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nll_ps_ouss_gradient <-
function(params, frequencies, powers, time_step, series_size){
PSexpected = ps_ouss(frequencies, power_o=params[1]^2, lambda=abs(params[2]), power_e=params[3]^2, time_step=time_step, series_size=series_size);
alpha = -1/PSexpected + powers/PSexpected^2;
LL_grad = c(0,0,0);
LL_grad[1] = alpha %*% (2*params[1] * ps_ouss_gradient_wrt_power_o(frequencies, power_o=params[1]^2, lambda=abs(params[2]), power_e=params[3]^2, time_step=time_step, series_size=series_size));
LL_grad[2] = alpha %*% (sign(params[2]) * ps_ouss_gradient_wrt_lambda(frequencies, power_o=params[1]^2, lambda=abs(params[2]), power_e=params[3]^2, time_step=time_step, series_size=series_size));
LL_grad[3] = alpha %*% (2*params[3] * ps_ouss_gradient_wrt_power_e(frequencies, power_o=params[1]^2, lambda=abs(params[2]), power_e=params[3]^2, time_step=time_step, series_size=series_size));
return(-LL_grad);
}
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