Evaluate matrix equation at multiple timesteps

How can I evaluate a matrix equation at multiple timesteps? I've defined the following:

R=[1 0.5; 0.5 1];
M0=[1;1];
u0=[1;0];
x=linspace(0,1,100)
f=@(x) expm(-R.*x)*(u0-M0) + M0;
y=feval(f,x);

However, this gives an error as x is the 'wrong size' for matrix multiplication. However, I don't want to do matrix multiplication, but instead evaluate f at every value of x.

[Stephen23]

Even if x is a scalar, your code produces multiple y values:

>> x = 1;
>> expm(-R.*x)*(u0-M0)
ans = 
   0.19170
  -0.41483

Is this correct? Or do you expect one y value for each x value?

[Mark]

I expect two y values for each x value. That's correct. I just want that to be repeated for each x value (effectively x is a series of timesteps and I want to evaluate this at time step). I'm not sure what the best way to do that is in matlab. I could write a for loop etc. but that seems unnecessarily complicated.

Answer 1

[Stephan]

Hi,

try:

R=[1 0.5; 0.5 1];
M0=[1;1];
u0=[1;0];
x=repmat(linspace(0,1,100),2,1);
y = zeros(2,size(x,2));
f=@(x) expm(-R.*x)*(u0-M0) + M0;

for k = 1:size(x,2)
    y(:,k)=f(x(:,k));
end

plot(x(1,:),y(1,:),x(1,:),y(2,:))

result it:

Due to the matrix multiplication, i used a for loop. I think bsxfun should also be possible to do this.

Best regards

Stephan