Questions tagged [python]

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

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172 views

How to solve the integral-like energy equation with Sagdeev potential numerically in Python?

I am trying to numerically solve equation (6) of Lakhina 2021 in Python. The equation is $$\frac{1}{2}\left(\frac{d \phi}{d\xi}\right)^2 + S(\phi, M) = 0\, .$$ The Sagdeev potential expression is ...
3
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3answers
231 views

Convolute a gaussian kernel with a large array of off-grid centroids without looping? (how to make "A Thousand (Gaussian) Points of Light" )

For a finite object size diffraction simulator, I need to generate arrays which are the sum of thousands of instances of a Gaussian (or other) 2D kernel at centroids that will not fall in any ...
3
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2answers
2k views

Scipy OdeInt solver with Neumann boundary conditions

I'm using scipy.odeint to solve Fisher-Kolmogorov equation: \begin{equation} u_t = u_{xx}+u(1-u) \end{equation} The code can be found here. From Ablowitz and ...
3
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1answer
237 views

High frequency noise at solving diffusion equation

I'm trying to simulate a simple diffusion based on Fick's 2nd law. ...
3
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2answers
102 views

Compute $tr(A^TBC)$ in Python

I have to compute the trace of the product between three matrices $A,B,C$ in python, i.e. I have to compute $tr(A^TBC)$ and I was wondering what was a good way to do it in Python(here $A^T$ is the ...
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 ...
3
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2answers
193 views

Optimization of known function with respect to two unknown function arguments

I have a data set, composed of points $(x_i, y_i)$ for $i=1,N$. I also have a known function $F$, which maps these points $x_i$ to $y_i$ as such $F(x_i, a(x_i),b(x_i)) = y_i$, where $a(x_i)$ and $b(...
3
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2answers
2k views

Applying the result of Cuthill-McKee in SciPy

I have applied SciPy's implementation of the Cuthill-McKee algorithm to a $48 \times 48$ sparse non-symmetric matrix in Compressed Sparse Row (CSR) format and the output is an array of length $48$ ...
3
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3answers
5k views

Runge-Kutta Simulation For Projectile Motion With Drag

I am attempting to simulate projectile flight with drag. However, with a timestep of 0.1 seconds, I am consistently getting an error of ~0.1-1%. ...
3
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3answers
3k views

Caculating the mean of vector accurately

I am having trouble with calculating a mean of vector with sufficient accuracy. My current solution which works but it quite slow and has unpredictable performance: mean_sum = mean = math.fsum(values)...
3
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1answer
2k views

Numerical derivative in python

I am trying to take the numerical derivative of a dataset. My first attempt was to use the gradient function from numpy but in that case the graph of the derivative ...
3
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2answers
505 views

How to include penalty in a Objective Function with Python? GEKKO

I'm trying to include a "great M" penalty in my objective function. I want use the entry x vector values as entry values in a function. A fixed maximum value is took initially for the returned value ...
3
votes
1answer
394 views

Get the roots of a Hermite interpolating polynomial

I am using Python 3.7 to write a program that requires me to calculate the root of the Hermite interpolating polynomial, given two points $\epsilon_0$, $\epsilon_1$, the function ($d(\epsilon_0)$,$d(\...
3
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1answer
7k views

Python Vectorizing a Function Returning an Array

I have the following function that has been vectorized so that for every element in input array t, an array is output: ...
3
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2answers
285 views

How to separate text from the paper on a black and white page?

I tried to discretize an image into black and white and came into some difficult. The difference between the letters and paper is pretty clear to our eyes: However a simple thresholding trick doesn'...
3
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2answers
2k views

Hyperbolic Equation PDE (Python)

I'm trying to solve the following first order hyperbolic PDE problem using method of lines: Hyperbolic Equation: $u_t = -u_x$ with initial condition: $u(0,x) = 0, 0 < x < 1$ boundary condition: ...
3
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1answer
105 views

Lanczos algorithm for finding top eigenvalues of a matrix sum

I am trying to find the top k leading eigenvalues of a NumPy matrix (using python dot product notation) L@L + a*X@X.T, where $L$ ...
3
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1answer
430 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 ...
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 ...
3
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2answers
269 views

Solving ODE with "Jumpy" Coefficients

I'm numerically solving a linear coupled ODE of the form $$y^{\prime}(t) = \hat{M}(t)y(t)=\left[\begin{array}{cc}0& A(t)\\ B(t)& 0\end{array}\right]y(t),$$ and the difficulty I'm running into ...
3
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2answers
331 views

Chebyshev differentiation via FFT with a domain [a,b]

I want to ask something about Chebyshev differentiation via FFT, which can be used to obtain with spectral accuracy the derivative of a smooth function. See for instance this code in python, which ...
3
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1answer
1k views

How to transform this SOCP to the format required by cvxopt

I'm new to SOCP and want to try to get familiar with the format and how to solve it with cvxopt in python. However, for a simple toy example I'm struggling to get ...
3
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2answers
3k views

Small errors accumulate while solving ODE of motion

I'm trying to solve the ODE of motion: $$ \begin{align} x''=&\ -myu \frac{x}{r^3} \left(1+\frac{3}{2} {J_2} \left(\frac{{r_{\text{eq}}}}{r}\right)^2 \left(1-\frac{5z^2}{r^2}\right)\right) \\ ...
3
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1answer
1k views

Why am I not seeing faster neural network training after upgrading to a vastly better GPU?

I was previously running my neural networks using the Lasagne library to build and train neural networks in Theano on an NVIDIA GTX 750 Ti. I'm using a genetic algorithm to tune the hyperparameters of ...
3
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1answer
1k views

How can I solve wave equation for circular membrane in polar coordinates?

The original equation is $$\frac{1}{c^2} \frac{\partial^2 u}{\partial t^2} = \frac{\partial^2 u}{\partial r^2} + \frac{1}{r}\frac{\partial u}{\partial r} + \frac{1}{r^2}\frac{\partial^2 u}{\partial \...
3
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3answers
2k views

Averaging scattered data

I have multiple sets of measured data that can easily be visualized using a scatter plot (red and black points in the figure). If my measurements were perfect, the red and black points should lie on a ...
3
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1answer
144 views

How to get a more accurate cancelation

I shall try to get to the point, so let me know if there is something left and you need more details. I am solving a couple of equations that are not coupled explicitly, but their corresponding ...
3
votes
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: ...
3
votes
1answer
917 views

Is this the correct way for solving coupled 1d PDEs using finite difference methods?

I am trying to solve the following coupled PDEs: $$C_e\frac{\partial u(x,t)}{\partial t} = k_{ed}\frac{\partial^2u(x,t)}{\partial^2x} - G_{el}(u(x,t) - v(x,t)) + S(x,t)$$ $$C_l\frac{\partial v(x,t)...
3
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1answer
2k views

Applying Neumann boundaries to Crank-Nicolson solution in python

Consider the heat equation $$u_t = \kappa u_{xx}$$ with boundary conditions of $$u(x,0)=0\\ u(0,t)=100\\ u(l,t)=0$$ Numerical analysis by pyton can be done with ...
3
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1answer
443 views

Software for triangulating a point set (with restrictions)

I want to triangulate a point-set like the one below. I would like the triangulation of the point-set to have the following properties The triangles must have as vertices the black and orange points ...
3
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1answer
1k views

Solve log equations problem [SageMath]

Input var('x') solve((log((x**2 - x), 6) - log((6*x - 10), 6) == 0), x) Output [log(x^2 - x) == log(6*x - 10)] But real ...
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 ...
3
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1answer
521 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 ...
3
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1answer
3k views

Efficient ways to numerically evaluate matrix exponentials

What are some computationally efficient ways to solve matrix exponentials, i.e. functions of the form : $f(X)=e^{X}$, where $X$ is a square matrix? So far I have been able to diagonalise some ...
3
votes
1answer
757 views

Calculation of Mean Square Displacement for Brownian dynamics system with Lennard Jones interactions in python3

I have a problem getting a sensible result for the Mean Square Displacement (MSD) for a simulation of $N$ particles under Brownian dynamics with Lennard-Jones interaction between them with or without ...
3
votes
1answer
193 views

Calculate Transformation Matrix between two sensors

My question is if I can calculate the transformation matrix between two sensors. Each sensor provides a $4\times 4$ matrix for every timestep recorded. The sensors are moving and have some noise in ...
3
votes
1answer
138 views

Weighted QR Implementation

Say I want a QR decomposition of matrix $A$, where orthogonality of $Q$ is with respect to a generic non-degenerate positive-definite bilinear form $\phi$ (in my case, $\phi$ is "defined" by a finite-...
3
votes
1answer
201 views

Whitening transformation does NOT return a unit covariance matrix

For this question, I am using the following Wiki definition of Matrix whitening: Suppose $X$ is a random (column) vector with non-singular covariance matrix $\Sigma$ and mean 0. Then the ...
3
votes
1answer
884 views

Golub-Kahan-Lanczos Bidiagonalization Procedure implementation doesn't produce bidiagonal matrix

I'm trying to implement the aforementioned procedure using this website as a reference. At the end of the page the algorithm is described as follows: I think I've mapped the given algorithm to code ...
3
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1answer
61 views

why am I not getting a staircase for the rotation number?

I'm trying to understand the staircase map. Look at this map from the circle to itself: $$ x \stackrel{F}{\mapsto} \big[\omega + x + \tfrac{\epsilon}{2\pi} \sin (2\pi x) \big] \pmod 1 $$ Such a map ...
3
votes
1answer
13k views

2D Ising Model in Python

I am trying to calculate the energy, magnetization and specific heat of a two dimensional lattice using the metropolis monte carlo algorithm. ...
3
votes
1answer
391 views

Translating a nuclear norm constraint to an LMI constraint

I'm attempting to solve a convex optimization problem where one of the constraints is $$\|M\|_* \leq a$$ where $\|M\|_*$ denotes the nuclear norm of matrix $M$. I'm using CVXOPT in Python to solve ...
3
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2answers
686 views

Python environments for AMG and Gauss Seidel as solvers instead of preconditioners

I am working on block preconditioning and seemingly it is common to write customised Krylov solvers for them. Within each solver, the individual block linear system with preconditioners are ...
3
votes
1answer
655 views

Simple Runge-Kutta Scheme for nonlinear PDE

I am new to this community as well as to scientific programming. I programmed a simple 4th order Runge-Kutta for the 1-D Cahn-Hilliard Equation for some first simple calculations on pattern forming ...
3
votes
1answer
792 views

My calculated laser pulse duration is too large. Where am I wrong?

I am currently writing a small Python script to estimate the pulse duration from the optical spectrum. At the end, the idea is to observe the effects of the spectral phase on the pulse duration and ...
3
votes
1answer
3k views

Solving Advection (Convection) - Diffusion - Reaction Partial Differential Equation in Python

I am looking for library written in Python which will enable me to solve the coupled nonlinear equations which looks like: I need the library which will enable me to couple this solver to other ...
3
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2answers
1k views

Finding eigenvalues of a complex symmetric tridiagonal matrix

I am trying to find specific eigenvalues and -vectors of a large complex symmetric tridiagonal matrix (at least 10000x10000, and ideally larger). I know roughly which eigenvalues I am looking for, so ...
3
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2answers
2k views

How to plot orbit of binary star and calculate its orbital elements?

I have a set of dates, position angles ($\theta$) and angular separations ($\rho$) for visual binary star. For example: ...
3
votes
1answer
309 views

Calculating Error for Poisson Equation using Successive Over-Relaxation technique, Python

I am trying to solve the Poisson Equation $\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 32(x(x-1) + y(y-1))$ for a 61x61 grid using Python3 with boundary conditions being $T=...

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