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162 views

Discontinuity at Interface

The equation at the left of the interface is \begin{equation} \displaystyle\frac{\partial C_i}{\partial t} = D_i \nabla^2 C_i - z_i \frac{D_i}{RT}F \nabla \cdot (C_i \nabla \phi_2) \end{equation} ...
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0answers
84 views

Jacobi method converging then diverging

I am working to solve Poisson's equation in 2D axisymmetric cylindrical coordinates using the Jacobi method. The $L^2$ norm decreases from $\sim 10^3$ on the first iteration (I have a really bad guess)...
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0answers
988 views

BiCopter simulation in Matlab

I derived a bicopter dynamical model with two servos and two BLDC motors. And now am trying to simulate it using Matlab. As base for simulation I used this paper and this code Unfortunately, the ...
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1answer
604 views

On the fly/matrix free SVD of large sparse matrix

I am trying to apply SVD to large sparse matrices. I already compared the performances of Propack and irlba to those of the matlab svd and ...
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0answers
59 views

Comparison between of higher order interpolations

A while ago I came up with an algorithm which can be used to numerically solve optimal control problems, which basically came down to discretizing the control input $u(t)$ and interpolating this to ...
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0answers
59 views

CAS Problem with integrals

I got this problem thrown at me, unfortunately I lack context at the moment but I thought Maple or Mathematica would solve it anyways. I have a function $f$ over $x$ and $y$ such as this (Maple) <...
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0answers
44 views

Manipulating/Extracting Data and Developing Methods - Language Choice [closed]

As a general programming enthusiast and aspiring Bioinformatician student I have an intermediate understanding of computing (languages) as well as Java, and to a lesser extent C++. Having knowledge in ...
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0answers
50 views

A better way to compute a double integral involving a infinite series?

Let $D_{\nu}(.)$ is the parabolic cylinder function (http://mathworld.wolfram.com/ParabolicCylinderFunction.html) And $\Gamma(.)$ is the Gamma function. Define $s_y(\mu,\nu,t,z)=2^{\nu}\...
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0answers
60 views

Solving an LP greedily [closed]

I have the following LP: $$ \begin{array}{ll} \text{Minimize} & \sum_{j=1}^n x_j \\ \text{Subject to} & \sum_{j=1}^n a_{ij} x_j \geq b_i,~~~i\in\{1,\ldots,M\} \\ & 0 \leq ...
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0answers
55 views

Software to simulate behavioral economic models?

I am looking for a way to simulate behavioral economic models to illustrate the effects of changing parameters. I am familiar with statistical analysis (especially R), but I only have few programming ...
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0answers
855 views

How to adjust scikit-learn FactorAnalysis() settings to get scores output similar to one from factanal() in R?

I'm new to factor analysis and I need to compute factor scores using Python. I have R code to compute scores and I want to ...
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0answers
147 views

“Tunneling” optimization algorithm in Matlab

I was wondering if someone has implemented the "Tunneling algorithm" for the global minimization of a single variable function in Matlab. I am hoping to implement it on $[B, A - \lambda I]$. Where $A$...
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0answers
180 views

Symplectic Partitioned Runge Kutta method in Mathematica [closed]

I tried to solve Hamiltonian system ($Q$ is a vector of all generalized coordinates, $P$ - of generalized momentum) $$ \frac{\mathrm{d} Q}{\mathrm{d} t}=\frac{\partial H}{\partial P} \\ \frac{\mathrm{...
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0answers
105 views

How to compute this double integral?

Let $$T=1, K=100, S_0=100, \sigma=0.05, r=0.15. $$ Define $\nu:=\frac{2r}{\sigma^2}-1$ and $$H(y,z)=\frac{z e^{\pi^2 /4y}}{\pi \sqrt{\pi y}}\int_0^{\infty} e^{-z \cosh(u) -u^2/(4y)} \sinh(u) \sin(...
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0answers
114 views

C++ Library: What is the Most Efficient Library that Factorizes a Polynomial?

I need to know what library is the fastest one that can factorize a polynomial of large degree whose coefficients are big integers. I have tried NTL library to factorize a monic polynomial but it is ...
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0answers
74 views

Non-overlaping Domain decomposition - assemble of Laplacian

I am dealing with following 2-dimensional problem in the unit square domain $S_2$ $$- \Delta u (x,y) = f \ \text{in} \ S_2, \hspace{1.5cm} u(x,y) = 0 \ \text{on} \ \partial S_2$$ where $f$ is ...
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0answers
117 views

Reducing oscillations a 3D Alternating direction explicit scheme for the diffusion equation?

Hi I have made a 3D alternating direction explicit scheme for solving the diffusion equation, which will eventually replace a FTCS scheme in model of bubble dynamics in tissue. I have been testing it ...
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0answers
76 views

fixed point iteration to find out second order non-linear diff equations

I am working on some model analysis, getting two diff equations and after I convert them into matrix form, I have equations looks like $$ [A][X]=C\times\big(\exp([B][X])-1\big), $$ where $C$ is a ...
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0answers
213 views

Differences in answers between Python and Fortran [closed]

I am translating a piece of Fortran code into Python and am testing my code with a certain test case. All the results differ with 0.04% compared to the Fortran results. This is a very small ...
1
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1answer
190 views

solve linear system of equation of a large sparse symetric positive definite matrix

I want to invert large matrices ($10^4 \times 10^4$ to $10^6 \times 10^6$) but sparse (less than $100$ non-zero entries per line) on clusters with $16$ to $48$ processors per node. I'm looking for an ...
1
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0answers
127 views

Monte Carlo simulation [closed]

I am wondering if I am thinking correctly about the following problem : Define the box of the dimensions $(a,a,H)$ in the $X$,$Y$, and $Z$ directions, respectively. Insert $n$ particles into the box ...
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0answers
418 views

1D k-epsilon turbulence model in a turbidity current

I am trying to implement a 1D k-$\varepsilon$ turbulent model for a turbidity current, hence the conservation equation for $c$. I'm solving for the variables $u,c,k$ and $\varepsilon$. The remaining ...
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0answers
426 views

Pastix installation [closed]

I'm trying to install Pastix library, but I'm still having problems with missing libraries and I'm really helpless now. I started with copying LINUX-GNU.in as <...
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0answers
34 views

How can i get this number set to be recooperated from a product sum? [closed]

W==a(x)=2*(W* x)/41; I'm attempting to make a new type of compression algorithm. A rubber band ball type. I'm trying to make a software that extracts, from that formula, the secret volumes of number ...
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0answers
450 views

ANSYS Fluent: Defining External Force on a Cell Zone [closed]

I am using ANSYS Fluent 15 to simulate a case of fluid flow. In my case, I have three cell zones in my simulation, let's call them top, middle and bottom. My requirement is to put a vertical constant ...
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0answers
91 views

Monotonic convergence of Newton's method for boundary value problems [closed]

I’m interested in solving nonlinear elliptic boundary value problems of the type $$ -a\Delta u + f(u) = 0, $$ $$ u|_\Gamma = u_0 $$ by Newton’s method when its convergence is global and monotonic. ...
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0answers
69 views

Method of lines: explanation for high precision low resolution flux and vice versa

Could someone please explain what is meant with e.g high precision low resolution flux. Does it mean, that I use some higher order method (still first order) but with a more complex stencil and ...
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0answers
45 views

Relaxation - spreadsheet solution to recursive algorithm

I am setting up a simple model that uses recursion to iterate between known constraints - relaxation, in other words. I need a spreadsheet that allows: ...
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0answers
119 views

Implicit time integrator for Chebyshev collocation method for linear hyperbolic system

I want to solve linear hyperbolic system using Chebyshev collocation method. As this method puts severe constraint on the time step for the explicit time integration, I decided to switch to implicit ...
1
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0answers
167 views

Simple MCMC Algorithm in Matlab

I would be really glad to get some specific advise on how to implement a simple MCMC algorithm (in Matlab, if possible). I'm not yet too familiar with optimization methods. My problem goes as follows: ...
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0answers
354 views

How can I efficiently solve $Ax$=$b$ given $A$ is symmetric and contains very small (even negative) eigenvalues using EIGEN

Currently I am using the EIGEN C++ library to try to solve $x$ from the equation $Ax$ = $b$. One problem I encountered is that the matrix $A$ is a correlation matrix with size > 5000 and can ...
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0answers
65 views

“Damping factor” for a set of non-linear ODEs

I have a set of four non-linear ODEs representing a negative feedback. I have done parameter variation by random sampling to study the sensitivity of steady state and other dynamic properties to ...
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0answers
602 views

General algorithm to solve systems of symbolic equations

I want to simplify (solve) a system of linear + nonlinear symbolic equations as much as possible. the equations are of random orders, without differentiation. is there a general & well-known ...
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0answers
53 views

Execute commands when starting ipdb [closed]

I usually debug a python script by putting the following line into the source code: import ipdb; ipdb.set_trace() Then when I run the script, ipdb starts. Very ...
1
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0answers
30 views

Eigenvalue problem of the symmetric real operator which corresponds to the symmetric positive definite matrix

I have a real symmetric function $C(x,y)$ defined on $x,y\in[0,\infty)$, i.e. $C(x,y)=C(y,x)$. I want to solve the eigenvalues problem, i.e. find eigen values and eigen functions: $$\lambda \psi(x)=\...
1
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0answers
119 views

Conservation at grid interface in adaptive mesh refinement

I am using adaptive mesh refinement to solve one dimensional inviscid Burgers equation. However I am facing some difficulty to handle grid interfaces which are not uniform (coarse-fine grid interface)....
1
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1answer
328 views

extract exhaustive mutually exclusive intervals from larger set of intervals [closed]

I have a collection of time intervals with integer valued endpoints , e.g. (1,2), (2, 6) (5,6), and the number of events falling in each time interval, and I would like to determine if from them I ...
1
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0answers
489 views

scipy.integrate.ode ignores boundary conditions [closed]

I am trying to solve the 1-dimensional diffusion problem numerically using method of lines: $$ \frac{\partial c}{\partial t} =D \frac{\partial^2 c}{\partial z^2},$$ where the right hand side is ...
1
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0answers
138 views

Numerical integration when solving PDE: Simpsons rule and high frequency noise [closed]

I am solving a PDE, and one of the intermediate steps is to numerically integrate a function over a compact interval. The function is represented on a linearly spaced grid. I am using Simpsons rule (...
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0answers
669 views

radially averaged power spectrum of a binary image does not look like power law

It has been known that Fourier power spectrum somehow obeys power law therefore the slope of the spectrum can be used to calculate the fractal dimension of an image. Many people have used it for ...
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0answers
102 views

Is this problem statement good for a GPU?

I am used to using GPU hardware for large scale matrix operations and vectorizing mathematical operations on a continuous space which has been discretized for numerical computation, but this is a ...
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0answers
96 views

Elemental vs DPLASMA

I want to use one of these two libraries into my C++ project to basically invert a dense matrix (with Cholesky). Of course, I am interested in a distributed environment. Both libraries seem nice so ...
1
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0answers
50 views

Optimization of nonlocal stencil-like operator on subset of regular grid

I am trying to optimize the execution time for this particular piece of fortran code. Details: i_gc is a (ngpts, 3) array of containing (i,j,k) indices for each grid point. This is a subset of the ...
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0answers
49 views

Numerical Implementation of “integrates to some values” type constraint in convex solvers?

I am maximizing a linear functional subject to an integrates to one constraint. More explicitly, my problem is $$\begin{align} &\max_{x \in \mathbb{R}^n}\quad c \cdot x\\ &\text{subject to} \...
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0answers
77 views

Monte Carlo sampling of particle system for velocity dependent potential

When sampling configurations of point particles in statistical mechanics by means of (Markov chain) Monte Carlo, we may work with a potential that only depends on the positions of the particles, and ...
1
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0answers
171 views

Tips on improving stability in numerical scheme for non-linear PDE

I am solving a non-linear second order system of PDEs in two variables. The equations are too complicated to write out here, but an essential feature is that there is a propagating wave which then ...
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0answers
39 views

Aliasing question for a spectrally derived Lagrangian

Consider two functions $$X=\sum_{n=-N}^N i\ sign(n) y_n e^{-in\xi}; \quad \quad Y = \sum_{n=-N}^N y_n e^{-in\xi}.$$ where $y_n$ are the dependent variables of the system, and are functions of time. ...
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0answers
90 views

Gauss Integration over Zero Order Element

I'm working with the Boundary Element Method and want to integrate an expression over a triangular region. I would like to use Gauss Integration to do this, but I'm having trouble since the triangular ...
1
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0answers
40 views

Minimum effort merging of two sets

I have the following problem. I have two sequences of elements $A = [a_1,a_2,\cdots,a_n]$ and $B = [b_1,b_2,\cdots,b_m]$. I can build a matrix $D[n \times m]$ where $d_{ij} = d(a_i,b_j)$ My greedy ...
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0answers
112 views

How to curve fit an unknown function?

I have data which can be described by $y=f(x,z)$ where $z$ varies from 170 ~ 154. Now values given by $ks$ are known sample values that equals value given in the table header, $uks$ are unknown ...

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