4)
plot(H,'r-')
title('Enthalpy H')

And the function w/ the DEs:

function dx=rigid(t,x)
k0= 5e+10;
ER=9020;
dh1=-92.820; %%%kJ/kmol
dh2=-424.2;
dh3=-241.0;
cp1=125; %%%kJ/(kmol*K)
cp2=250;
cp3=75;
Tref=298; %K

dx=zeros(4,1);
dx(1)=-k0*exp(-ER/x(4))*x(1);
dx(2)=k0*exp(-ER/x(4))*x(1);
dx(3)=-k0*exp(-ER/x(4))*x(1);
dx(4)=k0*exp(-ER/x(4))*x(1)*(-dh1+dh2-dh3+cp1-cp2+cp3+x(4)*(cp1+cp2+cp3))/(-cp1*x(1)-cp2*x(2)-cp3*x(3));

The error shows in the main script in H. r doesn't seem to give me a result either though...

Any suggestions are welcome. Thanks :)

Answer 1

[Star Strider]

I’m not certain exactly what you’re doing, but you probably need to be using element-wise ‘dot’ operators. For your vector multiplication:

xp = x(:,1) .* x(:,4);

and for element-wise division here:

CA=x(:,1)./V(:,1);

See the documentation for Array vs. Matrix Operations for all the goodies.

[Peter P]

Hey thanks a lot! That actually made it work :)

Here are the changes I made

H=x(:,1).*(dh1+cp1.*(x(:,4)-Tref))+x(:,2).*(dh2+cp2.*(x(:,4)-Tref))+x(:,3).*(dh3+cp3.*(x(:,4)-Tref));
subplot(3,2,4)
plot(H,'r-')
title('Enthalpy H')

r=(k0)*exp(-ER./x(:,4)).*x(:,1);
subplot(3,2,5)
plot(r,'b-')
title('r')

Also FYI these are equations from energy and mass balance in a reactor.

[Star Strider]

My pleasure!

Thank you for the context. I recognised them as chemical kinetics equations, but not beyond that (undergraduate Chemistry major, but no ChemE experience).