Questions tagged [python]

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

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4answers
5k views

Memory efficient implementations of partial Singular Value Decompositions (SVD)

For model reduction, I want to compute the left singular vectors associated to the - say 20 - largest singular values of a matrix $A \in \mathbb R^{N,k}$, where $N\approx 10^6$ and $k\approx 10^3$. ...
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3answers
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Are there any "light-weight" FEM packages around?

Basically, FEM seems to be a problem that is pretty much "solved". There are numerous powerful frameworks existing, like Trilinos, PETSc, FEniCS, Libmesh or MOOSE. One thing they have in common: They ...
9
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1answer
561 views

How to solve a second order differential equation (diffusion) with boundary conditions using Python

I am having trouble implementing a model from a publication. Huang, K-L.; Holsen, T.M.; Selman, J.R. Ind. Eng. Chem. Res. 2003, 42, 15, 3620–3625 scihub link: https://sci-hub.se/10.1021/ie030109q I ...
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1answer
1k views

Numerical integration for modelling curve for superconductors (Python)

I am a physicist who is trying to model the current-voltage characteristics of a superconductor-superconductor junction. The equation for this model is: \begin{align} I(V) = \frac{1}{eR_{\mathrm{n-n}...
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9answers
942 views

Do I need to learn C?

I am a PhD student in Scientific Computing and over the past few months, I spent a good amount of time learning Python and C++ the right way. I feel that I have learnt C++ well and I can use Python to ...
8
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4answers
4k views

High Order derivatives of splines using SciPy

I have created a spline to fit my data in python using: spline=scipy.interpolate.UnivariateSpline(energy, fpp, k=4) The equation I want to use involves a ...
8
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2answers
272 views

Astoundingly large difference when evaulating trigonometric identity with NumPy

According to Wolfram Alpha and the Sage computer algebra system, the following identity holds: $$ \cos\left(\arctan\left(\frac{l_1-l_2}{d}\right)\right) = \frac{1}{\sqrt{1 + \frac{(l_1-l_2)^2}{d^2}}} $...
8
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2answers
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Updatable SVD implementation in Python, C, or Fortran?

I would like to do evolving factor analysis using the SVD: Given $m \times n$ data matrix $\mathcal{A}$, and for each $i$ from 1 to $m$, I want to calculate the singular values of: $$\mathcal{A}\...
8
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3answers
644 views

Accurate Way to Calculate Matrix Powers and Matrix Exponential for Sparse Positive Semidefinite Matrices

I do need to numerically calculate the following forms for any $x\in\mathbb{R}^n$, possibly in python: $x^T M^k x$, where $M\in\mathbb{R^{n\times n}}$ is a PSD sparse matrix, $n$ can be quite large ...
8
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3answers
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random number generation from cython

I want to make my python program fast by using cython, but my inner loop is still making slow python calls to the random number generator! Several years ago this same issue was raised by someone on ...
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3answers
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What does Python offer for distributed/parallel/GPU computing?

Using the SciPy/NumPy libraries, Python is a pretty cool and performing platform for scientific computing. I just wonder: When I have to go parallel (multi-thread, multi-core, multi-node, gpu), what ...
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3answers
13k views

Python solvers for mixed-integer nonlinear constrained optimization

I want to minimize a black box function $f(x)$, which takes a 8$\times$3 matrix of non-negative integers as input. Each row specifies a variable, whereas each column specifies a certain time period so ...
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2answers
13k views

Rearrange an ordinary matrix to block diagonal form

Is there an algorithm to rearrange a matrix into block diagonal form, given that the matrix is block diagonal in nature but randomized with an unwise choice of basis? In particular, are there any ...
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2answers
7k views

Solving non-linear singular ODE with SciPy odeint / ODEPACK

I want to solve the Lane-Emden isothermal equation [PDF, eq. 15.2.9] $$\frac{d^2 \!\psi}{d \xi^2} + \frac{2}{\xi} \frac{d \psi}{d \xi} = e^{-\psi}$$ with the initial conditions $$\psi(\xi = 0) = 0 \...
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1answer
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scipy.optimize.fmin_bfgs: "Desired error not necessarily achieved due to precision loss"

I am getting the warning in the post subject when attempting to optimize a function in Python with the scipy.optimize.fmin_bfgs function. The complete output: Warning: Desired error not necessarily ...
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2answers
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Solve non-linear set of three equations using scipy

I need to solve a non-linear set of three equations using scipy. However, I do not have any clue on which algorithm is suitable for my problem from a mathematical point of view (stability, convergence ...
8
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1answer
4k views

Numerical evaluation of an elliptic integral in python

Goal: I need to evaluate numerically an integral of the following form: $$ \int_0^\infty \frac{dx}{(a^2+x)\sqrt{(a^2+x)(b^2+x)(c^2+x)}} $$ where $a,b,c \in \mathbb{R}$ are in the interval $(1,1000)$....
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3answers
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fmincg implementation in Python

I'm trying to re-implement Neural Networks in Python. I implemented the cost function and the backpropagation algorithm correctly. I have checked them by executing its Octave equivalent code. But ...
8
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2answers
456 views

Filtering a dataset to get a more uniform distribution for neural network training

I'm looking into using artificial neural networks (ANN) to predict the reaction rates in my fluid instead of solving the full system of stiff ODEs. Some people from my lab have already done some work ...
8
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1answer
2k views

Numerical solution of Geodesic differential equations with Python

I have made a solver based on the SymPy.diffgeom library, where I use Scipy.Integrate to solve the following system of second order differential equations : \begin{align} u'' &+ \Gamma^0_{00}(u')...
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1answer
400 views

How reproducible are conda environments?

I am aiming at keeping my scientific studies and analyses reproducible: I am automating them as much as possible, I am sharing them, and I sharing them together with the execution environment(s) I've ...
8
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2answers
1k views

Minimum path on known potential surface

I'm searching for the minimum path between the minima of a potential surface that is already known on a grid. (source: http://www.math.nus.edu.sg/~matrw/string/) Any point on the path is at an ...
7
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5answers
10k views

Interpolate 2D data

I generated a cartesian grid in Python using NumPy's linspace and meshgrid, and I obtained some data over this 2D grid from an ...
7
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6answers
8k views

Python implementations of Gillespie's direct method

I'm looking for a decent implementation of Gillespie's Direct Method in Python, as if I code the algorithm myself I'm nigh positive I'll do it inefficiently. Anyone have a favorite?
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3answers
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Finding the first N roots of transcendental equation

I need to find the first $n$ roots of the transcendental equation \begin{equation} F(k) = J_m'(kr)Y_m'(k)-J'_m(k)Y'_m(kr) \end{equation} for integer values of $m$ and any $r \in [0,1)$ where $J'$ ...
7
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3answers
1k views

Tanh-sinh quadrature numerical integration method converging to wrong value

I'm trying to write a Python program to use Tanh-sinh quadrature to compute the value of \begin{equation} \int_{-1}^1 \frac{dx}{\sqrt{1-x^2}} \end{equation} but although the program converges to a ...
7
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3answers
2k views

How do I reliably generate random numbers in Python distributed across multiple nodes?

Consider the following scenario: I want to perform a large Monte Carlo simulation across a compute cluster with several nodes. To avoid excessive transmission of data, I am going to generate random ...
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4answers
23k views

Plot integral function with scipy and matplotlib

I want to plot a numerical integral function of some function $f$ using scipy and matplotlib. How can I do this? I tried the ...
7
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3answers
6k views

Calculating partial trace of array in NumPy

A simulation I'm doing requires me to calculate the partial trace of a large density matrix. I am trying to calculate it using tools from numpy, but my code seems to be having some problems. For ...
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2answers
4k views

Efficiently finding all (x,y,z) points within certain distance of point P

I am using Python, and I have a Pandas dataframe with hundreds of thousands, if not millions, of $(x,y,z)$ coordinates. I am looking to find an efficient method to index the original dataframe so that ...
7
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1answer
668 views

Correct eigenfunctions of Laplace operator by Finite Differences

I am trying to compute the eigenfunctions of the Laplace operator, i.e. finding $u$ in $$ -\nabla^2 u = \lambda u .$$ For now I am trying to do this in 1D, so $$ \nabla^2 = \partial_{xx} .$$ I am ...
7
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2answers
979 views

Python package for (adaptive) function plotting

Are there any mature Python packages that can plot functions, and possibly use adaptive sampling? I am looking to pass only a function (can be a numerical black box) and a range, and expect a plot as ...
7
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2answers
3k views

How to compute the wavelet approximation of a function?

For the function $f(x)=x$, how to compute the wavelet approximation using Haar basis? I'm new to wavelet, I'm looking for a package which will do something like this ...
7
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1answer
856 views

Why does LSODA fail to integrate the logistic function?

I'm comparing some of the different ODE integrators in scipy.integrate.ode on solving the logistic function: $$x(t) = \frac{1}{1+e^{-rt}}$$ $$\dot{x} = rx(1-x)$$ ...
7
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1answer
160 views

Why Is This Python Code Faster Than Fortran Wrapper with F2PY?

I am writing a proof-of-concept implementation of Newton's method for minimizing the negative log-likelihood term in a logistic regression model. I'm comparing the performance of a native python ...
7
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2answers
5k views

FEniCS: how to specify boundary conditions on a circle inside 2D mesh

I would like to numerically find a mutual capacitance of two stripes of metal on the opposites sides of a cylinder. The problem is obviously a 2D Laplace equation. I would like to find the potential ...
7
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3answers
14k views

plotting discontinuous functions

I need help plotting the Heaviside function: Real analysis often involves constructing bizarre functions which are intuitively correct, but ultimately wrong. See the great book Counterexamples in ...
7
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1answer
7k views

Schroedinger/Diffusion equation with Crank-Nicolson in Python/SciPy

I tried to make the question as detailed as possible. I have an extremely simple solver written for the Schroedinger equation but with imaginary time, which transforms it basically into the diffusion ...
7
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1answer
173 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 ...
7
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1answer
5k views

Poisson equation with Neumann boundary conditions

I'm trying to solve the Poisson equation with pure Neumann boundary conditions, $$ \nabla^2\phi = \rho \quad in \quad \Omega\\ \mathbf{\nabla}\phi \cdot \mathbf{n} = 0 \quad on \quad \partial \Omega $$...
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3answers
10k views

Python scripting in Paraview

I've been using the basic visualization features of Paraview. Now, I want to go further by writing python macros to handle some specific tasks. My question for the advanced users: Are there any ...
7
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3answers
886 views

How to handle large numbers of output data sets from a simulation/sensitivity analysis?

Somewhat related, but I think the question is distinct enough to justify a separate question. As a bit of background, I come from a observational/statistical Epidemiology background, working with ...
7
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1answer
794 views

Python trust region optimization code that allows ellipsoid-shaped trust regions

Are there any high quality trust region optimization implementations that allow nonspherical ellipsoid trust regions, and are written in Python, or are easy to call from python? By nonspherical ...
7
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0answers
93 views

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
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0answers
192 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
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0answers
238 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, ...
6
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2answers
2k views

Matrix multiplication accuracy Matlab vs Python

I am translating some Matlab code into Python and I having some problems regarding matrix multiplication accuracy. Assuming we have following data: ...
6
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2answers
1k views

Runge-Kutta in the presence of an attractor

Suppose you are solving a system of equations numerically that possesses an attractor (no matter the initial conditions set, all the different solutions will approach a specific set of values that ...
6
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2answers
225 views

Arbitrary Precision Optimization Libraries?

Are there any well-known optimization libraries (ideally with Python bindings or even in Python) supporting (unconstrained) minimization (of $f:\mathbb{R}^n \to \mathbb{R}$ for $n$ for $n\sim 10^1,10^...
6
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3answers
886 views

What is the best way to get erfi with scipy?

I want this: http://mathworld.wolfram.com/Erfi.html But apparently scipy does not have this in its extensive special functions library. http://docs.scipy.org/doc/scipy/reference/special.html It is ...

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