derivative

I am trying to do partial derivatives using sympy and I want to convert it to a function so that I can substitute values and estimate the derivatives at some values of t_1, t_2. The code I am using is as follows: import sympy as sp import numpy as np from sympy import init_printing init_printing() t_1,t_2,X_1,X_2,Y_1,Y_2,X_c1,X_c2,Y_c1,Y_c2,a_1,a_2,psi_1,psi_2,b_1,b_2= sp.symbols('t_1 t_2 X_1 X_2 Y_1 Y_2 X_c1 X_c2 Y_c1 Y_c2 a_1 a_2 psi_1 psi_2 b_1 b_2') X_1=X_c1 + (a_1 * sp.cos(t_1) * sp.cos(psi_1)) - ((b_1) * sp.sin(t_1)* sp.sin(psi_1)) X_2=X_c2 + (a_2 * sp.cos(t_2) * sp.cos(psi_2)) - ((b_2)

I'm simulating equations of motion for a (somewhat odd) system with mass-springs and double pendulum, for which I have a mass matrix and function f(x), and call ode45 to solve M*x' = f(x,t); I have 5 state variables, q= [ QDot, phi, phiDot, r, rDot]'; (removed Q because nothing depends on it, QDot is current.) Now, to calculate some forces, I would like to also save the calculated values of rDotDot, which ode45 calculates for each integration step, however ode45 doesn't give this back. I've searched around a bit, but the only two solutions I've found are to a) turn this into a 3rd order

Currently I have two numpy arrays: x and y of the same size. I would like to write a function (possibly calling numpy/scipy... functions if they exist): def derivative(x, y, n = 1): # something return result where result is a numpy array of the same size of x and containing the value of the n -th derivative of y regarding to x (I would like the derivative to be evaluated using several values of y in order to avoid non-smooth results). This is not a simple problem, but there are a lot of methods that have been devised to handle it. One simple solution is to used finite difference methods. The

I have a problem in using the apache commons math library. I just want to create functions like f(x) = 4x^2 + 2x and I want to compute the derivative of this function --> f'(x) = 8x + 2 I read the article about Differentiation ( http://commons.apache.org/proper/commons-math/userguide/analysis.html , section 4.7). There is an example which I don't understand: int params = 1; int order = 3; double xRealValue = 2.5; DerivativeStructure x = new DerivativeStructure(params, order, 0, xRealValue); DerivativeStructure y = f(x); //COMPILE ERROR System.out.println("y = " + y.getValue(); System.out