Questions tagged [scipy]

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

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38 views

Runge-Kutta fourth order method. Integrating backwards

I am using a Runge-Kutta fourth order method to solve numerically the usual equation of motion of a background scalar field in curved spacetime with a quartic potential: $\phi^{''}=-3\left(1+\frac{H^{...
3
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1answer
41 views

Scipy Spline Interpolation Parameter

Documentation in scipy.interpolate (found at https://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html) states: "The parameter variable is given with the keyword argument, u, which ...
3
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1answer
38 views

Conjugate Gradient for singular 2D poisson finite element with Neumann Boundary Conditions

Heavily edited question after I realised partly what the problem was I have programmed a simple 2D square finite element solution to the Poisson equation $-\Delta u = f$ The source function ...
4
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3answers
91 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. ...
5
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2answers
128 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
67 views

Preconditionning for solving a non-linear system of equations with least squares

I am trying to solve a large system of non-linear equations (about a few hundred equations and variable but with less variable than equations). Given that the system is really sparse and large I am ...
3
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1answer
71 views

Get the roots of a Hermite interpolating polynomial

I am using Python 3.7 to write a program that requires me to calculate the root of the Hermite interpolating polynomial, given two points $\epsilon_0$, $\epsilon_1$, the function ($d(\epsilon_0)$,$d(\...
4
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2answers
185 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 \...
1
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2answers
67 views

identifying peaks in data

I have data with peaks on some background, for example: The two prominent peaks at ~390 and ~450, as well as the much smaller peak at ~840. What are some options to programmatically find the position ...
3
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1answer
116 views

Plug-and-go Clebsch-Gordan computation in python?

I started a little project in python, under the assumption that it would be easy to find a routine for numerically computing Clebsch-Gordan coefficients in some library such as scipy. When it came ...
2
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1answer
232 views

Forward and backward integration — cause of errors

I write a test program to integrate foward on $[0,T_f]$ and then backward on $[T_f,0]$ from the endpoint of the forward integration an Hamiltonian system: $$ \dot q(t) = \frac{\partial H}{\partial p}(...
1
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0answers
44 views

Finite dimensional optimization problem over dynamical system

I am interested in solving numerically the following mathematical problem Consider an ode of the form $$ \dot q(t) = f(q(t),t_1,\ldots, t_N),\qquad t\in [0,T], $$ where $q\in \mathbb{R}^n$ is the ...
2
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1answer
69 views

User friendly scipy optimize wrapper package?

I'm creating too much throw away code for interfacing with the scipy optimize package in a user friendly way. (See code below for example of interruptible optimization that keeps last optimization ...
3
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1answer
65 views

Poisson image blending artifacts

I am trying to implement Poisson image blending as in the paper Poisson Image Editing. This is the task of filling in a masked region of an image by minimizing $$\min_f\int_\Omega \left | \nabla f - \...
2
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0answers
29 views

ILUTP in sparse.linalg.spilu?

In Matlab, an ILU with threshold and pivoting (ILUTP) can be passed by default as: setup.type = 'ilutp'; [L, U] = ilu(A, setup); Looking for an equivalent in ...
0
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0answers
39 views

Time sampling changes solution

I'm currently trying to solve a problem using numerical methods. The set-up is rather long, so I apologize in advance... TL;DR: My solutions change depending on how big my steps are and I don't know ...
3
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4answers
203 views

Numerical integration in Python with unknown constant

I’d like to solve the below equation for the unknown $T$: $$\int_0^\infty \frac{x^2}{\exp\left(\frac{x}{T}\right)-1}\kappa_x \mathrm{d}x = C,$$ where $C$ is a known constant and $\kappa_x$ is some ...
0
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0answers
51 views

Scipy basinhopping custom step update and constrained looping

I am searching for the global minimum of a certain function and trying to use its gradient (here same as Jacobin) to guide the step counter. However, my x is fix ...
0
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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
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1answer
122 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. ...
0
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1answer
69 views

Solve multi-dimensional optimization problem using basinhopping

I am searching for an optimization solution, which is a 8d vector representing 4 complex elements, where each element is within the complex circle with maximal radius 1.2. The objective function is: ...
2
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1answer
201 views

Memory and time requirements of the scipy sparse spsolve

I have a system of fairly large set of linear equations (approximately 30K equations). I am using scipy.sparse.spsolve to solve these equations. Initially, I tried ...
1
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0answers
637 views

Solve system of polynomial equations with Python

I have 5 at most 4th order polynomials in 5 variables, $$p_i(x_1,x_2,x_3,x_4,x_5) \qquad i = 1, \ldots, 5$$ where all coefficients are either rational or floating point. I'd would like to get the ...
-1
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1answer
212 views

Scipy Two-point Boundary value Problem

Nonlinear ODE Statement I would like to use scipy to solve the following: u'' + (u')^2 = sin(x) u(0)=0, u(1)=1 where u = u(x). Approach I am looking at the ...
1
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1answer
114 views

Minimize cost with Levenberg-Marquart method

I want to minimize a cost function of the form, $$ \min_{q,t}\left(q^T\left(\mathcal A + \mathcal B\right)q + t^T\mathcal C t+\delta t+\varepsilon Q(q)^TW(q)t+\lambda\left(1-q^Tq\right)^2\right) $$ ...
1
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1answer
74 views

SciPy 3d plotting Integral of $\int x^y dx$ for $y$ in $[-4,4]$

Ideally, I would like to get the symbolic/algebraic integral of the function and plot the resulting surface in 3d. I am not sufficiently versed in SciPy to know if this is even really possible.
1
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0answers
71 views

finding null space to a complex matrix

I need to solve the following equation: $$ \begin{pmatrix} \frac{\omega^2}{c^2}\varepsilon_x-\mu_z^{-1}k_y^2-\mu_y^{-1}k_z^2 & \mu_z^{-1}k_xk_y & \mu_y^{-1}k_xk_z\\ \mu_z^{-1}k_xk_y &\...
4
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2answers
189 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 ...
2
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1answer
199 views

Which SciPy nonlinear solver when Jacobian is analytically known and sparse?

I have a nonlinear function fun with n inputs and n outputs. I also have a function jac which calculates the Jacobian, which is ...
3
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0answers
144 views

Computing Small Eigenvalues with Sparse Symmetric Indefinite Mass Matrix

I want the eigenvalues of the following generalized eigenvalue problem: $$ Av = \lambda M v $$ where $A\in\mathbb{R}^{n\times n}$ is sparse, symmetric, and positive semi-definite $M\in\mathbb{R}^{n\...
1
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1answer
414 views

Ways to solve $Ax=b$ for a sparse (banded) $A$ with updates

I want to solve the time-dependent Schrodinger Equation using the Crank-Nicolson scheme. I end up with the following matrix equation ...
0
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1answer
63 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 ...
5
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1answer
518 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{...
3
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2answers
556 views

Integration of the Fermi distribution using Python

I want to calculate the carrier concentration of my semiconductor using this equation: $$ n(x) = \frac{m^*}{\pi\hbar^2}\int_{E_k}^{\infty}\frac{1}{1+\exp\left(\frac{E-E_f}{k_BT}\right)} \mathrm{d}E $$...
3
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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) $...
1
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1answer
124 views

Scipy odeint Unexpected Results

I am attempting to numerically integrate the equation $$\frac{\mathrm{dP} }{\mathrm{d} r}=-\left ( P+\rho\left ( r \right ) \right )\frac{m\left ( r \right )+4\pi r^{3}P}{r\left [ r-2m\left ( r \...
2
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1answer
899 views

Three dimensional irregular grid data interpolation to regular grid

I have three-dimensional radar reflectivity data obtained as voxels (scans, rays, altitudes). The data has been sampled at irregular spacings and I want to convert this into a regular grid. In ...
1
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1answer
796 views

How to Solve Optimisation Problems using Penalty Functions in Python

I am working on a implementing a simple quadratic optimisation problem: $$\min _x \; {\underline{x}}^T Q {\underline{x}}$$ $$s.t. \,\quad {\underline{\mu}}^T{\underline{x}} = R^*$$ $$ \quad \quad \...
2
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0answers
93 views

Left eigenvectors using ARPACK

I'm trying to find both the dominant $k$ left and right eigenvectors, that is, $$V_L\mathcal{A} = \Lambda V_L\\ \mathcal{A}V_R = V_R\Lambda\\ V_LV_R = I_{k\times k}$$ $V_L$ being the $k\times N$ ...
0
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1answer
720 views

How to define the derivative for Scipy.Optimize.Minimize

I am trying to use scipy.optimize.minimize to minimise a quadratic objective function: $f(x) =x^\top Q x$. As a start, I have successfully implemented this using the built-in Nelder-Mead Simplex ...
2
votes
1answer
900 views

Solving a system of quadratic equations in Python

I'd like to solve numerically a system of quadratic equations: $A_{11}x_1+A_{12}x_2+A_{13}x_3+B_{12}x_1x_2+B_{13}x_1x_3=C_1$ $A_{21}x_1+A_{22}x_2+A_{23}x_3+B_{21}x_2x_1+B_{23}x_2x_3=C_2$ $A_{31}x_1+...
1
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0answers
161 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
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1answer
37 views

Inverting a transition matrix with small grid size

Time is continuous time. I have a 3D state space, and transition rates across all of these. Using the transition rates, I can compute a generator matrix A ...
1
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1answer
114 views

Computation time of eigenvalues with ARPACK depends on what?

My goal is to compute the k smallest eigenvalues of large symmetric sparse matrices. For this purpose I use python scipy's eigsh method in shift-invert mode which uses ARPACK. The matrices usually ...
0
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1answer
270 views

``scipy.odeint`` giving different answer than analytical

I was using scipy.integrate.odeint function , the ode is $$\frac{y\ dx - x\ dy}{(x+y)^2} + dy = dx$$ with solution $$y^2 - x^2 - y = c (x + y)\ .$$ Solving it ...
1
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1answer
3k views

How to simulate 3D diffusion in python?

I want to simulate a simple 3D diffusion (e.g., an ink released from one side of a vessel) using SciPy. There are some tutorials for one-dimensional diffusion. ...
1
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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
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2answers
202 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 ...
0
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1answer
308 views

Correct use of scipy's sparse.linalg.spilu

I'm attempting to use scipy's spilu routine as a preconditioner and I'm finding bad performance for my application (solving a global linear system arising from a DG ...
-1
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1answer
1k views

Using scipy.odeint to solve coupled equations [closed]

I have a set of three coupled autonomous equations: ${y_{1}}\prime = y_{1}(\frac{\Omega_{m}}{y_{1}^3} + \frac{y_{3}^2}{6.0} + \frac{V(y_{2})}{2.H_{0}^2})$ $y_{2}\prime = y_{3}$ $y_{3}\prime = -3\frac{...