Questions tagged [numpy]

NumPy is the fundamental package for scientific computing with Python.

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61 views

First and second component of fft for circle approximation to periodic curve

I wanted to understand how the fast fourier transform work in numpy and for this I tried apply it on $n$ points of an ellipse $t_k = \frac{2\pi}{n-1}k$ with $k=1...n$ $$f_k = f(t_k) = (acos(t_k), bsin(...
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1 answer
83 views

Solving a polynomial with NumPy

I'm trying to do something that I thought would be very straightforward but somehow I'm struggling. I have a time series and I want to extrapolate it, assuming a linear trend, to forecast when will it ...
10 votes
1 answer
330 views

Is it possible to express an arbitrary tensor contraction in terms of BLAS routines?

I noticed that libraries like numpy and pytorch are able to perform arbitrary tensor contractions at speeds similar to comparably sized matrix multiplications. This leads me to believe that underneath ...
5 votes
2 answers
2k views

What algorithm(s) do numpy and scipy use to calculate matrix inverses?

I am solving differential equations that require inverting dense square matrices, and I wanted to know what algorithm(s) do numpy and scipy use to calculate matrix inverses?
1 vote
1 answer
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Improvement to naive gradient descent implementation for the Thomson problem

I have a Python program (available on github) that uses naive gradient descent to find approximate solutions to the Thomson Problem. It works surprisingly well, but I've been wondering if there's a ...
3 votes
0 answers
222 views

Helmholtz decomposition of a vector field in Fourier space with Python

I have a 3D vector field and I want to extract its divergence-free part (also called transverse component), using the Helmholtz decomposition. In principle, this can be done in the Fourier space, as ...
1 vote
1 answer
486 views

Float equality tolerance for single and half precision

Suppose the metric is abs(a-b) <= rtol * max(abs(a), abs(b)) i.e. math.isclose with ...
0 votes
1 answer
241 views

Specifying mesh spacing for DFT in numpy

I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...
11 votes
5 answers
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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1 answer
75 views

Compute a series of matrix multiplications and matrix norms quickly in Python

I need to compute a series of matrix multiplications involving 3x3 matrices and a series of matrix norms also involving 3x3 matrices and I wonder how I can set these computations up with numpy such ...
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100 views

About Convolution Theorem

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3 votes
1 answer
678 views

Time and memory required to diagonalize a 18000 by 18000 matrix using numpy in python

Can someone give an estimate of the Time and memory required to diagonalize a 20000 by 20000 complex hermitian matrix using numpy in python ?
1 vote
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117 views

Convolution/weighted average of two arrays in Python

I have an equation that I need to calculate numerically, but I am having doubts about my approach. I am cross-posting this question from Stack Exchange, because I am not getting any responses. This is ...
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58 views

Eigenvalues of same operator expressed in two different orthonormal basis are coming out different

I have an operator $H$. I express $H$ as a matrix in the orthonormalized $\{ |e > \}$ basis. Then I diagonalize it to obtain eigenvalues, let's say for example $H$ is $6 \times 6$ and the ...
1 vote
1 answer
636 views

Beta function and integral value

I have two values $a$ and $b$ where $a \ge 0$ and $b \ge 0$ and I have to calculate the formula below. $$ \frac{1}{2}\int_0^1\text{abs}\left[\left( \frac{p_i^{(a - 1)} \times (1 - p_i)^{(b - 1)}}{\...
0 votes
1 answer
112 views

How to convert from a non traditional CSV-style content (file with JSON data but its extension is .CSV) to a traditional CSV-style with Python?

CSV (even though once opened it does not contain a traditional CSV format I think it contains JSON data)[![1], when I try to open it as a TXT file I got this as shown in the first screenshot. When I ...
0 votes
1 answer
237 views

Find two lines around which points were randomly generated

Given a list of points that were randomly generated around two lines, find two new lines that match the original lines as closely as possible. Here's the function definition: ...
0 votes
1 answer
113 views

Planes in n-dimensional space

This is not a homework, but a hobby project, and maybe not all terms I use are correct - please help to fix. Imagine there are K vectors in n-dimensional space. I would like to: validate whether they ...
2 votes
0 answers
101 views

How to save multiplication computation time between a dense vector and a not that sparse matrix?

I am trying to compute $\mathbf{X}\mathbf{u}$ for many times in my algorithm, where $\mathbf{X}\in \mathbb{R}^{n\times m}$ and $\mathbf{u} \in \mathbb{R}^{m}$. The problem is that, during the ...
8 votes
3 answers
20k 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 ...
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0 answers
101 views

Advance a Interpolation

Note; No special knowledge of Pykrige is needed to answer the question, as I already mention examples in the question! Hi I would like to use Universal Kriging in my code. For this I have data that ...
2 votes
0 answers
450 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 ...
-1 votes
1 answer
157 views

Fitting gauss-hermite-parametrization to data?

I want to fit this data. I have the following model functions. Classic gaussian: def gauss_model(x, mu, sigma): return np.exp(-0.5*((x-mu)/sigma)**2) And ...
5 votes
1 answer
2k views

Rational functions in Python

I would like use Python to verify the following identities: $ \frac{1}{1-z} = 1 + z + z^2 + z^3 + \dots $ $ \frac{1}{1-z - z^2} = 1 + z + 2z^2 + 3z^3 + \dots $ $ q \prod_{n \geq 1} (1 - q^n)^{24} = ...
4 votes
0 answers
176 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 ...
1 vote
1 answer
75 views

Why does this implementation for Eisenstein integer pairs of Euclid's method for finding greatest common denominators get stuck for this one point?

My Math SE question determining if a coincident point in a pair of rotated hexagonal lattices is closest to the origin? explains the problem I have. I won't reproduce the whole thing in detail here, ...
5 votes
1 answer
841 views

Stochastic SIR using SDEint python package

I want to use the SDEint package to give a numerical solution (plot) of the following stochastic SIR model. Namely, a system of SDEs. $$\begin{cases} dS = -\beta SIdt - \sigma SIdW \\ dI = (\beta SI -...
4 votes
1 answer
538 views

Going to try to move some of my scipy/numpy calculation to a new GPU, how to avoid disappointing results?

update: I've refactored the question based on helpful advice in the linked meta. I'm a heavy user of Python's NumPy and SciPy (and not much else) and for years I could run anything I need on my laptop....
1 vote
0 answers
353 views

Trouble inverting complex matrix with numpy and scipy

I have some matrix-valued, complex data $Z(f)$ with $f\in\{f_0,f_1,\dots\}$ and $Z(f_i)$ being a 3x3 matrix. I require the inverse $Z^{-1}(f)$ in my workflow. After encountering some problems with my ...
5 votes
0 answers
122 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 ...
2 votes
2 answers
293 views

Calculate determinant of unitary matrices based on SVD implementation

I have a real square matrix $X$ which I need to perform a Singular Value Decomposition on. Now, performing the operation $$ X = USV^T $$ as $U$ and $V$ are orthogonal, we know that $\det(X)=\pm\det(S)$...
14 votes
1 answer
2k views

Fast Automatic Differentiation for numpy?

I would like to use automatic differentiation to calculate gradients to function written in numpy. I've come across a number of packages, including autograd tangent chainer But none of them seem ...
0 votes
2 answers
758 views

Is it possible to partition 2D data into bins such that each bin contains the same number of samples?

I am trying to sort data following a bivariate distribution into a numpy histogramdd, where each bin should contain the same number of data points (to the nearest whole sample). I expect that some ...
2 votes
1 answer
3k views

solve_ivp from scipy does not integrate the whole range of tspan

I'm trying to use solve_ivp from scipy in Python to solve an IVP. I specified the tspan ...
0 votes
2 answers
133 views

Implementation of $[X, \cdot]$ as an $n^2 \times n^2$ matrix, where $X$ is an $n \times n$ matrix

Let $M_n(\mathbb{R})$ denote the set of $n\times n$ matrices with real entries. I have an $n\times n$ matrix $X\in M_n(\mathbb{R})$, and I would like to implement the linear operator $[X, \cdot] : M_n(...
0 votes
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141 views

Getting euclidean distance between vector A and C without anyway of retrieving them when their distances with a common vector B is known

Motivation: My plan is to get the overall euclidean distance matrix for all the vectors in N number of dataset. Each dataset is basically an array of n-dimensional points. For e.g: A dataset can be ...
0 votes
0 answers
120 views

Plotting the motion of a positive charge in a cylindrically symmetric magnetic field

I want to plot the motion of a positive charge in a cylindrically symmetric magnetic field. I am assuming a cylinder around the z-axis, with the magnetic field going in clockwise direction. The B-...
1 vote
1 answer
1k views

Reason behind different outputs for Fast Fourier Transform in Numpy and Matlab

Here is the output of Numpy np.fft.ifft([0, 4, 0, 0]) array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j]) # may vary Here is the output of Matlab ...
5 votes
0 answers
186 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 ...
-1 votes
1 answer
634 views

Using ODE to plot particle-motion with scipy.integrate.solve_ivp

My Problem: A positively charged particle (mass = 2 * 10-27 kg) is moving along the x-axis. It is travelling in a homogenous magnetic field such that the field axis in z-direction. The energy of the ...
-2 votes
2 answers
221 views

numerical solution for differential equation

I have these 3 equations and i want to solve them with numerical methods. so I am using scipy library but I don't know how to solve 3 equations together. R, g, sigma and density are constants. \begin{...
3 votes
1 answer
208 views

Forming a particular (averaged) block matrix with numpy

Say I have a set of $n \times n$ matrices $A_1, ..., A_m$ as numpy arrays. I'd like to create the block matrix defined below. I'm looking for a clean, elegant, and easy-to-interpret way of doing this ...
1 vote
1 answer
272 views

How do I find the portion of a cell/voxel lying within a defined surface?

We have a 3-dimensional grid of voxels (or cells), with individual voxels being of volume $dx\,dy\,dz$ where $dx=dy=dz=1$. A cone-like surface is defined by some function, $z = f(x, y)$, which in ...
3 votes
1 answer
369 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*[email protected], where $L$ ...
0 votes
2 answers
95 views

Validating that a code is a good spherical code

Apologies if this is a trivial question. If that is the case I imagine I would benefit from someone explaining where my understanding is lacking. I am having some trouble interpreting the (putatively ...
-1 votes
1 answer
326 views

illegal use of ODEINT

given the following system: $$\frac{dP}{dt} = \alpha P(1-\frac{P}{K}) - \beta P I$$ $$\frac{dI}{dt} = \beta P I - \rho I$$ how do I solve the system numerically. as when I attempt to solve this is the ...
3 votes
0 answers
143 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: ...
0 votes
1 answer
5k views

Saving Data in Multiple Columns with np.savetxt

I have managed to write the following code for the following problem: Projectile's horizontal and vertical displacement are given by: $$ x = v_0 \, t \cos(\theta) $$ $$ y = v_0 \, t \sin(\theta) - \...
1 vote
0 answers
48 views

Interpolate location based on triangular sensor array

There are 3 sensors (A, B, C) on a plane, located in the corners of a (known) equilateral triangle. I want to calculate the (2D) location of an object (X) inside that triangle. One sensor returns one ...
-1 votes
1 answer
160 views

plotting $F=K \frac{q_1 q_2}{r^3}$ in python

I tryin to plot the position of electron in the hidrogen atom by Coulomb's law, $F=K \frac{q_1 q_2}{r^3}$ This is mi code ...