hessian-matrix

I need to create the Hessian matrix of a function given as: func <- expression(sin(x+y)+cos(x-y)) vars <- c("x", "y") I need the second order derivatives as expressions too, and I need to evaluate them lot of times, so I made a list of first order derivatives, and a list of list of second order derivatives. funcD <- lapply(vars, function(v) D(func, v)) funcDD <- list(); for (i in 1:length(vars)) funcDD[[i]] <- lapply(vars, function(v) D(funcD[[i]], v)) So far, it works. > funcDD [[1]] [[1]][[1]] -(sin(x + y) + cos(x - y)) [[1]][[2]] -(sin(x + y) - cos(x - y)) [[2]] [[2]][[1]] cos(x - y) - sin

I observed something strange while fitting an ARMA model using the function arma{tseries} and arima{stats} in R. There is a radical difference in the estimation procedures adopted by the two functions, Kalman filter in arima{stats} as opposed to ML estimation in arma{tseries}. Given the difference in the estimation procedures between the two functions, one would not expect the results to be radically different for the two function if we use the same timeseries. Well seems that they can! Generate the below timeseries and add 2 outliers. set.seed(1010) ts.sim <- abs(arima.sim(list(order = c(1,0

I have a set of simulation data where I would like to find the lowest slope in n dimensions. The spacing of the data is constant along each dimension, but not all the same (I could change that for the sake of simplicity). I can live with some numerical inaccuracy, especially towards the edges. I would heavily prefer not to generate a spline and use that derivative; just on the raw values would be sufficient. It is possible to calculate the first derivative with numpy using the numpy.gradient() function. import numpy as np data = np.random.rand(30,50,40,20) first_derivative = np.gradient(data)

Computing Hessian in tensorflow is quite easy: x = tf.Variable([1., 1., 1.], dtype=tf.float32, name="x") f = (x[0] + x[1] ** 2 + x[0] * x[1] + x[2]) ** 2 hessian = tf.hessians(f, x) This correctly returns [[ 8., 20., 4.], [20., 34., 6.], [ 4., 6., 2.]] In my real case instead of using one single variable x holding three values, I need to split it in two variables: x (holding the first two) and y (holding the last one). x = tf.Variable([1., 1.], dtype=tf.float32, name="x") y = tf.Variable([1.], dtype=tf.float32, name="y") f = (x[0] + x[1] ** 2 + x[0] * x[1] + y) ** 2 I tried a naive hessian =