Questions tagged [numpy]
NumPy is the fundamental package for scientific computing with Python.
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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 ?
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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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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 ...
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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)}}{\...
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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:
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 -...
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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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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 ...
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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....
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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 ...
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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 $\det(X)=\pm\det(S)$...
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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 ...
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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(...
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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-...
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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 ...
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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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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 ...
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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{...
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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 ...
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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*X@X.T, where $L$ ...
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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 ...
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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 ...
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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
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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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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:
$$ x = v_0 \, t \cos(\theta) $$
$$ y = v_0 \, t \sin(\theta) - \...
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Interpolate location based on triangular sensor array
There are 3 sensors (A, B, C) on a plane, located in the corners of a (known) equilateral triangle.
I want to calculate the (2D) location of an object (X) inside that triangle.
One sensor returns one ...
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plotting $F=K \frac{q_1 q_2}{r^3}$ in python
I tryin to plot the position of electron in the hidrogen atom by Coulomb's law,
$F=K \frac{q_1 q_2}{r^3}$
This is mi code
...
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Solve integral $ \int_{-\infty}^{\infty} e^{-x^2}dx$
i trying to solve this integral
$$\int_{-\infty}^{\infty} e^{-x^2}dx$$
I'm using this
CODE
...
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How to Invert a Poorly Conditioned Matrix
In my research, I need to invert a Fisher matrix in order to get a covariance matrix for me to do parameter estimation. Unfortunately, the values of Fisher matrix vary by many orders of magnitude, and ...
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Backwards Difference Implicit Method for Nonlinear Parabolic PDE in Python
Original Stack Overflow Question: https://stackoverflow.com/questions/65683788/indexerror-index-31-is-out-of-bounds-for-axis-1-with-size-31?noredirect=1#comment116218335_65683788
PDE: u_t = u_xx + u(...
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How to compare 2D vector fields and minimize the difference?
I want to compare the field of two electrical currents and compare the resulting field to a magnetic dipol field and find magnetic momentum that minimizes the difference of the two fields.
My current ...
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Help with vectorized computation where vector multiplication would need to create an additional dimension
I want to use vectorized computation (with python and numpy) to do some calculation involving bessel functions.
As is often the case, I need to calculate the sums of bessel functions of (infinit) ...
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The derivative of a gauss function via FFT and IFFT in Python
I have a problem with computing a derivative of a Gauss function using FFT and IFFT from NumPy library. I use the fact that
$$
\begin{equation}
\frac{d}{dx}f(x) = \frac{1}{\sqrt{2\pi}}\int{ike^{ikx}\...
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Help with modified bessel functions
I'm trying to parse the following expression (Eq. 35 in The Magnetic Field in the Vicinity of Parallel and Twisted Three-Wire Cable Carrying Balanced Three-Phased Current) in Python and calculate its ...
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Problem with recursive implementation of Subspace Iteration method in Numpy
I am having trouble with implementing the method of subspace iteration to find the eigenvalues and vectors of a random, symmetric matrix, A that is mxm with m = 10. ...
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Converting for loop from matlab to python
I am converting some MATLAB code in to python and have the encountered the error "ValueError Traceback (most recent call last)
in
1 for ig in range(nbas):
---->...
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Odeint error for nonlineal differential equations
I receive the following error when I run the code.
ODEintWarning: Excess work done on this call (perhaps wrong Dfun
type). Run with full_output = 1 to get quantitative information. warnings.warn(...
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How to take convolution of two arrays in Python by using NumPy?
Generally, we know that if we have this relation between Fourier transforms of three functions in frequency domain as:
$$\mathfrak{F}\{\mathsf{P}(t)\} = \mathfrak{F}\{\mathsf{Z}(t)\}\mathfrak{F}\{\...
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Fast nonzero indices per row/column for (sparse) 2D numpy array
I am looking for the fastest way to obtain a list of the nonzero indices of a 2D array per row and per column. The following is a working piece of code:
...
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Composite matrices in Numpy
Lets say I have four matrices A, B, C and D, and I want to combine them together into one new matrix for computation:
$$
\left( \begin{matrix}
A & B\\
C & D
\end{matrix}\right)
$$
How can I ...
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Best way to convert a sparse (containing zeros) covariance matrix into a correlation matrix?
I have a $100$x$100$ covariance matrix that looks like this.
Some rows/cols are all-zero because those corresponding elements are not present in the sample from which covariance is calculated. I'm ...
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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 ...
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Numpys `tensordot` and what is happening mathematically
I've encountered a program where np.tensordot was used, so I tried looking it up but I can't really understand what this function is doing...
I feel rather ...
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