matrix multiplication and root finding
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Mj=[cos (kj hj) i*sin(kj hj) /kj ; i*kj*sin(kj hj) cos (kj hj) ];
kj=sqrt(nj2*k02-x2);
Take n1=1.521;n2=2.66;k0=1;h1=1.5e-6;h2=1e-6
We take M=M1*M2;
Where M=( m11 m12;m21 m22) as usual in
Matrix;
How to multiply this matrix for M find the multiplication of matrix and find the value of
x;
and solve the eq
ns=1.512;
nc=1.2-i7;
gs=x2-ns2k02;
gc= x2-ns2k02;
f(x)=igsm11+gcm22)-m21+gsgcm12;
and solve the eq and value of x
采纳的回答
Vidhi Agarwal
2024-12-4
To solve the issue follow the given below steps:
- Define the matrices.
- Compute the matrix multiplication.
- Formulate the function.
- Solve the equation.
Modified code for the same is given below:
% Given values
n1 = 1.521;
n2 = 2.66;
k0 = 1;
h1 = 1.5e-6;
h2 = 1e-6;
ns = 1.512;
nc = 1.2 - 1i*7;
% Define symbolic variable for x
syms x
% Calculate k1 and k2
k1 = sqrt(n1^2 * k0^2 - x^2);
k2 = sqrt(n2^2 * k0^2 - x^2);
% Define M1 and M2 matrices
M1 = [cos(k1 * h1), 1i * sin(k1 * h1) / k1;
1i * k1 * sin(k1 * h1), cos(k1 * h1)];
M2 = [cos(k2 * h2), 1i * sin(k2 * h2) / k2;
1i * k2 * sin(k2 * h2), cos(k2 * h2)];
% Multiply matrices to get M
M = M1 * M2;
% Extract elements from M
m11 = M(1,1);
m12 = M(1,2);
m21 = M(2,1);
m22 = M(2,2);
% Define gs and gc
gs = x^2 - ns^2 * k0^2;
gc = x^2 - nc^2 * k0^2;
% Define the function f(x)
f = 1i * (gs * m11 + gc * m22) - m21 + gs * gc * m12;
% Use vpasolve for numerical solution
x_solution = vpasolve(f == 0, x);
% Display the solutions
disp('Numerical solutions for x:')
disp(x_solution)
For better understanding of basic matrix operation in MATLAB refer to the documentation https://www.mathworks.com/help/matlab/math/basic-matrix-operations.html.
Hope this helps!
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