Help with vector function

Hello! I'm new to mathlab. I'm not familiar with vector expressions much. I have a function to calculate the angles of my model using the iteration method. I need to rewrite it in the form of vectors. There are elements in the function that change dynamically (each iteration) - these are w and epsbeta. And they must be taken into account to calculate the angles (alpha and beta). I will be very grateful for your help. Here is the function that needs to be converted and the function from which epsbeta is taken.

function result = time_interval(funct, w0, w_const, one_iter, sum_time, iner_moment, alpha, beta, matrix)
    alpha = pi * alpha / 180;
    beta = pi * beta / 180;
    result = [];
    w = w0;
    for i = 1:sum_time / one_iter
        epsbeta = grad_find(1 + alpha * 180 / pi - 119 * fix(alpha * 180 / pi / 119) , 1 + beta * 180 / pi - 119 * fix(beta * 180 / pi / 119), matrix, funct) / iner_moment;
        w = w + epsbeta * one_iter;
        beta = beta + w * one_iter;
        alpha = alpha + w_const * one_iter;
        result = [result; sin(alpha), sin(beta)];
    end
end
function gradient_ = grad_find(alpha, beta, matrix, funct)
    x_value = alpha;
    y_vector = 1:size(matrix, 1);
    % Используем функцию gradient для вычисления производной по y
    dy_vector = gradient(funct(x_value, y_vector), y_vector);
    % Находим значение производной в точке beta
    gradient_ = interp1(y_vector, dy_vector, beta);
end

[Walter Roberson]

To vectorize this code successfully, funct would have to be able to operate in a vectorized manner.

Answer 1

[Shlok]

Hi,

I understand that you are trying to vectorise the code given above. In order to do this, you should follow the following steps:

• First determine which calculations can be done without relying on previous results.
• Make sure to compute constants and fixed values ahead of time using vectors, and store intermediate results to eliminate repetitive computations.
• Also, try to make use of various built-in functions available in MATLAB, such as 'cumsum' and 'arrayfun' for efficient array-based operations.

Here is the updated code:

function result = time_interval_vectorized2(funct, w0, w_const, one_iter, sum_time, iner_moment, alpha, beta, matrix) 
    alpha = pi * alpha / 180; 
    beta = pi * beta / 180; 
    
    num_steps = floor(sum_time / one_iter); 
    t_vector = (0:num_steps - 1) * one_iter;
    
    % Initialize vectors 
    alpha_vec = alpha + w_const * t_vector; 
    beta_vec = zeros(1, num_steps); 
    beta_vec(1) = beta; 
    
    w = w0; 
    
    % Compute modified angles for all steps 
    alpha_mod = 1 + alpha_vec * 180 / pi - 119 * fix(alpha_vec * 180 / pi / 119); 
    
    % Precompute epsbeta for each step 
    epsbeta_vec = arrayfun(@(i) grad_find(alpha_mod(i), 1 + beta_vec(i) * 180 / pi - 119 * fix(beta_vec(i) * 180 / pi / 119), matrix, funct) / iner_moment, 1:num_steps); 
    
    % Compute angular velocities for all steps 
    w_vec = w0 + cumsum(epsbeta_vec * one_iter); 
    
    % Compute beta values using cumulative sums 
    beta_vec(2:end) = beta + cumsum(w_vec(1:end-1) * one_iter); 
    
    % Compute result using vector operations 
    result = [sin(alpha_vec') sin(beta_vec')]; 
end 

Note that, in this case, results will be produced with an offset of one index, because we initialised the first element of ‘alpha_vec’ and ‘beta_vec’ with the base value.

To know more about vectorisation, you can refer to the following documentation link:

https://www.mathworks.com/help/releases/R2023a/matlab/matlab_prog/vectorization.html