# All Questions

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150 views

### What is a good introduction to mixed quantum-classical modelling

Currently, I have some experience with classical molecular dynamics simulations, and I've had undergraduate course in quantum mechanics (the course was "analytical" one, no approaches to computer ...
1k views

### Testing numerical optimization methods: Rosenbrock vs. real test functions

There seem to be two main kinds of test function for no-derivative optimizers: one-liners like the Rosenbrock function ff., with start points sets of real data points, with an interpolator Is it ...
105 views

### Existing software/scripts for spiral graphs?

I am looking for existing software or scripts to generate spiral graphs from cyclical (time) data, as presented by Webber and Muller. The graphs shown in the paper look like a great means of ...
132 views

### Factor a non-symmetric matrix into the product of a sparse symmetric matrix and a diagonal matrix plus a low rank correction

I have a non-symmetric matrix, where the non-symmetry only appears at a subset of points. This arises due to the particular manner on which boundary conditions are applied in a Cartesian grid method. ...
138 views

### Numerically designing a periodic 1D curve that maximizes an integral area objective and satisfies value, derivative, and frequency constraints

I need to write MATLAB program (or use an existing one) to obtain Fourier series coefficients. Let's say the series is going to approximate a 1D curve. The boundary conditions are: value of the ...
738 views

### Numerical Methods for the Schrodinger Equation

We are comparing the performance of various numerical methods that can be used to solve the Schrodinger's Equation for the Hydrogen Atom interacting with a strong laser pulse (too strong to use ...
1k views

### Boost::mpi or C MPI for high performance scientific applications?

The thing I dislike most about MPI is dealing with datatypes (i.e. data maps/masks) because they don't fit that nicely with object oriented C++. boost::mpi only ...
218 views

### How to efficiently compute the total least squares with an inequality constraint

I am looking for an efficient method to compute $$\sum_{i=1}^\left|B\right|\left|Ax_i-b_i\right|^2\rightarrow min$$ under the condition $$\forall i, x_i\ge 0,$$ where $A$ is an n-by-m matrix and $B$ ...
246 views

### Positive semi-definiteness of a (symmetric) matrix

Suppose a matrix $A\in\mathbb{R}^{n\times n}$ is given. Faced with a proof for $$x^TAx>0,$$ for a non-zero vector $x\in\mathbb{R}^{n}$, I was thinking to use the information of the spectrum of $A$ (...
1k views

### Termination Criterion of Golden Section Search

Reading an implementation of the golden section search, I came across the following termination test: $$| a - d | < \varepsilon ( |b| + |c| )$$ where $a < b < c < d$ are four points at ...
911 views

### Is the heat equation with Neumann boundary conditions well-posed?

For example I consider a heat equation that I want to solve numerically : $$u_t=u_{xx},$$ In order to have a uniqueness on a computational bounded domain I have to have boundary condition specified ...
116 views

### How to assure that a number only contains a certain range of digits?

Say I would like to generate a pseudo-random number, which only contains the digits 1, 4, 7 (this is arbitrary). My first guess would be to create and array "147" and create random numbers in the ...
472 views

### Priorities for learning computational methods, when should I write my own code vs. using libraries as a beginning graduate student?

I am beginning my graduate studies in engineering and will be working on computational science projects. I noticed that there has been some discussion about the advantages and disadvantages of ...
112k views

### What is the simplest way to do a user-local install of a python package?

I don't want to deal with virtualenv for a local Python installation, I just want to install a few packages locally without dealing with the PYTHONPATH environment ...
4k views

### Is it possible to access a GPU remotely (i.e., from another machine)? [closed]

I want to access a GPU on a computer remotely, and share this GPU with different desktops. I envision this sort of access as being similar to using a VNC. Is it possible to do something like what I've ...
611 views

### parametric linear programming

I have a linear programming problem min $c^T x$ $Ax\leq b$ However, in my problem, $A$ contains also some variables $y$, e.g. $$A = \begin{pmatrix} y_1 & 4 \\ 3 & y_2 \end{pmatrix}$$ I ...
128 views

### Handling inconsistent solutions obtained by PCA

In order to achieve a 2D representation $X\in\mathbb{R}^{n\times 2}$ of some high-dimensional data residing in $Y\in\mathbb{R}^{n\times k}$, I use PCA:$$X=Y\cdot U,$$where $U\in\mathbb{R}^{k\times 2}$ ...
459 views

### How do I configure PETSc to run long double precision or some other precision that is greater than default? [closed]

I'm installing PETSc for complex numbers with the C99 standard. I'd like to have it installed using a higher precision than the default (double, I presume) since that will most likely make the LU ...
863 views

### Can all eigenvalues of a Hermitian Toeplitz matrix be computed in $\tilde{O}(n)$ time?

I know there are "superfast" $O(n \log^p n)$ algorithms for solving Toeplitz linear systems. Is it possible to compute all eigenvalues of such a matrix with the same complexity?
214 views

### Drawing 3d projection of complex surface

I have a complex surface (real dimension 2) in $\mathbb{C}^2$ with coordinates $(z,w)$ given explicitely: for any $\xi \in \mathbb{C}$ I know points $w(\xi)$ of intersection of surface with complex ...
551 views

### Binary Integer Programming Problem Subject to a Set of First-Order DEs

Recently, I came across an optimization problem with binary decision variables which was constrained with a set of first-order differential equations (resulting from a continuous-time Markov chain ...
522 views

### Recommendations for a usable, fast GPL-compatible derivative-free numerical optimization library that can be interfaced to C++

I am dealing with optimization of functions for which I do not have derivatives available, and the optimization is not constrained. I am searching for a high quality GNU Public License-compatible ...
948 views

### How to compute the optimal ridge regression model

I found R function ridge.cv very useful. I would like to implement the equivalent function in MATLAB. As a starting point, I used MATLAB function ...
2k views

### PDE discretization with the method of rothe and the method of lines (Modular implementation)

The Heat equation is discretized in space with FV (or FEM), and a semi-discrete equation is obtained (system of ODEs). This approach, known as the method of lines, allows to easily switch from one ...
83 views

842 views

### Convex polytope volume and centroid calculation

I have troubles imagining how to compute a volume and centroid of an n-dimesional convex polytope. For a polygon (especially for convex polygon) the area and centroid are described in (wiki) by  A=...
2k views

### Nonblocking version of MPI_Barrier in MPI 2

I have a bunch of MPI processes exchanging request messages back and forth. Processes do not know which other processes will send them messages, or how many. Given this situation, I want an ...
208 views

### How should I report profiling/timing information about my code?

I've seen a lot of publications in Computational Physics journals use different metrics for the performance of their code. Especially for GPGPU code, there seems to be a great variety of timing ...
7k views

### Alternatives to Journal of Computational Physics

The Journal of Computational Physics has been an important outlet for computational science in the past, and I have published there before. For the benefit of those (like me) who have signed the ...
2k views

### Finite difference coordinate transformation for spherical polar coordinates

I have part of a problem that is described by the momentum conservation equation: $\frac{\partial \rho}{\partial t} + \frac{1}{\sin\theta} \frac{\partial}{\partial \theta}(\rho u \sin \theta) =0$ ...