Questions tagged [scipy]
SciPy is a Python-based ecosystem of open-source software for mathematics, science, and engineering.
0
votes
1answer
50 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:
...
1
vote
1answer
58 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
vote
0answers
200 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
votes
1answer
63 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 ...
0
votes
1answer
65 views
Minimize cost with Levenberg-Marquart method
I want to minimize a cost function of the form,
$$
\min_{q,t}\left(q^T\left(\mathcal A + \mathcal B\right)q + t^T\mathcal C t+\delta t+\varepsilon Q(q)^TW(q)t+\lambda\left(1-q^Tq\right)^2\right)
$$
...
0
votes
1answer
68 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
vote
0answers
65 views
finding null space to a complex matrix
I need to solve the following equation:
$$
\begin{pmatrix}
\frac{\omega^2}{c^2}\varepsilon_x-\mu_z^{-1}k_y^2-\mu_y^{-1}k_z^2 & \mu_z^{-1}k_xk_y & \mu_y^{-1}k_xk_z\\
\mu_z^{-1}k_xk_y &\...
3
votes
2answers
138 views
Moore-Penrose pseudoinverse of singular rank degenerate matrix
I am trying to attain the Moore-Penrose pseudoinverse of a very large, very sparse, rank-degenerate, singular, and square matrix. ($75000 \times 75000$, near rank). The matrix is a graph Laplacian and ...
2
votes
0answers
92 views
Which SciPy nonlinear solver when Jacobian is analytically known and sparse?
I have a nonlinear function fun with n inputs and n outputs. I also have a function jac which calculates the Jacobian, which is ...
3
votes
0answers
115 views
Computing Small Eigenvalues with Sparse Symmetric Indefinite Mass Matrix
I want the eigenvalues of the following generalized eigenvalue problem:
$$ Av = \lambda M v $$
where
$A\in\mathbb{R}^{n\times n}$ is sparse, symmetric, and positive semi-definite
$M\in\mathbb{R}^{n\...
1
vote
1answer
191 views
Ways to solve $Ax=b$ for a sparse (banded) $A$ with updates
I want to solve the time-dependent Schrodinger Equation using the Crank-Nicolson scheme. I end up with the following matrix equation
...
-1
votes
1answer
48 views
Is it possible to partition 2D data into bins such that each bin contains the same number of samples?
I am trying to sort data following a bivariate distribution into a numpy histogramdd, where each bin should contain the same number of data points (to the nearest whole sample).
I expect that some ...
4
votes
1answer
207 views
Solving for a set of coupled ODEs to get correct variable values
My question is about how I can solve a coupled system of ODE's, and print out the variables in a plot.
I am solving for an q value and an e value, seen in this set of coupled ODE's below:
$$
\begin{...
3
votes
2answers
230 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
votes
0answers
76 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
vote
1answer
109 views
Scipy odeint Unexpected Results
I am attempting to numerically integrate the equation
$$\frac{\mathrm{dP} }{\mathrm{d} r}=-\left ( P+\rho\left ( r \right ) \right )\frac{m\left ( r \right )+4\pi r^{3}P}{r\left [ r-2m\left ( r \...
2
votes
1answer
525 views
Three dimensional irregular grid data interpolation to regular grid
I have three-dimensional radar reflectivity data obtained as voxels (scans, rays, altitudes). The data has been sampled at irregular spacings and I want to convert this into a regular grid. In ...
1
vote
1answer
471 views
How to Solve Optimisation Problems using Penalty Functions in Python
I am working on a implementing a simple quadratic optimisation problem:
$$\min _x \; {\underline{x}}^T Q {\underline{x}}$$
$$s.t. \,\quad {\underline{\mu}}^T{\underline{x}} = R^*$$
$$ \quad \quad \...
3
votes
0answers
71 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
votes
1answer
436 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
624 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
vote
0answers
118 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
33 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
vote
1answer
95 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
votes
1answer
220 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
vote
1answer
2k 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
vote
0answers
47 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,...
3
votes
2answers
157 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
votes
1answer
185 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
votes
1answer
835 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{...
1
vote
0answers
116 views
Numerical integral of oscillating function with known zeros
I have a function that I need to numerically integrate from $0$ to $+\infty$, given by:
$$I = \int_0^{+\infty} \mathrm{d}x\,x\,T^2(x)f(x)$$
where $T^2$ is an interpolated function that goes to $1$ ...
1
vote
1answer
436 views
Confusion about determining the jacobian in a rootfinding algorithm
I have written some Python code to determine the numerical roots of the following non-linear equation:
$$f_m=\tan\lambda_m - \frac{\lambda_m}{1+a}$$
where $\lambda_m\gt0$ and $a\geq0$. The code is:
<...
1
vote
5answers
4k views
Fast c++ library to solve very big sparse systems
I am working on a project with electrical circuits, where I am trying to compute the voltages at all the nodes of an electrical circuit. I know that the electrical circuit is a perfect grid, so each ...
1
vote
0answers
91 views
solving numerically a 2D integral by using simps and quad combined
I have the following function
$$f(x,y) =\left(\frac{1}{\exp(x-E_f)+1}-\frac{1}{\exp(x-y-E_f)+1} \right)\frac{1}{\sqrt{4-xy}}$$
I want to integrate it using Python 3. The domain of the $y$ variable ...
2
votes
2answers
1k views
Plotting Voigt Function in Python
I've been trying to plot the following function in Python:
$H(a,u) = \frac{a}{\pi} \int_{-\infty}^{\infty}\frac{exp(-y^2)}{a^2 + (u - y)^2}dy $
But I keep receiving the following error:
...
4
votes
2answers
1k views
Small errors accumulate while solving ODE of motion
I'm trying to solve the ODE of motion:
$$
\begin{align}
x''=&\ -myu \frac{x}{r^3} \left(1+\frac{3}{2} {J_2} \left(\frac{{r_{\text{eq}}}}{r}\right)^2 \left(1-\frac{5z^2}{r^2}\right)\right) \\
...
1
vote
0answers
494 views
Tridiagonal Solver in Python
I have a code I'm working on that involves solving a 1D Schrodinger equation using a Crank-Nicolson time step. The code is written in NumPy/SciPy, and I was doing a bit of profiling and discovered ...
1
vote
0answers
233 views
How to use “fill_factor” in spilu (scipy) [closed]
I am using spilu (incomplete LU decomposition for sparse matrix) in scipy:
https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.sparse.linalg.spilu.html
However there is an option call "...
2
votes
1answer
281 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
2k views
scipy optimize fsolve or root
I have a function:
delt=1 #trial
def f(z):
return ((1-2*z)*np.exp(-delt/z))/(((1-z)**(2+delt))*(z**(2-delt)))
I also have a variable:
...
2
votes
1answer
176 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 ...
3
votes
0answers
281 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 ...
1
vote
0answers
429 views
Numerical Double integration with endpoint singularity in scipy Python gives incorrect answer
I am trying to integrate the following function in Python,
$\int_{0}^{\infty}\int_{0}^{\infty} \dfrac{e^{-x-y}}{B(x,y)}dx dy$,
where $B(x,y)$ is the beta function - $B(x,y) = \int_0^{1}a^{x-1}(1-a)^{...
1
vote
2answers
840 views
stop condition in scipy.integrate.ode for stiff system
I'm using Python scipy.integrate.ode, and I want to stop my integration at a certain condition. So I use the integrator "dopri5" and use the method "set_solout" to specify a function for my stop ...
1
vote
0answers
66 views
Convert scipy integration with one step to matlab integration
Scipy integration allows us to do ode integration one adaptive timestep at a time and do something to it. However, matlab ode needs us to specify a timespan , and determine the adaptive timestep ...
1
vote
0answers
71 views
vectorizing optimization or root finding [closed]
I need to find the roots of a function. I am currently using scipy.optimize.fsolve
...
3
votes
1answer
575 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
0answers
90 views
vectorizating function integration scipy python
I need to implement the following in python:
For a given discrete time series Zt (t=0 to T), find smallest t such that:
$c\sum_{s=0}^t e^{[k(Zt-Zs)+m(t-s)]} >= \frac{p*}{1-p*} $
where c,k,m are ...
8
votes
1answer
540 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)$$
...
0
votes
1answer
340 views
Use of scipy sparse in ode solver
I am trying to solve a differential equation system
$$x´=Ax\quad \text{with } x(0) = f(x)$$
in Python, where $A$ indeed is a complex sparse matrix.
For now i have been solving the system using the ...
