numerical-integration

I'm struggling with using scipy.integrate, I used tplquad, but how can I used integrate to get the volume of (truncated)sphere? Thanks import scipy from scipy.integrate import quad, dblquad, tplquad from math import* from numpy import * R = 0.025235 #radius theta0 = acos(0.023895) #the angle from the edge of truncated plane to the center of sphere def f_1(phi,theta,r): return r**2*sin(theta)*phi**0 Volume = tplquad(f_1, 0.0,R, lambda y: theta0, lambda y: pi, lambda y,z: 0.0,lambda y,z: 2*pi) print Volume To truncate by angle it is convenient to use a spherical coordinate systems. Assuming the

Is it possible to do triple integration in R without using the cubature package? based on the answer in this post InnerFunc = function(x) { x + 0.805 } InnerIntegral = function(y) { sapply(y, function(z) { integrate(InnerFunc, 15, z)$value }) } integrate(InnerIntegral , 15, 50) 16826.4 with absolute error < 1.9e-10 For example, to code this triple integral : I tried InnerMostFunc = function(v) { v + y^2 } InnerMostIntegral = function(w) { sapply(w, function(x) { integrate(InnerMostFunc, 1, 2)$value }) } InnerIntegral = function(y) { sapply(y, function(z){integrate(InnerMostIntegral, 1, 2)

I'm trying to implement the trapezoidal rule in Python 2.7.2. I've written the following function: def trapezoidal(f, a, b, n): h = float(b - a) / n s = 0.0 s += h * f(a) for i in range(1, n): s += 2.0 * h * f(a + i*h) s += h * f(b) return s However, f(lambda x:x**2, 5, 10, 100) returns 583.333 (it's supposed to return 291.667), so clearly there is something wrong with my script. I can't spot it though. You are off by a factor of two. Indeed, the Trapezoidal Rule as taught in math class would use an increment like s += h * (f(a + i*h) + f(a + (i-1)*h))/2.0 (f(a + i*h) + f(a + (i-1)*h))/2.0 is

I have started to work through this book ( Computational Physics Exercise 5.4 ) and its exercises and I got stuck with the following question: Write a Python function J(m,x) that calculates the value of Jm(x) using Simpson’s rule with N = 1000 points. Use your function in a program to make a plot, on a single graph, of the Bessel functions J0, J1, and J2 as a function of x from x = 0 to x = 20. I have created the following code to evaluate the first part of the question but not sure if even this is correct: def f(x, t): return 1 / pi * (math.cos(x - t * math.sin(x))) def float_range(a, b, c):