Questions tagged [python]

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

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Can we sparse solve a few eigenvalues specified by index range?

I need to solve a few eigenvalues of a large sparse matrix specified by their index range. These indices are according to the whole eigenspectrum sorted in algebraic (not absolute value) ascending ...
7 votes
0 answers
299 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 ...
7 votes
0 answers
289 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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5 votes
0 answers
68 views

How to troubleshoot numerical instability using finite difference for steady-state non-linear heat conduction equation

I have a problem which I believe is numerical instability when trying to solve a heat conduction equation using finite difference. The short version is that when the parameter $I=80.3$ I get the blue ...
5 votes
0 answers
200 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}\...
5 votes
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686 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 ...
5 votes
0 answers
421 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: $$ \frac{1}{x^2}\frac{d}{dx}\left(Gam \frac{dL}{dx}\right)+L\left(\frac{a^2x^2}{Gam}-m^2\right)=0 $$ ...
5 votes
0 answers
466 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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5 votes
0 answers
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 ...
5 votes
0 answers
252 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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4 votes
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131 views

How amenable is this 2D Frenkel–Kontorova-like energy minimization problem in Python to the use of a modest PC + GPU? (Heavy reliance on indexing)

@Richard's answer to Going to try to move some of my scipy/numpy calculation to a new GPU, how to avoid disappointing results? is quite helpful, and as promised I've added a simple running example ...
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4 votes
0 answers
49 views

Pass forward intermediate results during iterative optimization

To investigate a counter-current flow heat exchanger while considering temperature dependent physical properties (such as specific heat $c_\textrm{p,i}$, heat conductivity $\lambda_\textrm{i}$, ...
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4 votes
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78 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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4 votes
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673 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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4 votes
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419 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 votes
0 answers
307 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 votes
0 answers
90 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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3 votes
0 answers
123 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 votes
0 answers
371 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\...
3 votes
0 answers
98 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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3 votes
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105 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 ...
3 votes
0 answers
206 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 ...
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3 votes
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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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3 votes
0 answers
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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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3 votes
0 answers
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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3 votes
0 answers
164 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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2 votes
1 answer
70 views

Spurious oscillations in solving diffusion problems using finite elements

I've been struggling with this problem for a while so I hope someone can help me here. I'm trying to solve the McNabb-Foster equations for hydrogen diffusion in metals using a simple 1D finite element ...
2 votes
0 answers
89 views

Numerical solution to integro-differential equation

The time dynamics of an atom interacting with a reservoir of spectral density $J(\omega)$ are obtained by solving the following integro-differential equation: $$ \frac{\mathrm{d}c(t)}{\mathrm{d}t} = - ...
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2 votes
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62 views

Numerical solution to the Tolman-Oppenheimer-Volkoff equations for any equation of state (numerical or analytical)

I've been working on a code to solve the Tolman-Oppenheimer-Volkoff (TOV) equations for a while and recently I've got it right but only for one specific equation of state, the bag model, which is not ...
2 votes
0 answers
65 views

How to solve the following SDP with cvxpy in Python?

The SDP problem is $$ \min_{Z \in S^{n},Y \in S^{m}} {\rm trace}(Z) +{\rm trace}(Y)\\ {\rm s.t.} \begin{bmatrix} Y & X\\ X^T & Z \end{bmatrix} \succeq 0\\ X \in C $$ Where $C$ is a convex set....
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2 votes
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149 views

How can I reduce the artifact in "Thin Plate Spline" interpolation?

At the Top "right", there is the 2D-density plot of the recorded data (actual), fewer in number. Recorded data has been sampled a on the 8 arms of a regular octagon. These 8 arms are placed ...
2 votes
0 answers
111 views

Numerical instability in the inverse Laplace transform

I have a problem with Laplace inversion and my function is not numerically stable for the Laplace inverse, but I do not understand the cause of this problem. Here is my code and graph of this problem. ...
2 votes
0 answers
106 views

solve Ax=b for outrigger A matrix python

I implement Crank-Nicolson 2D finite-difference method. I get a matrix A which is banded with 1 band above and below the main diagonal, but also contains 2 additional bands , further apart from the ...
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2 votes
0 answers
68 views

Cyipopt fails to converge for NLP problem which fmincon() can solve

I'm currently trying to implement a python script for solving a constrained nonlinear optimization problem with ~800 variables and 2 constraints, one linear and one nonlinear. There already exists a ...
2 votes
0 answers
70 views

Efficient way of calculating a cumulative integral with prefactor

I have a grid of points $x_i$ and corresponding function values $y_i=f(x_i)$. I'm interesting in something like the cumulant of $f$, but it has an awkward prefactor. The desired quantity we'll call $$...
2 votes
0 answers
315 views

How to write a simple finite element solver in python in order to solve Poisson equation in 2D

I would like to write a simple finite element solver in python in order to solve 2D Poisson equation and then visualize it. $$ -\nabla^{2} u(x,y)=f(x,y), \quad x,y \quad in \quad \Omega\\ u(x,y) = u_D ...
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2 votes
0 answers
107 views

Split Operator 2D-->3D

I am trying to modify my simulations on population dynamics using the split-operator method from 2D two-level real Hamiltonain $$H_{2D} =T(x,y)\otimes1_2 +\begin{pmatrix} -z & y\\ y & z\\ \...
2 votes
1 answer
160 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. ...
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2 votes
0 answers
289 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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2 votes
0 answers
89 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 ...
2 votes
0 answers
85 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 ...
2 votes
0 answers
205 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 ...
2 votes
0 answers
126 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 ...
2 votes
1 answer
135 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 ...
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2 votes
1 answer
306 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 ...
2 votes
1 answer
272 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'...
2 votes
0 answers
142 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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2 votes
0 answers
387 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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2 votes
0 answers
134 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 ...
2 votes
0 answers
2k views

Solve system of polynomial equations with Python

I have 5 at most 4th order polynomials in 5 variables, $$p_i(x_1,x_2,x_3,x_4,x_5) \qquad i = 1, \ldots, 5$$ where all coefficients are either rational or floating point. I'd would like to get the ...