Questions tagged [python]

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

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172 views

fastest way to compute many small dot products

I have two n-by-3 blocks contiguous in memory ("n vectors of length 3") and I'd like to compute the dot product between each of the rows as fast as possible. In numpy, using ...
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192 views

Implementation of Lanczos method that returns tridiagonal matrix

The Lanczos method can be used to obtain extremal eigenpairs of sparse symmetric or hermitian matrices. I know there are several implementations of the Lanczos method (as well as Arnoldi, Davidson, ...
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129 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}\...
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462 views

Symmetric sparse direct solvers in scipy

scipy.linalg.solve, in its newer versions, has a parameter assume_a that can be used to specify that the matrix $A$ is symmetric ...
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531 views

Solving a PDE implicitly by iteration in python

Connected to this question here on Computational Science, I've posted a follow-up question on how to solve a PDE using an implicit scheme like Crank-Nicholson in general in this question on SO. But I ...
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354 views

Avoiding divergent solutions with `odeint`? shooting method

I am trying to solve an equation in Python. Basically what I want to do is to solve the equation: $$ \frac{1}{x^2}\frac{d}{dx}\left(Gam \frac{dL}{dx}\right)+L\left(\frac{a^2x^2}{Gam}-m^2\right)=0 $$ ...
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1k views

Python - calculation time derivative and laplacien by finite differences

I would like to determine a temporal derivative and a Laplacian by the finite differences method to solve the heat equation in a 1-dimensional case. My aim is to get the sources term that is why I ...
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243 views

Negative viscosity stabilized by fourth order terms

I am trying to solve a "Navier-Stokes"-type problem where the viscosity is negative. Of course this renders the equation unstable and thus I add a fourth order term, so the entire equation becomes: $$...
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54 views

Solving multiple linear regression in parallel

I am working on a problem where I need to solve approximately 500 Million Linear Regressions (OLS). What would be the most efficient way to do this (e.g. using GPU or a some framework that can do this ...
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409 views

Iteratively finding both left and right eigenvectors for non-symmetric complex matrix

I have a complex, non-Hermitian matrix $\mathbf{A}$, for which I need to find a few eigenvalues and eigenvectors in the generalised eigenvalue problem: $$\mathbf{A}\cdot \mathbf{x} = \lambda \mathbf{...
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37 views

Help with restart functionnality in sef-made GMRES solver in python

I am new to this forum and to computational science in general. I started to learn numerical liner algebra on my own and would like to code a GMRES solver in python (no preconditioner for the time ...
3
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1answer
88 views

Parameters estimation with fewer variables than parameters

I am trying to estimate parameters, 4 of them, by fitting a system of 3 ordinary differential equations. I am using a model published that was using 3 parameters and gave a good fit to the data, and I ...
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55 views

Difference between wave vector and density matrix in numerical calculation of Schrödinger equation

I solved Schrödinger equation for a following tow-level time-dependent Hamiltonian numerically in two ways: ...
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84 views

Python routine to calculate shape resonances of H2

I am currently doing a project in which my aim is to write a program that can be used to calculate single and multi-channel shape resonances. So I'm looking at bound states and quasi-bound states. ...
3
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275 views

Computing Small Eigenvalues with Sparse Symmetric Indefinite Mass Matrix

I want the eigenvalues of the following generalized eigenvalue problem: $$ Av = \lambda M v $$ where $A\in\mathbb{R}^{n\times n}$ is sparse, symmetric, and positive semi-definite $M\in\mathbb{R}^{n\...
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92 views

Inconsistency in optimize.minimize

I am trying to fit a time-dependent curve at each time step. I do so in minimizing along $x_c$ the quadratic error between the curve and a reference solution $ 1/(1 + \exp\left(\sqrt{S}(x-x_c)\right) $...
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364 views

Open source implementation of Multiscale Combinatorial Grouping

I would like to use Multiscale Combinatorial Grouping for my PhD research. However, I am restricted to use open-source implementations and this one runs on Matlab. Does anyone know of an equivalent ...
3
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97 views

How to optimize for decay constant in exponential-like function?

I've got a data set of points $M_O .. M_N$ for time points $t_0 .. t_N$, where $N$ is approximately 10-20, and the spacing of time is not uniform (i.e., $t_{i+1}-t_i$ is not constant for all i). It is ...
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2k views

Efficiently creating an adjacency matrix from a lattice in numpy

I have an $n$ by $m$ numpy array representing a rectangular lattice $L$, where each site contains a one or a zero, representing two different materials. I'm modelling heat flow across this lattice. ...
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1k views

Polynomial Fitting with Least Squares using Numpy and Scipy

I am trying to fit data to a polynomial using Python - Numpy. The points, with lines sketched above them are as in the picture. I am trying to fit those points to a polynomial of 4. or 5. degree. ...
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2k views

BFGS Fails to Converge

The model I'm working on is a multinomial logit choice model. It's a very specific dataset so other existing MNLogit libraries don't fit with my data. So basically, it's a very complex function ...
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160 views

Is there an easy way to read a PetscBag into a python dict?

I'm using a PetscBag to store the input parameters of my program. At some point, I'm going to need to use python to plot these parameters against some output parameters, and ...
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37 views

Adding a "cost term" to a linear regression, so solution values are minimized

I'm using Python's optimize.lsq_linear method to run a linear regression with the bounds set between 0% and 100% power usage. ...
2
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69 views

Errors in Integral Estimate of Gaussian using Trapezoidal Rule

I'm trying to estimate the percentage error in computing the integral of a Gaussian via composite trapezoidal rule versus via an exact formula. To do this I've generated a gaussian with mean 0, ...
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63 views

Divergence on wave equation simulation

I'm currenly working on my own PDE solver for non-linear simulations in python. I've done succesfully simulations for KdV and Fisher's equation, but now I'm playing with second order derivatives in ...
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83 views

Finding the extrema of a transition probability function for a quantum walker on a graph

The goal Implement some Python code to find the extrema points of a function that is strongly oscillating. The background Let $G$ be a connected graph with $n$ points with Laplacian matrix $L(G)$. We ...
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83 views

Numerical simulation of magnetic dipole in a inhomogeneous magnetic field

Goal: I want to use Python to illustrate how a magnetic dipole with magnetic moment m2 moves in a non-homogeneous magnetic field in a 2D-Plane. This field is generated by another magnetic dipole with ...
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110 views

Understanding Illumination Optimisation Problem

I am a newbie to convex optimisation and I am learning with the aid of CVXPY. I am requesting for clarity on the illumination problem as described in Boyd & Vandenberghe lecture 1 slides here. I ...
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1answer
79 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 ...
2
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1answer
178 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'...
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47 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, ...
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296 views

Heisenberg Model python : Specific heat capacity for spin 2

I have the correct plot for specific heat capacity when I am using the formula which is $C_V$ = differentiation of entropy with respect to temperature. However, When I try to calculate $C_V$, by using ...
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101 views

Efficient algorithm to determine the intersection volume of simple convex polyhedra

TLDR: Is there an efficient algorithm to compute the intersection of polyhedra with 8 or fewer vertices? I have two sets of FEM meshes for one geometry (one exhibiting a skin effect). I have to ...
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349 views

Showing date in Paraview's Annotate Time Filter

I have a time dependent data set where each frame corresponds to a certain date. I need to show the time annotation, much like what Annotate Time Filter does, but show the date instead of time as a ...
2
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126 views

2D reaction-diffusion system simulation

I am a complete beginner in numerical simulation and I am pretty lost about how to tackle this problem. I have been trying for some time to find the steady state (or simulate), the following system ...
2
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268 views

Finding integer/lattice points (coordinates) inside a polytope/polyhedra?

I am using Python but I wouldn't mind changing language. All I have gotten from my research are tools to count the number of (lattice) points inside a region given the equations for the planes that ...
2
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0answers
131 views

Precision not improving by decreasing step-size in nonlinear Schrödinger

I tried to simulate soliton propagation by solving the nonlinear Schrödinger equation using the split-step Fourier method. The following is an example of the Matlab code copied from a textbook. ...
2
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192 views

Optimizing for loops by using Einstein summations instead

I have some Python code containing a couple of for loops, which I would like to optimize by using low-level functions. My first approach is to use ...
2
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0answers
271 views

minimalistic library for classical molecular mechanics force-field in C/C++/Python

I would like some classical molecular mechanics forcefield library or super-simple program which does not have any external dependences, so that I can plug it into my software without worry of "...
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2k views

Using RK2 Method to solve the simple harmonic oscillator of a horizontal mass on a spring (1D)

Being new to numerical analysis techniques, in particular RK2, I decided the best way to jump in is by using python to solve the well known mass-spring oscillator using RK2 techniques. My problem is ...
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0answers
302 views

How to reuse permutation-orderings within scipy's SuperLU-wrapper?

i'm solving sparse linear equations within scipy 0.18 which internally resorts to SuperLU (after umfpack got removed due to license-issues). Current, i'm doing a complete re-factorization in each ...
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0answers
124 views

Clustering similar words and mapping to numbers in Python

I'm familiar with kmeans to cluster data points, but not text.. So I have one column of words in cvs format, which I want to cluster those which have similar word or more, and then mapping those ...
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227 views

Very long running time for Haase and Muller (2014) coded in Python + Gurobi

I have read the paper of Haase and Muller (2014) where they present the linear reformulations of the multinomial logit choice probabilities and compare different approaches. I have tried for an ...
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248 views

scipy.linalg.sparse.eigsh does not work for generalised eigenvalues

I asked this question over at StackOverflow and someone told me that I'd get a better answer here. So here's my problem: I'm working on a machine learning project which involves doing a Principal ...
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0answers
176 views

Is it worth switching to timesteppers provided by PETSc if I can't write down a Jacobian for my problem? Case study with "the amoeba" toy problem

I am considering using petsc4py instead of scipy.integrate.odeint (which is a wrapper for Fortran solvers) for a problem ...
2
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0answers
458 views

Solving constrained BVP, singular Jacobian

The boundary value problem is $$ \begin{cases} \dot{x}_i = \begin{cases} (0.5D^{-1}\psi)_i, \text{ if }(0.5D^{-1}\psi)_i \le 0 \\ 0 \text{, otherwise} \end{cases} \\ \dot{\psi} = 2\Sigma x \\ x(0) =...
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349 views

Adaptive Finite Element Method - Laplace

I'm currently attempting to turn my code for solving the laplace equation using finite element approximations into an adaptive one using the dual weighted residual as my error estimator: i.e. my ...
2
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0answers
461 views

Return derivative vector from odeint scipy function

I have the following function that I want to implement in scipy.integrate.odeint ...
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0answers
784 views

Solving a system of 4 coupled PDEs representing variable diffusivity

I have four partial differential equations representing mass conservation of two compressible fluid phases (marked by subscripts $p1$ and $p2$) in two different continuum media (marked by subscripts $...
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770 views

Precession of Mercury Python simulation

I was trying to simulate the precession of Mercury based on the perturbed solution: $$\frac{1}{r}=\frac{m}{B^{2}}(1+e\cos\phi+3\frac{m^{2}}{B^{2}}(1+e\phi \sin\phi +e^{2}(\frac{1}{2}-\frac{1}{6}\cos2\...