Help with vector function

Question

Anton Ivanov 2023-12-10

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评论： Walter Roberson 2024-8-7

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

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Walter Roberson 2024-8-7

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

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Answer 1

Shlok 2024-8-7

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在 MATLAB Online 中打开

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