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NumPy is the fundamental package for scientific computing with Python.

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Consider the regularized logistic regression problem: $$\min_{\theta \in \mathbb{R}^n}\sum_{i=1}^m \ln \left(1+e^{-y_i\theta^T x_i}\right)+\frac{\lambda}{2}\big\lVert\theta\big\rVert^2_2.$$ Here, $y_i ...
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I have learnt scientific computing back in the time when C and C++ were the thing, and I'm relatively new to ...
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Let’s suppose we are working in a discrete setting with fixed intervals and want to compute the area under a known continuous function without taking the limit as Δx → 0. Example: Consider the ...
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We all learned in Calc 1 how to take derivatives of polynomials. What we were probably not told, is that this is but one possible expression of a function, in terms of a "power series", and ...
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I have two time series X and Y of length ~2 million. I have a parameter window_size which is ...
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So, we have to calculate eigenvalues and eigenfunctions for this one assignment. In short, we are using a Quantum Harmonic Oscillator. If you want to read the full thing , Here: The probability ...
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I should write a Rayleigh quotient iteration function x, k = rayleigh iterate(A,x0, eig), which takes a matrix A, an initial vector x0, and an approximate eigenvalue eig as arguments and returns an ...
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I’m writing some Python code using NumPy. Since I got an overflow warning, I decided to check for underflows as well at all places in the code, using ...
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Given a special orthogonal matrix $O$ (i.e: $OO^T = 1$ and $\det(O) = 1$), I am trying to efficiently find a matrix $X$ such that $O = e^X$ and $X = -X^T$ using Python (NumPy & SciPy). One obvious ...
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I have the following expression that I need to calculate for some matrices: $$ \sum_{k}c_{t,i,k}\sigma^\prime\left(w_tX_t+b_t\right)_k\left(\sum_\ell w_{t,k,\ell}\tilde{X}_t^{w,\ell}\right) $$ I could,...
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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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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 ...
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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 ...
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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?
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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 ...
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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 ...
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Suppose the metric is abs(a-b) <= rtol * max(abs(a), abs(b)) i.e. math.isclose with ...
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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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Can someone give an estimate of the Time and memory required to diagonalize a 20000 by 20000 complex hermitian matrix using numpy in python ?
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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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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 ...
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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)}}{\...
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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: ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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I want to use the SDEint package to give a numerical solution (plot) of the following stochastic SIR model. Namely, a system of SDEs. $$\begin{cases} dS = -\beta SIdt - \sigma SIdW \\ dI = (\beta SI -...
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@Richard's answer to Going to try to move some of my scipy/numpy calculation to a new GPU, how to avoid disappointing results? is quite helpful, and as promised I've added a simple running example ...
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I have some matrix-valued, complex data $Z(f)$ with $f\in\{f_0,f_1,\dots\}$ and $Z(f_i)$ being a 3x3 matrix. I require the inverse $Z^{-1}(f)$ in my workflow. After encountering some problems with my ...
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update: I've refactored the question based on helpful advice in the linked meta. I'm a heavy user of Python's NumPy and SciPy (and not much else) and for years I could run anything I need on my laptop....
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I have a problem which I believe is numerical instability when trying to solve a heat conduction equation using finite difference. The short version is that when the parameter $I=80.3$ I get the blue ...
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I have a real square matrix $X$ which I need to perform a Singular Value Decomposition on. Now, performing the operation $$ X = USV^T $$ as $U$ and $V$ are orthogonal, we know that $\det(X)=\pm\det(S)$...
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I'm trying to use solve_ivp from scipy in Python to solve an IVP. I specified the tspan ...
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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(...
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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-...
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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 ...
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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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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 ...
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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{...
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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 ...
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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$ ...
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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 ...
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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 ...
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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 ...
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I solved Schrödinger equation for a following tow-level time-dependent Hamiltonian numerically in two ways: ...
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