MATLAB: How to solve 3 equations dependent each other

dependentequations

Hello. How to code this situation?

In this situation i need to calculate all angular velocities from time 0s to time 5400s with increase by 0.1s and graph them.

I have all the initial values:

wxi = 0.0065
wyi = 0.0066
wzi = 0.0067

And constant values:

NT = 3.6 * 10^-10
Jx = 2.1 * 10^-3
Jy = 2.0 * 10^-3
Jz = 1.9 * 10^-3

Actually i thought it is going to be easy but when i write the code for wx, i realized that wx is increasing with time but wz and wy in the equation are constant values. Which kind of loop should i use? Thanks for the answers!

Best Answer

Actually i thought it is going to be easy but when i write the code for wx, i realized that wx is increasing with time but wz and wy in the equation are constant values.

Just copy the value in 3 different variables, then do the calculation.

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MATLAB: Looping while changing integer

No loop needed

nu = 1 : max_nu;
roll=-0.01-0.002*nu;
pitch=0.01+0.002*nu;
yawn=0.005+0.002*nu;
Wx=0.0002+0.0001*nu;
Wy=0.0003+0.0001*nu;
Wz=0.0004+0.0001*nu;

MATLAB: How to speed up matrix operations with lots of scalar constants involved

If you have a modern Matlab version >= 2016b, use the auto expanding instead of an explicit repmat:

% Ipc = repmat(I(:,jt2),[1,npmax(jz)-1]);
Ipc = I(:,jt2);
... CnE(:,1:npmax(jz)-1,jl)) .* Ipc * dt / hb

I guess, that dt and hb are scalars (please do not let the readers guess!). Then remember, that Matlab evaluate the code from left to right:

Y = X * dt / hb

is equivalent to:

Temp = X * dt;
Y    = Temp / hb;

These are 2 matrix operations. But you can combine the scalar operations:

Y = X * (dt / hb)

This is 1 matrix operation and a cheap scalar division.

As Matt J has explained already, operating on subarrays as in |dCnE(:,2:npmax(jz)) is expensive. Better crop the data, such that you can omit the ugly indexing.

I cannot run it by my own, because you did not provide the input values, but compare it optically:

Ipc=repmat(I(:,jt2),[1,npmax(jz)-1]);
dCnE(:,2:npmax(jz))=(sigma0*CnZ(:,2:npmax(jz),jl)-sigma*CnE(:,2:npmax(jz),jl)+ ...
      vs2*sigma*CnE(:,1:npmax(jz)-1,jl)).*Ipc*dt/hb+CnB(:,2:npmax(jz),jl)*(1-exp(-dt/tau2))...
      +vs2*(beta0*CnZ(:,1:npmax(jz)-1,jl).*(Ipc.^2))*dt/(2*hb)-CnE(:,2:npmax(jz),jl)/tau1*dt;

or:

c1 = 1 - exp(-dt / tau2);   % Calculate constants outside the loops!
Ipc  = I(:,jt2);
dCnE = (sigma0 * CnZ(:, :, jl) - sigma * CnE(:, :, jl) + ...
       vs2 * sigma * CnE(:, :, jl)) .* (Ipc * (dt / hb)) + ...
       CnB(:,:,jl) * c1 + ...
       (vs2 * beta0 * dt / (2*hb)) * CnZ(:, :, jl) .* (Ipc .^ 2) - ...
       CnE(:, :, jl) / (tau1 * dt);

This can be simplified a little bit for the CnE term:

dCnE = (sigma0 * CnZ(:, :, jl) + ...
       CnE(:, :, jl)) .* (Ipc * ((vs2 * sigma - sigma) * dt / hb)) + ...
       CnB(:,:,jl) * c1 + ...
       (vs2 * beta0 * dt / (2*hb)) * CnZ(:, :, jl) .* (Ipc .^ 2) - ...
       CnE(:, :, jl) / (tau1 * dt);

Methods:

Combine the scalar operations to reduce the number of matrix operations.
Move constants out of the loop.
Crop the data outside the loops instead of applying an a:b indexing in each iteration.
Use auto-expanding instead of inflating by repmat. bsxfun is sometimes faster or slower than auto-expanding - try it.
Avoid repeated calculations. In your case e.g. Ipc(:,1)*dt/hb is computed several times. Using this avoids this:

C1 = I(:, jt2) * (dt/hb);

The latter includes another idea: You inflate I(:,jt2) at first by Ipc = repmat(...), and waste time with cropping out a subvector Ipc(:,1) later on. Better create the subvector once only: Ipc = I(:,jt2).

Finally: Replace

        non0=Cn0(:,jl);
        non0(non0<0)=0;
        Cn0(:,jl)=non0;

by:

        Cn0 = max(Cn0, 0);

and move it outside the loops, because you do not use the cleaned values inside the loop.

Best Answer

Related Solutions

MATLAB: Looping while changing integer

MATLAB: How to speed up matrix operations with lots of scalar constants involved

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