All Questions

Suppose I have the system: $$\dot{x} = Ax+Bu\\ y=Cx+Du$$ and the following Hamiltonian matrix: $$H=\begin{pmatrix} A & \frac{1}{2}B^TB\\ -CC^T&-A \end{pmatrix}$$ I want to find the ...

I was curious if anyone could help or provide a reference for the proof to the following lemma Lemma: Let $P_{1}$ be the set of polynomials of the first degree and let $W = w(x) : w \in C([0,1]), ...

I'm working with the tight-binding model, and I'm trying to learn the basics of how to compute the Density of States (DOS) $N(E)$ numerically. The DOS is given by $$N(E) = \frac{1}{N}\sum_k \delta(...

I have been looking at an interesting book "Pharmacokinetic-Pharmacodynamic Modeling and Simulation" by Peter Bonate on pharmacokinetic models: the models of how medical drugs work their way through ...

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 - \...

I've done some PCA on my own, and am familiar with the basic concepts of how PCA components are calculated and applied. However, I'm working on a research project and am confused as to how to ...

I am making a toy code in Python to solve the advection equation $$u_t + cu_x = 0$$ with, for example, periodic boundary conditions. Background information The numerical grid is specified like this: ...

For a given integer $n\in\mathbb{N}^*$, I want to find a pair $(x,y)\in{\mathbb{N}^*}^2$ such that $x*y=n$ and $|y-x|$ is as small as possible. A naive algorithm I found is : ...

I have a dataset $\{x_i, y_i\}_{i=0}^{n-1}$ where $x_0 < x_1 < \cdots x_{n-1}$ (not uniformly spaced), and, in addition $y_0 < y_1 < \cdots y_{n-1}$. So it feels natural to assume that $...

I am making my own finite difference computational magnetohydrodynamic code in Fortran 90. Looking at other codes they appear to calculate for example their $x$-derivatives, bb of their variables, e.g....

I am trying to solve the 2D laplace equation, $\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0; \qquad 0 \lt x \lt 1, \quad0 \lt y \lt 1$ Subjected to the boundary ...

How can I use BLAS/LAPACK to compute $$ B^{-1}AB^{-T} $$ where $A\in\mathbb{R}^{n,n}$, $B\in\mathbb{R}^{m,n}$ is full rank matrix with $m>n$, and $B^{-1}y:=\arg \min_{x} \|Bx-y\|_{2}$. In theory, ...

I'm making a NVT Monte Carlo (MC) simulation code with only short range interaction. I found many MC tutorial codes (usually Lennard-Jones system) in online. However, most of them are doing energy ...

I am trying to solve the following problem: Given a binary matrix $\mathbf{A} \in \{0,1\}^{m \times n}$ and a vector $\mathbf{b} \in \mathbb N^n$, does there exist a binary vector $\mathbf{c} \in \{...

Most Riemann solvers I've come across can solve the Riemann problem only under certain conditions such as convexity of the equation of state. But what happens if the fluid enters a metastable state or ...

I have an unconstrained minimization problem of many variables for which I know the gradient exactly. I turned to the conjugate gradient method contained in ...

I am new to the computer cluster and I am so confused with these terms, could you please explain them? Regards, Vricc

I'm looking at random vectors $z$ of size $d^2$ which can be written as $z=x\otimes y$ where $x$,$y$ are random vectors in $\mathbb{R}^d$ with following second moments known -- $E[XX']$, $E[YY']$ and $...

I am trying to implement the model given in http://proceedings.mlr.press/v84/andersen18a/andersen18a.pdf where they have used mean-field variational inference for posterior inference, but I want to ...

I want to calculate the following equation: $$\frac{\theta \Gamma \left(\kappa+1,\frac{o}{\theta }\right)-o \Gamma \left(\kappa,\frac{o}{\theta }\right)}{\Gamma (\kappa)}+o+s$$ with $s>0, o>0, ...

I am searching a solution method for the following equation system of equation systems: Let $A \in \mathbb{R}^{n \times n}$ be an invertible Matrix, $f, b_1, b_2 \in\mathbb{R}^n$ given vectors and $ ...

Many times in fourier approximation we come across integrals such as $$\int_0^1 e^{-\gamma\int_0^xu_0(\eta)d\eta}dx$$ where $\gamma$ is a constant and the data for $u_0$ is provided as a discretely ...

I need to compute the kinetic energy cascade using a finite volume solution in an equally spaced grid. I wonder if it is more correct to first compute the kinetic energy in the space (or time) domain, ...

I am currently working on remeshers for my simulations (academic purpose) and I try to find a method to remesh previous meshes using Gmsh. The first mesh (normalMesh.msh) was created using a .geo file ...

I'd like to know how Ansys computes the slope (=stiffness matrix) at point x1 in figure. I'm studying the way in which Ansys uses the Newton-Raphson method when there are nonlinearities. In the slide ...

In this sample program I'm doing the same thing (at least I think so) in two different ways. I'm running this on my Linux pc and monitoring the memory usage with top. Using gfortran I find that in the ...

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

I am currently working on a remeshing algorithm for Abaqus using Gmsh as part of my Bachelors thesis and I seem to be stuck at some point. I am able to remesh .geo and .msh files using the script ...

I need an efficient way to take square root of a matrix which is a sum of diagonal matrix and rank-1 matrix. More specifically it's the following matrix $$A=D-uu'=\text{diag}(u)-uu'$$ Where entries ...

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

Some numerical debugging led me to the minimal example below. I'm observing relative error of 0.75 on individual elements. Is there a way to estimate/bound this error without resorting to higher ...

I am applying optim() function in R to obtain maximum likelihood estimates of the fixed effects and random effects in a model with bivariate random effects. The ...

If $u_1$ and $u_2$ are solutions of (weak-form) Laplace equation on a connected domain $\Omega$, with Dirichlet boundary values $u_{\partial\Omega, 1}$ and $u_{\partial\Omega, 2}$, respectively. If $$...

I have a TTree in ROOT with 1000 events and 15 variables associated to each of them. I would like to convert this in its entirety to an hdf5 dataset. How do I organise my data in HDF5 Groups such that ...

Take an image $f$ with some characters on it (below, hjFu3). Let's apply a filter $h$ on it to obtain a second image $g$ where the text is not visible. Is there a way to compute what kind of filter $...

I need to import data from file in order to describe the structure of a network. I used the following: weights = readtable('weights192.txt'); W = weights{:,:}; ...

I'm doing homework, which I have to build a code that resolves a system of linear equations. But I'm having a problem. I have to use a matrix and a column matrix in the 3 functions. But, when I do a ...

Background for the question I am currently working on a Matlab code in which the systems of linear equations $Ax_1 = b_1$, $Ax_2 = b_2$, ... have to be solved. As the matrix $A$ is constant during ...

The usual story of Givens rotations vs Householder reflections is that Householder reflections are better if you want to map a long vector to $e_1$, while Givens is better if you want to map a 2-...

When I use the newton's method or hybrid solver in the GSL package to deal with 1-D or multidimensional root solving problems, the code frequently crashes when the solver requests function value ...

I have a derivative of a function, and Octave displays it as an expression: 10____ ⎛ 10 ⎞ ╲╱ 11 ⋅⎜- ── + log(11)⎟ ⎝ 11 ⎠ This is ...

Can the following strictly convex optimization problem be reformulated into a standard form that is also a strictly convex problem? $$\begin{align} &\text{Minimize }\frac{1}{2} x^T Q x + a^T x + ...

Let's say that we have the function $$f(x) = 1- \frac{\sqrt{1 + x^2}}{1 + x^2/2}$$ for small $x$. What I am asking is the following: I am going to solve this function numerically for $10^{-10}<...

I have a transformation matrix $K$ which transfers elastic constitutive matrix $C$ between two coordinate systems. According to textbooks such as T.C.T. Ting's "Anisotropic Elasticity", the elastic ...

Given is an increasing finite sequence of positive numbers $z_{1} ,z_{2},.....z_{n}$. Which of the following two algorithms is better for computing the sum of the numbers? ...

I want to implement a CUDA solver for the 2D shallow water equations using adaptive timestepping with a Courant number fixed by the user. The algorithm pseudocode looks something like this: ...

I already posted it on Physics SE, but maybe this is a better place: I have a 5D integral being calculated with a Monte Carlo uniform random sampling. The issue is that the region of integration is ...

Say I want a QR decomposition of matrix $A$, where orthogonality of $Q$ is with respect to a generic non-degenerate positive-definite bilinear form $\phi$ (in my case, $\phi$ is "defined" by a finite-...

There are many philosophies in different software engineering disciplines about how libraries should cope with errors or other exceptional conditions. A few of the ones I've seen: Return an error ...

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. ...