derivative

When I try to differentiate a symbol with SymPy I get the following In : x=Symbol('x') In : diff(x,x) Out: 1 When I differentiate the symbol respect to its conjugate the result is In [55]: diff(x,x.conjugate()) Out[55]: 0 However, when I try to differentiate the conjugate of the symbol SymPy doesn't do it In : diff(x.conjugate(),x) Out: Derivative(conjugate(x), x) This is still correct, but the result should be zero. How can I make SimPy perform the derivative of a conjugate? I'm not sure about the mathematics if diff(conjugate(x), x) should be zero. The fact that diff(x,x.conjugate()) gives

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 would like to evaluate higher order derivatives of some function f in R . Two possibilities are available to me. Either I determine a general expression for f (k) , the k -th derivative of f (which I can do in my particular case), and then I evaluate it; Or I take advantage of the capacities of R to perform symbolic derivative (function D() ). What are the advantages of 1 over 2? Let us say that f (k) is not a recursive formula. What if f (k) is recursive? Any hint will be appreciated. G. Grothendieck Symbolic differentiation is less error prone than doing it by hand. For low orders I would

I'm a beginner in python. I've recently learned about Sympy and its symbolic manipulation capabilities, in particular, differentiation. I am trying to do the following in the easiest way possible: Define f(x,y) = x^2 + xy^2. Differentiate f with respect to x. So f'(x,y) = 2x + xy^2. Evaluate the derivative, e.g., f'(1,1) = 2 + 1 = 3. I know how to do 1 and 2. The problem is, when I try to evaluate the derivative in step 3, I get an error that python can't calculate the derivative. Here is a minimal working example: import sympy as sym import math def f(x,y): return x**2 + x*y**2 x, y = sym

I would like to understand how the gradient and hessian of the logloss function are computed in an xgboost sample script . I've simplified the function to take numpy arrays, and generated y_hat and y_true which are a sample of the values used in the script. Here is a simplified example: import numpy as np def loglikelihoodloss(y_hat, y_true): prob = 1.0 / (1.0 + np.exp(-y_hat)) grad = prob - y_true hess = prob * (1.0 - prob) return grad, hess y_hat = np.array([1.80087972, -1.82414818, -1.82414818, 1.80087972, -2.08465433, -1.82414818, -1.82414818, 1.80087972, -1.82414818, -1.82414818]) y_true

I'm working on an algorithm to find peaks in a List object. I'd thought up what I thought was a good (or good enough) algorithm for doing this by looking at a point and it's neighbors and, if it was a peak, adding it to the results list. However, given some recent results, I don't think this method works as well as I'd initially hoped. (I've included the code I'm currently using, and hope to replace, below). I've done a little work with LabView before and I know that the way their module finds peaks/valleys works for what I need to do. I did some research into how LabView does this and found

I need help with calculating derivatives for model output wrt inputs in Keras. I want to add a regularization functional to the loss function. The regularizer contains the derivative of the classifier function. So I tried to take the derivative of model output. The model is a MLP with one hidden layer. The dataset is MNIST. When I compile the model and take the derivative, I get [None] as the result instead of the derivative function. I have seen a similar post, but didn't get answer there either: Taking derivative of Keras model wrt to inputs is returning all zeros Here is my code. Please

Is there an easy way to calculate the derivative of non-liner functions that are give by data? for example: x = 1 / c(1000:1) y = x^-1.5 ycs = cumsum(y) plot (x, ycs, log="xy") How can I calculate the derivative function from the function given by ´x´ and ´ycs´? Was also going to suggest an example of a smoothed spline fit followed by prediction of the derivative. In this case, the results are very similar to the diff calculation described by @dbaupp: spl <- smooth.spline(x, y=ycs) pred <- predict(spl) plot (x, ycs, log="xy") lines(pred, col=2) ycs.prime <- diff(ycs)/diff(x) pred.prime <-