vectorized operations on symbolic functions
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Hi, Can we apply vectorized operations on symbolic functions to avoid loops?
syms x1 x2 x3; % symbolic variables
y = x1^3/3 + x2^2/2 - x3; % symbolic function y
X = rand(500,3) % each row representing a combination of x1 x2 x3
I used for loop, but it is taking more time.
y_values = zeros(size(X,1))
for ii = 1:size(X,1)
y_values(ii) = subs(y, [x1, x2, x3], X(ii,:));
end
I have tried following but since there is inconsistency between sizes of old and new it don't work for me.
y_values = subs(y, [x1, x2, x3], X); % Evaluate the function for all combinations in matrix X
Thanks
采纳的回答
syms x1 x2 x3; % symbolic variables
y = x1^3/3 + x2^2/2 - x3; % symbolic function y
% Generate a random matrix X with 500 rows and 3 columns
X = rand(500, 3); % each row representing a combination of x1 x2 x3
% Evaluate the symbolic function y for each row in X
% Convert the matrix X to a cell array where each row is a separate cell
X_cell = num2cell(X, 2);
% Use cellfun to apply the subs function to each cell (row) of X_cell
y_values = cellfun(@(row) subs(y, [x1, x2, x3], row), X_cell);
% Convert y_values to a double array if needed
y_values = double(y_values);
disp(y_values(1:10))
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2 个评论
Muhammad Uzair
2024-2-19
Dyuman Joshi
2024-4-21
Note that using num2cell and subsequently cellfun is not efficient.
更多回答（5 个）
syms x1 x2 x3; % symbolic variables
y = x1^3/3 + x2^2/2 - x3; % symbolic function y
X = rand(500,3); % each row representing a combination of x1 x2 x3
ynum=matlabFunction(y) %convert to a numeric function
yvalues=ynum(X(:,1),X(:,2),X(:,3))
Better to use a function handle -
x = rand(500,3);
y = @(x) x(:,1).^3/3 + x(:,2).^2/2 - x(:,3);
out1 = y(x)
For more information, refer to these documentation pages -
2 个评论
Muhammad Uzair
2024-2-19
Your best approach then might be to make your input variables have the individual pages already as a third dimension:
x = randn(3, 1, 500);
y = randn(1, 6, 500);
z = x.*y;
size(z)
The formula here is of course completely made up, it would depend on what your formula for this 3x6 matrix is.
Yet another method, you can define your symbolic parameter as a matrix symbolic
n = 500;
X = sym('X', [500 3]);
% I assume here you want a element wise power ('.^') instead of matrix power
y = X(:,1).^3/3 + X(:,2).^2/2 - X(:,3); % symbolic function y
X_val = rand(500,3); % each row representing a combination of x1 x2 x3
y_values = double(subs(y, X, X_val)) % Evaluate the function for all combinations in matrix X
size(y_values)
syms x1 x2 x3; % symbolic variables
y = x1^3/3 + x2^2/2 - x3; % symbolic function y
X = rand(500,3); % each row representing a combination of x1 x2 x3
y_values = double(subs(y, {x1, x2, x3}, {X(:,1), X(:,2), X(:,3)}));
y_values(1:5)
rng("default")
syms x1 x2 x3; % symbolic variables
y = x1^3/3 + x2^2/2 - x3; % symbolic function y
X = rand(500,3) % each row representing a combination of x1 x2 x3
y_values = arrayfun(@(i)double(subs(y,[x1,x2,x3],[X(i,1),X(i,2),X(i,3)])),1:size(X,1))
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