Algorithms that integrate functions over one or more dimensions using approximation techniques, instead of exact, closed-form solutions using symbolic algebra and calculus. Includes concepts like adaptive quadrature, Monte-Carlo methods, finite element analysis, Markov chains.
In the script below, in the for loop for calculating the double integrations, I keep receiving an error, and I'm unsure why:
Error using *
Inner matrix dimensions must agree.
Error in @(t,p)-sin(t)*(G(:,1)*cos(p)+H(:,1)*sin(p))
Error in…
I'm new to C++ and I'm trying to write/edit a code that integrates numerically a function using the trapezoidal rule. This works fine as long as I only pass the name of the function. However, if I pass the function with two parameters this obviously…
I have rather lengthy system of equations saved in a function file, system3. I need one of the parameters in this system to change dependant on time. I have created a second function, calculate_a1, that produces a vector of the parameter a1 at each…
Is there a way to write the outputs of t and x of this example to a txt file instead of the console. Thanks!
This is the example I copied from Odeint website.
#include
#include
using namespace std;
using…
I'm attempting to implement a Trapezoidal rule that utilizes previous function evaluations in order to avoid redundant computation. Two things: a) computed results are not converging and I'm a little unsure of why. I'll post of the mathematics…
I'm writing a test tomorrow and I'm contemplating doing everything on Matlab, to save time.
Some questions require numerical integration of datapoints (points, not necessarily functions).
E.g.
C=[0 1 5 8 10 8 6 4 3 2.2 1.5 0.6 0];
I've used…
I'm trying to find the area under a curve in the region both above the x-axis (from y = 0 to +inf) and below the x-axis, (y = 0 to -inf), separately.
As far as I can figure out, I can use
int = trapz(x,y)
to get the area under the curve, but not as…
from scipy.integrate import quad
from math import sqrt
f = lambda x, a: a**2 * x # here a is a constant.
F = lambda x, a: quad(f, 0, x, args=(a,))[0]
rho = 5
I need to compute the integral of
1/sqrt(F(rho,a)-F(s,a)),
s is from 0 (lower limit) to…
I am trying to calculate the area under each peak in a graph that I plotted with a set of x and y co-ordinates,
I don't have a function for (x,y), and so I haven't been able to find an appropriate method to do the same.
the co-ordinates are
{
[10…
Here is a snippet of my code.
from scipy.integrate import quad
from numpy import exp, log, inf
def f(x):
return log(log(x))/(x*log(x**2))
val, err = quad(f, exp(), exp(2))
val
I know the code is structured correctly but I cannot format the…
I have to integrate with respect to E, with it's lower and upper limits as the first value of my log10(E) column that I'm printing for each source and upper limit as the last value of the same column.
My function is: fo E^-spectralindexexp(-tau1),…
I have some problems with plot. Exatlct solution here is true, but eulerbmethod gives the same curve, but much lower
import numpy as np
import matplotlib.pyplot as plt
# Define parameters
f = lambda x, y: 2*x
h = 0.1
x = np.arange(-10, 10, h)
x0 =…
It could be a simple question. I am trying to understand numerical integration in Matlab. For a unit circle,
fun = @(x) sqrt(cosd(x).^2+sind(x).^2);
q = integral(fun,0,360);
The answer is 360.0000, whereas I expect it to be 2*pi. Note that the…
In Gauss-legendre integration we need to find zeros of the legendre function but i can't find a way to write code that enable me to do that?
I understand there are list of "xi"s out there by which this function equals to zero but can we write…
