Using dlarray with betarnd/randg (2024)

function [Z, U1, U2] = forward_pass(alpha, beta)

% Generate uniform random variables

U1 = rand();

U2 = rand();

% Generate Gamma(alpha, 1) and Gamma(beta, 1) using the inverse CDF (ppf)

X = gaminv(U1, alpha, 1);

Y = gaminv(U2, beta, 1);

% Combine to get Beta(alpha, beta)

Z = X / (X + Y);

end

function [dZ_dalpha, dZ_dbeta] = backward_pass(alpha, beta, U1, U2, grad_gaminv)

% Differentiate gaminv with respect to the shape parameter alpha and beta

dX_dalpha = grad_gaminv(U1, alpha);

dY_dbeta = grad_gaminv(U2, beta);

% Compute partial derivatives of Z with respect to X and Y

X = gaminv(U1, alpha, 1);

Y = gaminv(U2, beta, 1);

dZ_dX = Y / (X + Y)^2;

dZ_dY = -X / (X + Y)^2;

% Use the chain rule to compute gradients with respect to alpha and beta

dZ_dalpha = dZ_dX * dX_dalpha;

dZ_dbeta = dZ_dY * dY_dbeta;

end

function grad = grad_gaminv(U, shape)

% Placeholder for the actual derivative computation of gaminv with respect to the shape parameter

% Here we use a numerical approximation for demonstration

delta = 1e-6;

grad = (gaminv(U, shape + delta, 1) - gaminv(U, shape, 1)) / delta;

end