How can I create this function?

I need help writing a function that will carry out the following:

y(x) = Bj*Cj(x)*aj

where Cj = diag[exp(im*k*x),exp(-im*k*x)]

Bj and aj are not dependent on x

How can I write code for this in MATLAB?

Answer 1

[CARLOS RIASCOS]

I did this for you, I hope it serves you.

    % Definition of constants:
    k=2; 
    Bj=[1 2; 3 4]; %In this case Bj is a matrix of size 2x2,
                   %of real numbers,you can modify this.
    aj=[1; 1];     %In this case aj is a vectorof size 2x1,
                   %of real numbers,you can modify this.

    %This is the definition of your function:
    Y=@(x)(Bj*diag([exp(k*x(1)*1i),exp(-k*x(2)*1i)])*aj);

    %To test, if x is a constant, define the vector only with
    % that constant(expl: x = 5, so here you define x = [5 5]); if x is
    %a vector of variables, you define it as it is here in the code:
    x=[1 2];

    Y=Y(x);
    disp(Y) %Check the value in Command Window.

[Amanda Lococo]

Thank you! Is there a way I can use one specific value of Y(x) in a formula? For example, Bj and aj are also functions so I have written this so far, but a (when j is not 0) needs to be equal to inv(Cj(x))*inv(Bj)*T*B(1)*a(1). When I display B(1) it gives me back a value of one, which isn't right so I'm not sure how to code it.

for j = 1:layers
    B = @(j)([1 1; im*Z(j,1) -im*Z(j,1)]);
    B = B(j);
    C = @(j)([exp(im*k(j,1)*x(j,1)) 0; 0 exp(-im*k(j,1)*x(j,1))]);
    C = C(j);

      if j == 1
          a = @(j)(inv(B)*V(:,1));
          a = a(j);
      else
          a = inv(C)*inv(B)*T*      %this is where I need to add

Answer 2

[CARLOS RIASCOS]

This code should return in the variables: B_mtrx_a, C_mtrx_a, a_; a "history" of calculations of matrix B, C and vector a. Observe the command window to show the calculations for each iteration of the for loop.

    clear all

    im=1i; %Imaginary part

    % You should modify these variables:
    Z = [1;2];  
    k = [1;2];
    X = [1;2];
    V = ones(2);
    T = ones(2);
    %  Definition of the functions:
    B = @(x)([1 1; im*Z(x,1) -im*Z(x,1)]);
    C = @(x)([exp(im*k(x,1)*X(x,1)) 0; 0 exp(-im*k(x,1)*X(x,1))]);

    layers = 2;
    %pre-allocation, to save the history of calculations.
    B_mtrx_a = [];
    C_mtrx_a = [];
    a_a = [];

    for j = 1:layers

    B_mtrx = B(j); C_mtrx = C(j);
    disp('B:')
    disp(B_mtrx)
    disp('C:')
    disp(C_mtrx)

    B_mtrx_a = [B_mtrx_a B(j)];
    C_mtrx_a = [C_mtrx_a C(j)];

    if j == 1
      a = inv(B_mtrx)*V(:,1);
      a_a = [a_a a];
      alfa = B_mtrx; beta = a; %You save the specific
                               %values in auxiliary variables.
    else
      a = inv(C_mtrx)*inv(B_mtrx)*T*alfa*beta;  
      a_a = [a_a a];
    end
     disp('a:')
    disp(a)
    end

[Amanda Lococo]

Awesome! Thanks again!