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Questions tagged [numpy]

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NumPy is the fundamental package for scientific computing with Python.

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160 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 $\det(X)=\pm\det(S)$...
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1answer
180 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 ...
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2answers
119 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(...
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43 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-...
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0answers
127 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 ...
4
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0answers
56 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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1answer
167 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 ...
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2answers
90 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
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1answer
40 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 ...
3
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1answer
108 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*X@X.T, where $L$ ...
0
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2answers
87 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 ...
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1answer
96 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 ...
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1answer
171 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 ...
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0answers
56 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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1answer
1k 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) - \...
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0answers
41 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 ...
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1answer
95 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 ...
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1answer
94 views

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 ...
2
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1answer
184 views

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 ...
4
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1answer
269 views

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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1answer
189 views

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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0answers
59 views

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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2answers
199 views

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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1answer
149 views

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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0answers
23 views

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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1answer
211 views

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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0answers
55 views

how can I plot specific iterations?

I have made this code for an explicit Euler method but I want to plot only the 0,1,25,50 iterations not all of them.How can I do it? ...
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1answer
115 views

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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0answers
341 views

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}\{\...
3
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1answer
324 views

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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1answer
150 views

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 ...
2
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1answer
111 views

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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1answer
128 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 ...
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1answer
144 views

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 ...
4
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2answers
438 views

Fastest Way to Mutiply $10^4$ 2x2 Matrices

In a code that I work with (written in python, but also tagging as matlab because numpy is so close and I could use it if need be), we use a transfer matrix method to compute the properties of a ...
5
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1answer
107 views

How do I globally change the precision of a piece of code in Python to debug it?

I am solving a system of non-linear equations using the Newton-Raphson method in Python. This involves using the solve(Ax,b) function (...
2
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1answer
281 views

Numerical stability in the product of many matrices

I have to calculate in numpy the matrix-product of many matrices (~400). Are there common practices to increase numerical stability? If this is relevant, the matrices are $300\times 300$ orthogonal ...
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0answers
103 views

Calculate integrals using numpy.fft

Good evening, I would like to understand why I do not get the correct result: I assume that I know my function on discrete data points and expand it as a discrete Fourier transform: $\text{sin}(x)=\...
7
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0answers
180 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 ...
3
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1answer
2k views

Numerical derivative in python

I am trying to take the numerical derivative of a dataset. My first attempt was to use the gradient function from numpy but in that case the graph of the derivative ...
0
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0answers
106 views

Smoothing FFT result

I am trying to calculate the spectrum of Bremmstrahlung, which involves calculating the Fourier transformed acceleration. I am solving a non-linear ODE to numerically calculate the acceleration in the ...
2
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0answers
348 views

What algorithm do BLAS and ATLAS use for matrix multiplication?

I have searched and what I understood was that they use the naive one with several memory and cache optimizations. However, I wanted to know whether they are using the Strassen or the Coppersmith-...
4
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1answer
669 views

Diagonalize a unitary matrix with orthogonal matrices using numpy

An important component of the Cartan KAK decomposition for 2 qubit operations is to diagonalize a 4x4 unitary matrix using orthogonal (not unitary, purely real orthogonal) matrices. That is to say, ...
0
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1answer
1k views

Implementing structured grid boundary conditions using NumPy arrays?

I am making a toy code in Python to solve the advection equation $$u_t + cu_x = 0$$ with, for example, periodic boundary conditions. Background information The numerical grid is specified like this: ...
6
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2answers
4k views

Is there an efficient way to form this block matrix with numpy or scipy?

Is there an efficient way to form this block matrix with numpy or scipy? $$ \left[ \begin{array}{cccc} \mathbf{B} & \mathbf{0} & \cdots & \mathbf{0}\\ \mathbf{AB} & \mathbf{B} & \...
1
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1answer
547 views

Doing computations on a very large numpy array: streaming the calculation vs out-of-core memory

I am trying to perform a calculation in numpy that depends on several parameters, and involved the creation of many intermediate arrays. These intermediate steps involve integrals over more parameters....
2
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1answer
84 views

numpy.outer without flatten

$x$ is an $N \times M$ matrix. $y$ is a $1 \times L$ vector. I want to return "outer product" between $x$ and $y$, let's call it $z$. z[n,m,l] = x[n,m] * y[l] ...
1
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2answers
499 views

Numpy FFT gives me a pulse shorter than it should be. Not sure what I am doing wrong

I've created a code (Python, numpy) that defines an ultrashort laser pulse in the frequency domain (pulse duration should be 4 fs), but when I perform the Fourier Transform using DFT, my pulse in the ...
5
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2answers
438 views

Python: vectorizing a structured linear system solve

Overview I am looking for a way to solve a structured linear system in Python without using a for loop (preferably using vectorization, if possible). Background Consider the following linear system:...
2
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1answer
176 views

Problem of multiplication of big (sparse) matrix with numpy (python)

I wanted to multiply two simple (big and sparse) matrix with numpy. And I saw that the calculation fails when matrices are too big. If i take $X$ a random vector (size $n$). With pandas, I ...

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