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Questions tagged [scipy]

SciPy is a Python-based ecosystem of open-source software for mathematics, science, and engineering.

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When is Newton-Krylov not an appropriate solver?

Recently I have been comparing different non-linear solvers from scipy and was particularly impressed with the Newton-Krylov example in the Scipy Cookbook in which they solve a second order ...
boyfarrell's user avatar
  • 5,409
16 votes
3 answers
17k views

What is the fastest way to compute all eigenvalues of a very big and sparse adjacency matrix in python?

I'm trying to figure out if there is a faster way to compute all the eigenvalues and eigenvectors of a very big and sparse adjacency matrix than using scipy.sparse.linalg.eigsh As far as I know, this ...
Noam Peled's user avatar
13 votes
3 answers
6k views

How are scientific computing workflows faring on Apple's M1 hardware

The initial wave of reviews for Apple's M1 hardware are out, and there's lots of generic benchmarks and data on workflows on professional programs for creative users, but I haven't seen anyone talking ...
Fomite's user avatar
  • 2,393
13 votes
1 answer
2k 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 ...
Stephen Bosch's user avatar
12 votes
5 answers
13k views

Dynamically ending ODE integration in SciPy

I have a light ray moving through space-time, i.e. a curve in $\mathbb{R}^4$, parametrized by some variable λ. The exact trajectory, i.e. the coordinate functions $x^μ(λ)$ of the curve are given by ...
balu's user avatar
  • 243
9 votes
3 answers
822 views

Is LAPACK behind the cutting edge of dense linear algebra?

I have been digging into some numerical linear algebra lately, and reading in particular about how LAPACK solves symmetric eigenvalue problems. I noticed that the ...
Grayscale's user avatar
  • 211
9 votes
1 answer
454 views

Forcing an ODE solver to preserve the norm

I have an ODE of the form $$ \frac{dy}{dt} = -i H y \enspace .$$ where $y$ is a complex vector and $H$ is a time dependent Hermitian matrix. The norm of the solution $y(t)$ at any point in time ...
Krastanov's user avatar
  • 193
9 votes
1 answer
889 views

Matrix Balancing Algorithm

I have been writing a control system toolbox from scratch and purely in Python3 (shameless plug : harold ). From my past research, I have always complaints about ...
percusse's user avatar
  • 393
8 votes
3 answers
4k 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 ...
Michael's user avatar
  • 1,463
8 votes
1 answer
5k views

Numerical evaluation of an elliptic integral in python

Goal: I need to evaluate numerically an integral of the following form: $$ \int_0^\infty \frac{dx}{(a^2+x)\sqrt{(a^2+x)(b^2+x)(c^2+x)}} $$ where $a,b,c \in \mathbb{R}$ are in the interval $(1,1000)$....
Eric Kightley's user avatar
8 votes
1 answer
2k views

Numerical solution of Geodesic differential equations with Python

I have made a solver based on the SymPy.diffgeom library, where I use Scipy.Integrate to solve the following system of second order differential equations : \begin{align} u'' &+ \Gamma^0_{00}(u')...
imranal's user avatar
  • 425
8 votes
2 answers
1k views

Minimum path on known potential surface

I'm searching for the minimum path between the minima of a potential surface that is already known on a grid. (source: http://www.math.nus.edu.sg/~matrw/string/) Any point on the path is at an ...
tmartin's user avatar
  • 209
7 votes
4 answers
34k views

Plot integral function with scipy and matplotlib

I want to plot a numerical integral function of some function $f$ using scipy and matplotlib. How can I do this? I tried the ...
student's user avatar
  • 231
7 votes
3 answers
9k views

Can numpy.linalg.solve use back substitution when possible?

The question is if Python Numpy library can use back subsitution to solve Ax=b if possible, that is, if A is lower triangular? Do numerical linear algebra packages do this? I would think Numpy would ...
BBSysDyn's user avatar
  • 239
7 votes
4 answers
9k views

Algorithm for high quality 1/f noise?

How can I generate arbitrarily high quality $1/f$ noise, for use in a model? My model involves a lot of feedback, over a large number of iterations, with a very high bandwidth, so I'd like the $1/f$ ...
Seth's user avatar
  • 173
7 votes
2 answers
6k views

Solve non-linear set of three equations using scipy

I need to solve a non-linear set of three equations using scipy. However, I do not have any clue on which algorithm is suitable for my problem from a mathematical point of view (stability, convergence ...
albert's user avatar
  • 203
7 votes
1 answer
956 views

Why does LSODA fail to integrate the logistic function?

I'm comparing some of the different ODE integrators in scipy.integrate.ode on solving the logistic function: $$x(t) = \frac{1}{1+e^{-rt}}$$ $$\dot{x} = rx(1-x)$$ ...
joh's user avatar
  • 173
7 votes
2 answers
3k views

Numerical Integration with Convergence Factor with SciPy: Problem with Improper Integral

I would like to perform the numerical integration of an integral of the form $$ \int_{-\infty}^\infty e^{i \omega 0+} G(i \omega, \mathbf{v}) d \omega ,$$ or, using the symmetry $G(i\omega)^* = G(-i \...
RogueDodecahedron's user avatar
6 votes
3 answers
4k views

Computing numeric derivative via FFT - SciPy

I wrote the following code to compute the approximate derivative of a function using FFT: ...
Leonardo Araujo's user avatar
6 votes
2 answers
5k 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} & \...
drerD's user avatar
  • 161
6 votes
1 answer
326 views

Accelerating the computation of scipy.sparse.linalg.expm_multiply

I have a tridiagonal antiHermitian matrix ($-i*Hami*t$) with nonzero elements only along the upper diagonal and lower diagonal, and the goal is to know the action of exponential of such matrix on a ...
code437's user avatar
  • 63
5 votes
3 answers
5k views

Integration of the Fermi distribution using Python

I want to calculate the carrier concentration of my semiconductor using this equation: $$ n(x) = \frac{m^*}{\pi\hbar^2}\int_{E_k}^{\infty}\frac{1}{1+\exp\left(\frac{E-E_f}{k_BT}\right)} \mathrm{d}E $$...
ju.'s user avatar
  • 153
5 votes
2 answers
2k views

What algorithm(s) do numpy and scipy use to calculate matrix inverses?

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?
kamy rez's user avatar
5 votes
2 answers
464 views

Number of function calls and jacobian calls in scipy.root

Just as an exercise, I am numerically solving the following system of equations: $$ \begin{equation} \begin{cases} x^2 + y^2 = 32 \\ 3x + 7y = 15 \end{cases} \end{equation} $$ ...
Tarik's user avatar
  • 173
5 votes
3 answers
758 views

Maximize a function of an orthogonal matrix

I'm trying to write up a small code that, given a set of normal vibrational modes for a molecule, will convert them to localized vibrational modes. To do this I'm following the procedure from J. Chem. ...
Tyberius's user avatar
  • 1,023
5 votes
1 answer
13k views

Why is my curve_fit not producing the covariance matrix and the correct values for the unknown variables?

I am trying to fit supernova data into a scipy.curve_fit function. However, when my code runs, the values of the unknown variables given by ...
Ani007's user avatar
  • 53
5 votes
1 answer
188 views

Algorithm to factorize matrix whose many rows are already of upper triangular form?

I have a matrix whose many rows are already in the upper triangular form. $$\begin{bmatrix} x_{11} & x_{12} & x_{13} & x_{14} & x_{5} \\ 0 & x_{22} & x_{23} & x_{...
Akira's user avatar
  • 207
5 votes
2 answers
9k views

SciPy interpolation with Univariate Splines

I have coded a routine for interpolation with B-splines, only to discover later that this functionality is already included in Python's SciPy. However, I do not understand one parameter in the SciPy ...
seb's user avatar
  • 994
5 votes
1 answer
2k views

Solving for a set of coupled ODEs to get correct variable values

My question is about how I can solve a coupled system of ODE's, and print out the variables in a plot. I am solving for an q value and an e value, seen in this set of coupled ODE's below: $$ \begin{...
Nicole I.'s user avatar
5 votes
5 answers
10k views

scipy.sparse: Set row/column in sparse matrix to the identity without changing sparsity

I'm using the SciPy sparse.csr_matrix format for a finite element code. In applying the essential boundary conditions, I'm setting the desired value in the right ...
tonymac's user avatar
  • 211
5 votes
1 answer
1k views

Solving a system of nonlinear PDEs by minimization

I have two coupled nonlinear partial differential equations of the form: $ \begin{align} \dot{u} -f(u,u',u'',v,v',v'')=0 \\ \dot{v} -g(u,u',u'',v,v',v'')=0 \end{align} $ The boundary conditions are ...
Echows's user avatar
  • 207
5 votes
1 answer
1k views

How to know which LAPACK's function is used by Scipy's eig function?

As far as I understood, scipy.linalg.eig use wrappers from scipy.lapack to compute the eigenvalues and eigenvectors of a matrix. ...
user avatar
5 votes
1 answer
265 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 (...
Abel Thayil's user avatar
5 votes
1 answer
5k views

Solve rate equations with different reaction orders using SciPy ode

The image below illustrates the kinetic scheme I am trying to model. My first example focuses on the conversion of the wood-oil to non-volatiles and volatiles. The rate equations are as follows: $$ ...
wigging's user avatar
  • 325
5 votes
1 answer
398 views

Quantify integration error of scipy ode / ODEPACK

I am trying to integrate a 2nd order ODE with potential several singularities using the lsoda solver wrapped in scipy.integrate.ode(). I would like to put an error bar on the solution or at least ...
jensv's user avatar
  • 133
5 votes
0 answers
129 views

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 ...
Ken Grimes's user avatar
5 votes
0 answers
111 views

Check if LinearOperator is symmetric

I have a scipy.sparse.linalg.LinearOperator object. I'd like to check if its associated matrix is symmetric without actually instantiating the matrix in the most ...
Alex L's user avatar
  • 213
5 votes
0 answers
1k views

Symmetric sparse direct solvers in scipy

scipy.linalg.solve, in its newer versions, has a parameter assume_a that can be used to specify that the matrix $A$ is symmetric ...
Federico Poloni's user avatar
5 votes
0 answers
540 views

Optimisation of matrix exponential

I have a 7000x7000 sparse matrix (scipy), which I want to exponentiate. I've tried using scipy.sparse.linalg.expm, which works quite well for smaller matrices (takes a few seconds for a 1000x1000 ...
ferros's user avatar
  • 51
5 votes
0 answers
554 views

Iteratively finding both left and right eigenvectors for non-symmetric complex matrix

I have a complex, non-Hermitian matrix $\mathbf{A}$, for which I need to find a few eigenvalues and eigenvectors in the generalised eigenvalue problem: $$\mathbf{A}\cdot \mathbf{x} = \lambda \mathbf{...
DaveP's user avatar
  • 161
4 votes
2 answers
11k views

Tikhonov regularization in the non-negative least square - NNLS (python:scipy)

I am working on a project that I need to add a regularization into the NNLS algorithm. Is there a way to add the Tikhonov regularization into the NNLS implementation of scipy [1]? [2] talks about it, ...
user3259573's user avatar
4 votes
3 answers
28k views

scipy odeint - Excess work done on this call

I'm newbie both in calculus and Python/Scipy so I apologize if this question is too dumb. I'm trying to model flow between two pressure vessels. Let's say we have two points and a link between them ...
Farid83's user avatar
  • 143
4 votes
2 answers
552 views

Leveraging scipy for matrix free finite elements

This will be a very general question. I have a 3D finite element code in Python which I would like to extend to handle "large" problems (~10^8 unknowns in the global system). Right now I am using the ...
user3482876's user avatar
4 votes
4 answers
11k 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 ...
Pagol's user avatar
  • 143
4 votes
2 answers
5k views

Number of equations and precision of SciPy's integrate.odeint()

Is there any reason why SciPy's integrate.odeint() should become less precise when the number of equations increase? I'm trying to solve these two sets of differential equations: $\frac{dy_1}{dx} = ...
Sachin Kumar's user avatar
4 votes
2 answers
8k views

Numerical evaluation of a Gaussian Integral in Python?

Goal I'm trying to write code to compute the normalized Gaussian in the following, $$ \begin{equation} \int_{-\infty}^{\infty} \frac{1}{ \sigma \sqrt{2 \pi}} \exp\bigg( - \frac{(x - \mu)^{2}}{2 \...
Zophikel's user avatar
  • 143
4 votes
2 answers
1k views

scipy odeint: sum of conservative ode equations does not remain zero as it is being solved -- is this normal?

Let us say we have the following equations: dy1/dt = f(y1, t) [1] dy2/dt = g(y2, t) [2] The equations are such that they are "conservative", i.e. the ...
bzm3r's user avatar
  • 659
4 votes
2 answers
709 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 ...
feik's user avatar
  • 143
4 votes
1 answer
809 views

How to solve a BVP with known parameters?

I need to solve a boundary value problem (BVP) of second order, where the equation depends on several know parameters, which are geometric parameters and material constants. I would like to solve this ...
Ken Grimes's user avatar
4 votes
1 answer
119 views

Plotting optimum as a function of parameter in the objective

I am trying to minimize a 2d function using scipy.optimize. Specifically I want to plot the minimum value of the function fun as a function of the parameter wjk. The problem is that I cannot pass wjk ...
Shama's user avatar
  • 41

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