NumPy is the fundamental package for scientific computing with Python.
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1answer
30 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 ...
6
votes
0answers
100 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
71 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
53 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
229 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
65 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
74 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
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0answers
44 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
266 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
140 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
108 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
201 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
45 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,...
2
votes
2answers
612 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
650 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
106 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
56 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 ...
6
votes
2answers
179 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
69 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
204 views
How to broadcast my matrix exponentiation
I'm trying -to no avail- to broadcast the following piece of code in Python:
...
2
votes
1answer
125 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 ...
1
vote
0answers
461 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 ...
3
votes
1answer
338 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) $$
where $T_k(x) = \cos(k\, \...
3
votes
1answer
330 views
integral including a vector
I need to calculate the integral of this function
def f(z):
return ((1-2*z)*np.exp(-d/z))/(((1-z)**(2+d))*(z**(2-d)))
Here d is a constant. I am using this ...
1
vote
1answer
55 views
nodal lines of wave-function $\psi(x,y) = \sin 12x \sin y + (1 + \epsilon) \sin x \sin 12y$
I am trying to reproduce this figure of nodal lines of a wavefunction from this work of Berry $$\psi = \sin 2r\,x \sin y + (1 + \epsilon) \sin x \sin 2r\,y$$
Here the image. The first is $\epsilon = ...
1
vote
0answers
586 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
79 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
132 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 ...
2
votes
0answers
94 views
Is the numerical resolution of this huge sparse polynomial system tractable?
I'd like to find numerically a solution to a sparse system of 2000000 polynomial equations of degree 3 with 50000 variables and integer coefficients (or at least to decide whether or not a solution ...
1
vote
1answer
94 views
Vectorizing list of different functions for Gradient Descent
I am new to machine learning and statistical analysis and am having trouble figuring how I should go about a problem I have. I believe that I understand the gradient descent algorithm and how it ...
9
votes
3answers
3k views
What does Python offer for distributed/parallel/GPU computing?
Using the SciPy/NumPy libraries, Python is a pretty cool and performing platform for scientific computing. I just wonder: When I have to go parallel (multi-thread, multi-core, multi-node, gpu), what ...
2
votes
0answers
521 views
Efficiently creating an adjacency matrix from a lattice in numpy
I have an $n$ by $m$ numpy array representing a rectangular lattice $L$, where each site contains a one or a zero, representing two different materials. I'm modelling heat flow across this lattice. ...
3
votes
1answer
237 views
(numpy/scipy) Build a random vector given mean vector and covariance matrix
After running several calculations with numpy, I end with the mean vector and covariance matrix for a state vector. Is there a way with numpy or scipy to sample a random vector around this mean and ...
11
votes
2answers
4k views
Complexity of matrix inversion in numpy
I am solving differential equations that require to invert dense square matrices. This matrix inversion consumes the most of my computation time, so I was wondering if I am using the fastest algorithm ...
4
votes
1answer
3k views
Python Vectorizing a Function Returning an Array
I have the following function that has been vectorized so that for every element in input array t, an array is output:
...
5
votes
2answers
101 views
How to read the number of periods of this complicated graph?
I have two data sets that are quasi-periodic. They have the same period and can be seen clearly by eye. For example when $x\in(100,200)$, both of them have about 32 periods.
Below is a zoom-in of the ...
1
vote
0answers
160 views
Inverse quadratic method only makes one iteration - python
I'm tryin' to implement this method with python3 but i don't solve the problem. This is my code:
...
4
votes
3answers
6k views
LCM builtin in Python / Numpy
I can write a function to find LCM (lowest common multiple) of an array of integers, but I thought it must have been implemented in numpy or scipy and was expecting something like ...
2
votes
3answers
2k views
Runge-Kutta Simulation For Projectile Motion With Drag
I am attempting to simulate projectile flight with drag. However, with a timestep of 0.1 seconds, I am consistently getting an error of ~0.1-1%.
...
4
votes
1answer
1k views
Alternatives to numpy.einsum
Given an $n_1 \times \cdots \times n_k \times g \times g$ tensor $A$ (i.e. a collection of $g \times g$ matrices) and an $n_1 \times \cdots \times n_k \times g$ tensor $b$ (i.e. a collection of ...
3
votes
0answers
135 views
matplotlib contourplot for $\log z$ in the Complex Plane $\mathbb{C}$
I tried using Python's matplotlib on the logarithm and here is what I got, a kind of starburst pattern. Since the angle jumps between $\theta = 0$ and $\theta = 2\pi$, contour assumes there is a ...
2
votes
0answers
267 views
My calculated laser pulse duration is too large. Where am I wrong?
I am currently writing a small Python script to estimate the pulse duration from the optical spectrum.
At the end, the idea is to observe the effects of the spectral phase on the pulse duration and ...
0
votes
1answer
1k views
How do I correctly multiply vectors and matrices in Python and MATLAB?
I have been trying for 2-3 days now to get L2 regularized logistric regression to work in Matlab (CVX) and Python(CVXPY) but no success. I am fairly new to convex optimization so I am quite frustrated....
11
votes
1answer
624 views
Can an approximated Jacobian with finite differences cause instability in the Newton method?
I have implemented a backward-Euler solver in python 3 (using numpy). For my own convenience and as an exercise, I also wrote a small function that computes a finite difference approximation of the ...
1
vote
2answers
480 views
Python, numpy and complex functions (PDE's)
Update 4
I have almost given up on getting this right. This is the solution to the time-independent Schrodinger's equation, so the analytical solution is:
$\psi(x,t) = \psi(x,0)e^{\frac{-iE t}{\hbar}}...
0
votes
1answer
109 views
Scipy min warning meanings?
What does "Desired error not necessarily achieved due to precision loss" mean in the context of the scipy_fmin methods? I can't ...
0
votes
1answer
74 views
Mathematical error when attempting to represent step function using fourier series
I am attempting to work through a very simple problem.
Determine the Fourier series expansion for the following heat PDE problem with ICS and BCS:
$$ u_{t} = \alpha^2u_{xx}$$
$$ u(0, t) = u(L, t) =...
6
votes
1answer
289 views
roots of polynomials with small coefficients
I would like to compute the roots of a polynomial with exponentially small coefficients.
$$ \sum_{n=0}^N a_n \frac{z^n}{\sqrt{n!}} \tag{$\ast$}$$
where $a_n$ are Normal random variables with mean $0$...
0
votes
1answer
536 views
roots of polynomials of high degree: LinAlgError: Eigenvalues did not converge
I wrote a simple script to generate random polynoimals $\displaystyle f(z)= \sum_{k=0}^N a_k \frac{z^k}{\sqrt{k!}} $ of high degree and find their roots. For more discussion on random polyomials see ...
3
votes
1answer
102 views
Riemann surfaces: computing $f(z) = \int_0^z \frac{dx}{\sqrt{P(x)}}$
I am trying to validate that the Schwartz-Christoffel mapping does indeed take the upper-half plane $\mathbb{H} = \{ z: \mathrm{Re}(z) > 0\}$ to a polygon.
This involves integrals of functions ...
