Questions tagged [python]

A general purpose high-level programming language that emphasizes ease of code syntax and readability.

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1answer
2k views

Solving Lotka-Volterra Equations on Python

I'm trying to plot Lotka-Volterra Equations using Python. I am a real beginner when it comes to Python. I have these two equations: $$\frac{dR}{dt}=\alpha R-\gamma RF$$ and $$\frac{dF}{dt}=-\beta F+\...
2
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1answer
137 views

Why is $1/r^2$ force law giving spiral trajectory?

I have written a program to solve for Newton's 2nd Law of motion for a given force law, in 2D polar coordinates. It is known that if the force law is of the form $k/r^2$,we get conic sections as ...
0
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1answer
296 views

How to use cumtrapz correctly?

I have tried to do a trapeze integration with f(x)=x^2, where I know how the antiderivative looks like, so F(x) = (1/3)x^3 Here's my code, just like I tried: ...
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0answers
164 views

Plotting a Magnetic Field in Spherical Coordinates in Python

I am modeling a Helmholtz Coil as two dipoles from far away and I want to plot the magnetic field. $$\mathbf{B}(\mathbf{r}) = \frac{\mu_0 |\mathbf{m}|}{4\pi r^3}\left(2\cos\theta\,\hat{\mathbf{r}} + \...
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3answers
167 views

I wrote a 2D Finite Element program for Axial Loaded Plates, but the results are unexpected

TLDR: I used Python to write a 2D Finite Element program using 'Constant Strain Triangles' and my beam keeps pointing slightly upwards instead of straight sideways (like the force). I'm new to FEA and ...
0
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0answers
133 views

scipy's solve_ivp returns erroneous results for a stiff differential equation

I'm using scipy's solve_ivp for solving a stiff differential equation. I'm using method BDF for solving the same. I have already used MATLAB's ode23s and I'm getting correct results in MATLAB. However,...
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0answers
149 views

A parallelized GMRES solver?

My application calls for solving a dense, 40,000 x 40,000, ill-conditioned linear system. The native SciPy GMRES solver with preconditioning has worked well for my application and solving a single ...
3
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1answer
46 views

Ising NiO model energy

I am simulating Ising model for NiO. I have simulated for 2d,3d,triangular lattices, and have tried to do the same with NiO model. There are papers which say that the ground state energy is around -...
0
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1answer
335 views

Norm constraint in CVXPY

I'm trying to implement the algorithm outlined in https://arxiv.org/abs/1211.5608 on a small scale. I have a linear operator $\mathcal{A}$ which is defined as $$\text{trace}(A^*_l(hm^*))$$ where $$A_l ...
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0answers
33 views

Comparing custom linear regression solver to SciPy equivalent in Python

From a given data set, I set out to complete a task which is below Fit the data of the previous exercise to fit Eq. (8.18) using the SciPy function ...
2
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1answer
76 views

Question regarding the energy computation of the Ising-Spin Model

In most of the Monte-Carlo-Algorithms I studied, I found, at the place where they compute the energy, always a line of code, where they divided by four. For example, this code-snippet is taken from ...
3
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1answer
431 views

Why is 'scipy.sparse.linalg.spilu' less efficient than 'scipy.linalg.lu' for sparse matrix?

I have a matrix B which is sparse and try to utilize a function scipy.sparse.linalg.spilu specialized for sparse matrix to ...
5
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1answer
168 views

Algorithm to factorize matrix whose many rows are already of upper triangular form?

I have a matrix whose many rows are already in the upper triangular form. $$\begin{bmatrix} x_{11} & x_{12} & x_{13} & x_{14} & x_{5} \\ 0 & x_{22} & x_{23} & x_{...
3
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2answers
873 views

Computing numeric derivative via FFT - SciPy

I wrote the following code to compute the approximate derivative of a function using FFT: ...
3
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1answer
301 views

Fast nonzero indices per row/column for (sparse) 2D numpy array

I am looking for the fastest way to obtain a list of the nonzero indices of a 2D array per row and per column. The following is a working piece of code: ...
2
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1answer
91 views

Determining the voxels between two boundary surfaces

Issue description I am working on human brain tACS simulations where I have the models of the skin, skull, csf, brain and ventricles in STL format. The shape does not matter and there are no ...
3
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1answer
1k views

Getting a list of coordinate points of a Cartesian grid in Python

I have a regular three dimensional Cartesian Grid with numpy.linspace(a1,an,na), numpy.linspace(b1,bn,nb), numpy.linspace(c1,cn,nc) along their respective ...
5
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0answers
131 views

How to numerically evaluate this double Integral?

I want to evaluate the following integral: $$\int_{0}^{60} \ \left(\int_{0}^{2z} 0.5\cdot t \left(\mathrm{erf}(t-a) -1 \right)J_{0}(qt)\mathrm{d}t \right)^2 \mathrm{exp}\left(-\frac{(z-a)^2}{2s^2}\...
1
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1answer
146 views

Composite matrices in Numpy

Lets say I have four matrices A, B, C and D, and I want to combine them together into one new matrix for computation: $$ \left( \begin{matrix} A & B\\ C & D \end{matrix}\right) $$ How can I ...
3
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1answer
151 views

Suggestions for scientific computing projects to undertake to sharpen core skills

Currently I am completing all exercises in books like "Introduction to Python for Science and Engineering, David Pine" and "Guid to Scientific Computing in C++, Pitt-Francis, Whitley". I am looking ...
0
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1answer
36 views

How to implement tolerance checking within a for loop whilst performing a numerical integration using a trapezoidal function?

Currently, I have this working code where I have been able to successfully calculate the integration for standard results. But in terms of precision, how could I achieve a good tolerance? ...
1
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1answer
68 views

Newman algorithm yielding different result to what is given in his paper

Summary I am trying to implement Newman's algorithm for community detection, outlined in this paper. I am testing my implementation against one of the datasets used in that paper to benchmark the ...
1
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1answer
264 views

Solving an ODE using odeint in Python and continuing the integration

The following relates to the linked question: Scattering of waves in a symmetrical potential (using python) I have attempted to solve the problem for $U(r)$ using ...
0
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1answer
159 views

How to change the value of a variable at some point lying in the time interval of solver in solve_ivp

The following code solves a differential equation with scipy: ...
2
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1answer
649 views

How can I evaluate more accurate energy eigenvalues from Schrodinger equation using shooting method?

I am trying to use the "shooting method" for solving Schrodinger's equation for a reasonably arbitrary potential in 1D. But the eigenvalues so evaluated in the case of potentials that do not have hard ...
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1answer
22 views

Python: Getting second output variable from minimizing a computationally intensive function on first outputs

I have a function in python that is quite computationally expensive to evaluate, of the form: ...
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1answer
666 views

solve_ivp - Overflow encountered in double_scalars

I'm modeling an electron that orbits the nucleus. Of course, charged particles radiate away there energy so it'll crash into the nucleus. My approach has been to to evaluate the coulomb force and add ...
2
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1answer
288 views

How to implement Simpson's rule for double integral (without numeric limits of first integral)

I want to use Simpson's rule to evaluate the following double integral: $$\int_{a}^{b}\left|\int_{0}^{z}x\cdot \mathrm{erf}(x-10)\cdot J_{0}(x) \mathrm{dx}\right|^{2}\exp(-0.5*(z-40)^2)\mathrm{dz} $$ ...
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0answers
58 views

Scipy.integrate.odeint is returning curves with almost the same frequency for different damping ratios, shouldn't they be different?

I am trying to solve the ODE for a harmonic oscillator using Scipy's odeint solver for different dampening factors. I'm using the following code, based off of this example: ...
2
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1answer
376 views

Coding of the Legendre polynomial and the infinite sum using python

I'm looking to code the following function: $$|g(\theta)=\frac{1}{2k}\sum_{\ell=0}^{\infty} (2\ell +1)\sin(2\delta_{\ell})P_{\ell}\cos(\theta)|^2$$ ...
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2answers
77 views

Distributed computation with computers around me

I know for large amounts of data there are online computation services or supercomputers or Beowulf cluster. For a small quantity of data, a good computer is enough. But sometimes, for medium qty of ...
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0answers
414 views

Using Spherical Bessel Functions in Python

My question relates to using spherical Bessel functions in Python. If my ODE contains a spherical Bessel function of the form $$j_\ell(tx)$$ and similarly $$y_\ell(tx)$$ for given values of $t$ and $...
1
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1answer
199 views

Translating the Euler code in scipy's solve_ivp

My code is based on the similarity transformation X=VZ.I simulate the model for transformed equations involving Z by replacing ...
0
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0answers
372 views

Solving nonlinear pendulum using Runge-Kutta 4 for smaller steps

I am trying to solve nonlinear pendulum using 4th order Runge-Kutta method for limits between a=0.0 to b=110 seconds and simulated the results to observe the pendulum movement. But when I increase the ...
2
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1answer
265 views

Numerical calculation of Wannier function in optical lattice

I am working out some optical lattice band structures (example here). I have no issue with setting up the eigenvalue equation: $$ H_{jj'}c_{j'}=Ec_{j'} $$ Where $H$ is the tri-diagonal matrix that ...
2
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1answer
107 views

Best way to convert a sparse (containing zeros) covariance matrix into a correlation matrix?

I have a $100$x$100$ covariance matrix that looks like this. Some rows/cols are all-zero because those corresponding elements are not present in the sample from which covariance is calculated. I'm ...
2
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1answer
869 views

Vectorised second order ode solving in python

I am trying to write a python program that simulates the motion of a large number of particles by numerically integrating a second order ordinary differential equation. I first split the ODE into two ...
3
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2answers
176 views

Solving a Boundary Value Question $\frac{d^2y}{dx^2}=y\cos(x)+\frac{\sin(x)}{x^2+2}$ using Python

I'm looking to solve this boundary value question using the shooting method! $$\frac{d^2y}{dx^2}=y\cos(x)+\frac{\sin(x)}{x^2+2}$$ given the initial values: $$y'(x=-1)=-1\\y'(x=5)=0$$ I'm aware of ...
2
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1answer
186 views

Double Integral with Gauss- Hermite for one component

I am trying to perform the following integral $$\int_{0}^{2\pi}\int_{0}^{+\infty} \frac{r'\left(e^{-r'^2/2\sigma^2}\right)\left(r-r'\cos(\theta-\theta')\right)}{r^2+r'^2-2rr'\cos(\theta-\theta')}dr'...
-1
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1answer
171 views

Plot of a function involving an integral and value changing parameters [closed]

I'm trying to plot the cross section with respect to the photon energy $h\nu$ but for $\gamma = 1.0, 1.2, 2.0 $ in the same axes $\sigma = \left[\left(\frac{\xi_{eff}}{\xi_{0}}\right)^2 \frac{n_r}{\...
3
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1answer
522 views

Setting up optimization problem in GEKKO

I have the following dynamical system, $\frac{d \phi}{dt} = -M^TDM\phi \tag{1}\label{1}$ $\frac{d \hat\phi}{dt} = -M^T\tilde{D}M\hat \phi \tag{2} \label{2}$ $\eqref{1}$ represents the exact ...
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2answers
250 views

Convolution in Python

I have an integral of a convolution between two functions. How can I calculate this in Python? It is a continuum convolution.
-1
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1answer
141 views

Numpys `tensordot` and what is happening mathematically

I've encountered a program where np.tensordot was used, so I tried looking it up but I can't really understand what this function is doing... I feel rather ...
7
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1answer
165 views

Numerically stable and fast sum of last K elements in sequence

Suppose I have a long, possibly infinite, sequence $x := [x_1, x_2, ...]$, and I want to use it to compute another sequence $y:=[y_1, y_2, ...]$ where each element is the sum of the last K elements of ...
0
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1answer
122 views

Is this behaviour normal for a Lennard-Jones monte carlo simulation?

I am simulating a Lennard-Jones fluid using MC simulation. The code always uses a reduced unit. I want to find the potential energy of the system. Periodic boundary condition implemented. I have ...
-1
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1answer
112 views

How to get free energy surface of a 3d Ising Spin system using Monte Carlo simulation?

I am doing a Monte Carlo Simulation of the properties of a 3D Ising Spin system. I want to get the free energy surface of the spin system from the simulation. It is a magnetization vs free energy ...
0
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0answers
116 views

2D diffusion equation using Finite Volume Method

i am working on an assignment problem: Consider a two-dimensional rectangular plate of dimension L = 1 m in the x direction and H = 2 m in the y direction. The plate material has constant thermal ...
0
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1answer
192 views

Why the magnetisation shows abrupt behaviour for this 3D ising spin system

I am trying to simulate a 3D Ising spin system (+1 & -1) using Monte Carlo Metropolis Algorithm. I want to get different physical quantities from this simulation like magnetization, Average Energy,...
2
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0answers
55 views

Lexicographically order matrix into a vector

I am trying to implement the algorithm contained in this article here. It is about solving a 2 and 2.5D Fredholm integral, focused on bidimensional NMR experiments. I've made significant progress, ...
4
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1answer
287 views

Absence of Discontinuity in Specific Heat Plot Simulated by Ising Model

I am working on 2D Ising model, when I plot "specific heat vs temperature", I can't see any discontinuity at critical temperature around Tc ~ 2.7K. I am enclosing results of all other thermodynamic ...

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