Questions tagged [scipy]
SciPy is a Python-based ecosystem of open-source software for mathematics, science, and engineering.
274
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handling symbolical and numerical nested integrals
I'm working on reproducing a calculation from this paper https://arxiv.org/abs/1712.03972 for my thesis but I'm struggling with how to properly implement the nested integrals in Python, specifically ...
- 101
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votes
2
answers
1k
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10th-order Runge-Kutta Method
I want to apply the 10th-order Runge-Kutta method, but I am having trouble finding the coefficients. I read Ernst Hairer's article, he used the stage s=17 and ...
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Use of scipy.linalg.cython_lapack.dgbsv in cython script
I was working into accellerating a solver for baded matrix using cython.
The base case is the following pure python code :
...
- 35
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1
answer
130
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Preconditioner Implementation with matrix-free methods (sparse iterative solvers)
How can I define preconditioners (SPILU, SPAI, etc.) for sparse iterative methods (TFQMR, GMRES, CGS, etc.) for the matrix-free left-hand side? I defined $Ax=b$ using matrix-free $A$ (with ...
- 11
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53
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Solve beam equation with elastic term using scipy solve_bvp
I want to solve the beam equation with distributed load and elatic term (which depends on how much the beam interact with the terrain) :
$$
EI\frac{d^4w}{dx^4}+k*(w(x)-t(x))=q(x)
$$
where $q(x)$ is a ...
- 35
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vote
1
answer
208
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How to run scipy.optimize.minimize with L-BFGS-B for maxiter (completely)
I want to run the below code for maxiter = 20001. I don't want it to stop by some default criteria.
...
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55
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Find peaks method for finding elusive peaks
I'm currently utilizing the find_peaks function to identify peaks within this spectrum. However, despite consulting similar queries on Stack Overflow, my attempts to incorporate features such as ...
- 31
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62
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How to calculate the numerical integration and plot the result in python?
I am trying to solve the question below in McQuarrie Physical-Chemistry book.
The first step of the exercise, I solved. However, the second step involves a numerical integration. I can develop a code ...
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1
answer
85
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BSplines from scipy not defined on whole range of the knots
I am looking at the construction of BSplines out of curiosity. I created a small code that uses scipy.interpolate.BSpline to create basic splines. I get the following basic splines for order 0, 1 and ...
- 173
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1
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65
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solve_ivp method=ODE23 time step not decreasing in order
My time step with the function scipy.integrate.solve_ivp is not decreasing in t_span fluctuating (reaching values below or ...
2
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1
answer
126
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Different Results for Double Pendulum
In this study, (Hidden Fractals in the Dynamics of the Compound Double Pendulum) the authors provide various fliptime fractals (of a double pendulum) for different length combinations. However, when I ...
- 121
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68
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scipy exp model fitting: prevent coefficients blowup
I'm trying to fit a few X-Y points that look like exponential.
I used the following scipy code:
...
- 23
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answers
67
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Hyperbolic integral of the second kind
The elliptic integral of the second kind is given by
$$
E(t,m) = \int_{0}^t \sqrt{1-m \sin(s)^2} \operatorname{ds}
$$
and there is for instance a scipy function ellipeinc that computes it.
The ...
- 121
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49
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using scipy.sparse.linalg.eigsh for degenerate states in Bose Hubbard model
I am currently writing a code for the Bose-Hubbard model, and I am calculating the ground states and single-particle density matrix for different values of U and J. As U=0, one would see how the ...
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2
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153
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BFGS Constrained Optimization Failure Due to Precision Loss
I am trying to optimize the following objective function according to some constraints. However, the optimization fails at the first iteration with the message that the desired error was not ...
1
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2
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490
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optimizing piecewise linear objective functions (perhaps non convex) with equality constraints
When I do my project, I need to optimize piecewise linear objective functions (perhaps non convex) with equality constraints.
The piecewise linear objective function may be not convex like this in the ...
- 11
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109
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How to minimize a numerical integration in python?
I need some help to minimize a numerical integration. It's about a classical problem in physics (hydrogen atom). It can be solved analytically but I need to solve it numerically in Python.
We have an ...
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83
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Singular Matrix Error in Incomplete LU Decomposition
I’m currently working on solving the following PDE:
$$\begin{equation}
-(\mu_x \frac{\partial^2 u}{\partial x^2} + \mu_y \frac{\partial^2 u}{\partial y^2}) = f(x, y)\end{equation}$$
Where a right hand ...
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answers
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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?
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1
answer
136
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Numerical calculation of Lyapunov exponents using SciPy's built-in solve_ivp
I have previously successfully implemented the QR decomposition method in MATLAB to calculate Lyapunov exponents for Lorenz equations. See here.
This method integrates the stacked system, i.e. the ...
- 307
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112
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How to use a custom OdeSolver in Scipy's solve_ivp
In Scipy's solve_ivp documentation, we see the method argument can be either a string or a user-defined ...
- 307
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2
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476
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Number of function calls and jacobian calls in scipy.root
Just as an exercise, I am numerically solving the following system of equations:
$$
\begin{equation}
\begin{cases}
x^2 + y^2 = 32 \\
3x + 7y = 15
\end{cases}
\end{equation}
$$
...
- 173
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178
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Solving system of ODEs, where time derivative approaches infinity due top initial condition
I am trying to solve a problem in python using scipy's solve_ivp. The system of ODEs I am trying to solve is for coupled where I am solving for two time-dependent ...
- 23
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1
answer
177
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Weights for equidistant samples in power law fitting
I am working on fitting analytical curves to experimental data obtained in real viscoelastic tests (in fact, static creep tests).
The setting of the problem is:
the experimental data I have is a set ...
- 23
2
votes
1
answer
314
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2D integrals in Python with specified points of interest
Note: This is my first question on stackexchange; please tell me if I'm doing something incorrectly.
I am trying to calculate a series of a 2D integrals in Python with an integrand that has several ...
- 23
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vote
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answers
321
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Using solve_ivp for a PDE: how to handle multiple time-dependent variables?
I am trying to build a Python code that solves a set of coupled differential equations which will be spatially discretized by the method of lines advancing in time. I am planning to use ...
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2
votes
2
answers
482
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Solving IVP backward in time via python
I'm having difficulty solving an initial value problem (IVP) in Python backwards in time.
The code is at the end of this post.
First, please let me state my simplified problem.
The forward IVP is ...
- 21
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0
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34
views
Matching the limits of integration with the proper variables in a complicated case when using scipy.integrate.nquad
I need to integrate expressions containing powers of the function:
...
6
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1
answer
416
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 ...
- 63
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vote
1
answer
146
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Possible bug with scipy.optimize SHGO sobol: TypeError: <lambda>() takes 1 positional argument but 3 were given
I have been trying to perform some global optimization with SciPy optimizer SHGO
and I've had issues with the sampling method 'sobol'. Specifically, I get an error ...
- 31
2
votes
2
answers
100
views
How do I evaluate the numerical solution at a point that isn't on the mesh
I'm trying to code a fixed-point method to solve the following system using scipy.integrate
$$
u_{n+1}(s)=\int_0^TK_\lambda(t,s)\left(\lambda u_n(t)+\sigma(t)+f(t, ...
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2
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66
views
How to program the convergence of a sequence of systems of integral equations using Scipy
I'm trying to solve the problem
where $u_n$ and $v_n$ are sequences that converge to the solution $u$ and $v$ and $\lambda$, $\sigma$, $f$ and $g$ and K_lambda are all given.
I thought of using the ...
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1
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157
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Solving Transcendental equation involving special functions becoming nightmare any one can help?
Simply i want to solve for schrodinger equation for finite potential well problems in spherical coordinates. For case in which l=0 . It is simple but when l changes. The solution are spherical ...
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1
answer
139
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Need help to fully understand SciPy's odeint's reported step sizes, eval times, # of funct calls & total proc. time (re. question in Astronomy SE)
A recent question in Astronomy SE Numerical Programming using odeint takes more than 17 minutes got me interested in looking closer at SciPy's odeint.
The problem is a modified orbital mechanical ...
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164
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Scipy.root not converging even when provided with initial guesses very close to solution
I've made a previous question here and also in SO wondering why only the fsolve solver converges for the simple one dimensional unsteady conduction problem
$$ \frac{\partial T}{\partial t} = \alpha \...
- 133
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2
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572
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Why is this scipy.root code not converging?
I'm running a test problem to set up larger problems. Solving the simple unsteady heat equation via finite differences:
$$ \frac{\partial T}{\partial t} = \alpha \frac{\partial^2T}{\partial x^2}$$
$\...
- 133
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votes
1
answer
181
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Solve 1st order ODE in using `scipy`
I've been trying to solve the following equation
$$
y(t)=-A\cdot\frac{\mathrm{d} y}{\mathrm{d} t}+B\cdot\left(\frac{\mathrm{d} y}{\mathrm{d} t}\right)^{2}+C
\\
y(t=0)=y_{0}\\
$$
where $A$, $B$, and $C$...
2
votes
2
answers
1k
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Why does `scipy.optimize.minimize(...)` fail with this toy constrained minimisation case?
I'm learning scipy.optimize.minimize. I thought of a simple function to see how it works:
$$f(x) = x$$
With the goal to minimise $f(x)$, subject to the constraint ...
- 123
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vote
1
answer
96
views
Solving basic barystochrone problem in python
I am trying to solve $\frac{u''}{1+u'^2} - \frac{1}{2(1-u)} = 0$ subject to $u(0)=1, u(1)=0$.
If I understand how to do this properly, I first do the variable substitutions:
$u = y$, $y_1 = y; y_2 = y'...
- 355
3
votes
1
answer
125
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Interpolating 2D data on a hemisphere in order to have $C^2$ function but no overshoot
I am interpolating a 2D dataset on a hemisphere, and I am currently using scipy.Rbf that I like for its simplicity.
I am defining the norm of the interpolator with ...
- 63
2
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1
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788
views
Beta function and integral value
I have two values $a$ and $b$ where $a \ge 0$ and $b \ge 0$ and I have to calculate the formula below.
$$
\frac{1}{2}\int_0^1\text{abs}\left[\left( \frac{p_i^{(a - 1)} \times (1 - p_i)^{(b - 1)}}{\...
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2
answers
2k
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Fix step size with scipy.integrate.RK45 and scipy.integrate.LSODA
I am trying to numerically integrate a differential equation using scipy.integrate.RK45 and/or scipy.integrate.LSODA.
Now, I am trying to fix the integration step sizes of both solvers. This, however, ...
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3
votes
1
answer
131
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Scipy solve_ivp sensitivity to random phase shifts
I am trying to solve a coupled system of ODE's using the solve_ivp function from scipy. The general form of the equation is given via
$$\dot{y}(t) = M(t)y(t).$$
The time dependence of matrix is ...
- 31
3
votes
1
answer
1k
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Using the Kramers-Kronig (Hilbert) transform in Python
I am trying to use the Kramers-Kronig algorithm to transform the real and imaginary contributions to the anomalous scattering factor from a diffraction anomalous fine structure (DAFS) experiment.
I ...
2
votes
1
answer
823
views
How to extract intermediate calculation results from an SciPy ODE function in python?
I have a bit lengthier ODE function which was simulated by using Scipy solve_ivp function. During this simulation I calculated many parameters but as the output, I am taking out put only some other ...
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103
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How to save multiplication computation time between a dense vector and a not that sparse matrix?
I am trying to compute $\mathbf{X}\mathbf{u}$ for many times in my algorithm, where $\mathbf{X}\in \mathbb{R}^{n\times m}$ and $\mathbf{u} \in \mathbb{R}^{m}$. The problem is that, during the ...
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1
answer
2k
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scipy.optimize.root not converging and RuntimeWarning
I am trying to solve the following problem:
$$ \frac{d^2y}{dx^2}=\sinh(y) $$
Where the boundary conditions are: $y(0)=-1$, and $ \frac{dy(x\rightarrow \infty)}{dx}=0 $. Through central difference ...
- 23
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vote
1
answer
803
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Finding the parameters of a function via curve fit
I'm trying to estimate the parameters (v, n, k) defined in fit_func. I tried the default least squares fit but I couldn't find the parameters successfully.
...
- 433
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656
views
Curve fitting using a piecewise polynomial
I am trying to fit a piecewise polynomial function
Code:
...
- 433
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1
answer
56
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Scipy QZ documentation
The scipy.linalg.qz function implements generalized Schur decomposition for a pair of matrices A, B such that
(A, B) = (Q @ AA @ Z*, Q @ BB @ Z*), where ...
