Questions tagged [numpy]
NumPy is the fundamental package for scientific computing with Python.
105
questions
2
votes
1answer
79 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 ...
1
vote
0answers
66 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)=\...
6
votes
0answers
99 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
votes
1answer
96 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
votes
0answers
65 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 ...
0
votes
0answers
86 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
votes
1answer
72 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
votes
1answer
86 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:
...
5
votes
2answers
166 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?
$$
\left[
\begin{array}{cccc}
\mathbf{B} & \mathbf{0} & \cdots & \mathbf{0}\\
\mathbf{AB} & \mathbf{B} & \...
1
vote
1answer
43 views
Doing computations on a very large numpy array: streaming the calculation vs out-of-core memory
I am trying to perform a calculation in numpy that depends on several parameters, and involved the creation of many intermediate arrays. These intermediate steps involve integrals over more parameters....
2
votes
1answer
35 views
numpy.outer without flatten
$x$ is an $N \times M$ matrix.
$y$ is a $1 \times L$ vector.
I want to return "outer product" between $x$ and $y$, let's call it $z$.
z[n,m,l] = x[n,m] * y[l]
...
1
vote
1answer
138 views
Numpy FFT gives me a pulse shorter than it should be. Not sure what I am doing wrong
I've created a code (Python, numpy) that defines an ultrashort laser pulse in the frequency domain (pulse duration should be 4 fs), but when I perform the Fourier Transform using DFT, my pulse in the ...
5
votes
2answers
362 views
Python: vectorizing a structured linear system solve
Overview
I am looking for a way to solve a structured linear system in Python without using a for loop (preferably using vectorization, if possible).
Background
Consider the following linear system:...
2
votes
1answer
58 views
Problem of multiplication of big (sparse) matrix with numpy (python)
I wanted to multiply two simple (big and sparse) matrix with numpy. And I saw that the calculation fails when matrices are too big.
If i take $X$ a random vector (size $n$). With pandas, I ...
0
votes
1answer
34 views
Specifying mesh spacing for DFT in numpy
I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...
0
votes
1answer
61 views
Creating an Interpolation of a w = f(x,y,z) function
I am trying to finish a series of interpolation functions.
The problem is more related with organizing the data than how to do the interpolations.
Using the RegularGridInterpolator, I created this ...
0
votes
1answer
194 views
Problems with python's interp 2D
I am writing some functions to interpolate data. While using interp2D, somehow, a sample matrix works but when I change the size of the matrix, it returns an error.
...
1
vote
1answer
56 views
Minimizing the used memory in diffusion simulation using Python
I am recently dealing with a diffusion simulation project and I have come up with the following code:
...
0
votes
1answer
2k views
Python Finite Difference Schemes for 1D Heat Equation: How to express for loop using numpy expression
Hello all,
I've recently been introduced to Python and Numpy, and am still a beginner in applying it for numerical methods. I've been performing simple 1D diffusion computations. I suppose my ...
0
votes
1answer
68 views
Numpy: How to permute array into indices of larger array? [closed]
I have an array of length L with N zeros, and L-N non-zero values. I have another array of length N. I would like to put the values of the shorter array into the positions of the longer array which ...
0
votes
1answer
1k views
Applying neumann boundary conditions to diffusion equation solution in python [duplicate]
For the diffusion equation
$$
\frac{\partial u(x,t)}{\partial t} = D \frac{\partial ^2 u(x,t)}{\partial x^2} + Cu(x,t)
$$
with the boundary conditions $u(-\frac{L}{2},t)=u(\frac{L}{2},t)=0$ I've ...
4
votes
2answers
217 views
Moore-Penrose pseudoinverse of singular rank degenerate matrix
I am trying to attain the Moore-Penrose pseudoinverse of a very large, very sparse, rank-degenerate, singular, and square matrix. ($75000 \times 75000$, near rank). The matrix is a graph Laplacian and ...
0
votes
1answer
66 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 ...
8
votes
0answers
361 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 ...
3
votes
0answers
84 views
Inconsistency in optimize.minimize
I am trying to fit a time-dependent curve at each time step. I do so in minimizing along $x_c$ the quadratic error between the curve and a reference solution $ 1/(1 + \exp\left(\sqrt{S}(x-x_c)\right) $...
3
votes
1answer
58 views
why am I not getting a staircase for the rotation number?
I'm trying to understand the staircase map. Look at this map from the circle to itself:
$$ x \stackrel{F}{\mapsto} \big[\omega + x + \tfrac{\epsilon}{2\pi} \sin (2\pi x) \big] \pmod 1 $$
Such a map ...
1
vote
1answer
2k views
Why `import numpy as np` for scientific computing? [closed]
Why do scientists bother with the np for numpy?
(Note this is more a "philosophical"/reasoning question - let us assume that ...
1
vote
0answers
92 views
computing dual matrix trace norm and tensor gradient in python
I'm trying to write the following function in python:
$$
f_\mu(\mathcal X) = f_0(\mathcal X) + \sum_{i = 1}^n \max_{||\mathcal Y_{i(i)}|| \leq1} \alpha_i\langle \mathcal X_{(i)},\mathcal Y_{i(i)} \...
1
vote
1answer
271 views
Performing a random walk on a lattice that traps the particles
I am trying to solve this problem where we have a 1D-lattice of size 100 and the particle can start from any position in the lattice and moves randomly on it(with equal probability of moving to either ...
1
vote
0answers
171 views
Rank filter on an nXm array using python
I would like to apply a rank filter on an nXm numpy array. Let's say I have this array:
...
0
votes
1answer
1k views
Numpy.polyfit with regularization
I am trying to use the numpy polyfit method to add regularization to my solution.
My non-regularized solution is
...
0
votes
1answer
595 views
Numpy attributes not recognized in Numba [closed]
Numba offers JIT for Python. In its documentation it says "One objective of Numba is having a seamless integration with NumPy."
So why including some of the simplest features from numpy isn't ...
1
vote
1answer
860 views
Why doesn't multiplying two matrices with NumPy work sometimes? [closed]
Using NumPy and attempting to multiply matrices together sometimes doesn't work. For example
...
4
votes
1answer
489 views
Poor SVD reconstruction of singular matrix
I am trying to calculate the singular value decomposition of this matrix using numpy.linalg.svd .
However, reconstructing the matrix from the SVD gives a poor ...
1
vote
0answers
49 views
Update model parameter with new data, discarding old data
I have this dataset, and I am using y = (a * x^n) / (b + x^n) Hill function as the model, where a is the limit of the Hill curve,...
4
votes
2answers
2k 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 ...
1
vote
1answer
3k views
Python: Comparing 2D arrays and Returning independent values from those arrays [closed]
I'm sure this would be a common question, however yet to find an answer for.
Suppose I have two, 2D vectors in Python
...
2
votes
0answers
167 views
Optimizing for loops by using Einstein summations instead
I have some Python code containing a couple of for loops, which I would like to optimize by using low-level functions. My first approach is to use ...
1
vote
1answer
93 views
Fast table interpolation on regular time data for ODE
I am using scipy.integrate.odeint to simulate the reaction of a system with known input signals via integration. The simplified code below illustrates what I'm ...
5
votes
2answers
240 views
Speeding up a linear transform using Python
In an optical wavefront propagation problem, I need to do excessive Fourier-type computations:
...
0
votes
2answers
137 views
Trying to compute the error from comparing two arrays
Some context: I am working with the Black-Scholes model.. I have an explicit (Black-Scholes) formula which is the exact solution to my problem. I have written code which implements a finite-difference ...
2
votes
1answer
327 views
How to broadcast my matrix exponentiation
I'm trying -to no avail- to broadcast the following piece of code in Python:
...
1
vote
1answer
233 views
Power spectrum incorrectly yielding negative values
I have a real signal in time given by:
And I am simply trying to compute its power spectrum, which is the Fourier transform of the autocorrelation of the signal, and is also a purely real and ...
2
votes
1answer
939 views
Wrong amplitude of convolution using numpy fft
I try to convolve a rectangle function in [-1/2, 1/2] with itself using fft. The convolution should be a tent shaped function, see figure below.
The code is below. In the 3rd to last line I add /50 ...
4
votes
1answer
503 views
Chebyshev approximation by projection vs interpolation
Suppose we want to approximate a function $f: [a, b] \rightarrow \Re$ with a Chebyshev series:
$$ f(x) \approx \sum_{k=0}^n c_k \, T_k\left( \frac{2x-b-a}{b-a} \right) $$
where $T_k(x) = \cos(k\, \...
3
votes
1answer
938 views
integral including a vector
I need to calculate the integral of this function
def f(z):
return ((1-2*z)*np.exp(-d/z))/(((1-z)**(2+d))*(z**(2-d)))
Here d is a constant. I am using this ...
1
vote
1answer
63 views
nodal lines of wave-function $\psi(x,y) = \sin 12x \sin y + (1 + \epsilon) \sin x \sin 12y$
I am trying to reproduce this figure of nodal lines of a wavefunction from this work of Berry $$\psi = \sin 2r\,x \sin y + (1 + \epsilon) \sin x \sin 2r\,y$$
Here the image. The first is $\epsilon = ...
1
vote
0answers
999 views
Finding eigenvectors and eigenvalues of large matrices in Python's numpy
I am running a PCA analysis on a data set using Python's (v2.7.10) NumPy. I validated that my program works by running the PCA analysis on a smaller dataset and then confirming that I get similar ...
1
vote
1answer
95 views
Binary tensor operations in Nutils [closed]
How does one write general tensor contractions in the Python-based finite element package Nutils? For example, how does one write the contraction of a fourth-order elasticity tensor $\boldsymbol{C}$ ...
0
votes
2answers
173 views
Fast Python implementation of short-range interacting particles under Metroplis algorithm
Can anyone write a Python implementation of a set of particles interacting in 2D according to a short-range particle-particle force and evolving in time under a Metropolis algorithm, which randomly ...
