# All Questions

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11 views

### Passing data as arguments in ODE45

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{:,:}; ...
13 views

### Simulation of calculations in a tetrahedral matrix 1x1x1 [on hold]

I am trying to create an simulation of computational processes inside a three-dimensional vector matrix, which is 5 closed tetrahedrons. This is the introduction of a simple calculator into a grid of ...
12 views

### Problem about rotation matrix of elastic matrix

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 ...
10 views

### Monte Carlo domain not-so-dense

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 ...
26 views

### Weighted QR Implementation

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-...
299 views

### How should errors be reported in scientific libraries?

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 ...
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### How to find string similarity in 2 columns other than using fuzzy-wuzzy? [on hold]

from fuzzywuzzy import fuzz result=[] for i in range(len(data['output'])): result1=(fuzz.token_set_ratio(data['output'][i],data['input'][i])) result.append(result1) fuzz.token_set_ratio('...
24 views

### Fusing callbacks with FFTs: an open-source GPU FFT implementation?

I'm using cuFFT to do some 2D FFTs on matrices of size 2048x2048 or larger. The FFTs are preceded and followed by various scaling operations. These scaling operations are memory-bound, so they take ...
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### numerical instabilities in Fluid Dynamics, Finite Element Method

I'm looking for references to understand where the numerical instabilities come from in hydrodynamics in general, and notably when the Péclet number: $Pe>1$. I'm using the finite element method. ...
110 views

### Singular values of $X$ in $AX+XA=C$?

Suppose I have semi-positive definite matrices $A$ and $C$, is there an efficient approach to get top singular values of X entering the following expression? $$AX+XA=C$$ My matrices are 4k-by-4k ...
43 views

### Derivatives over a Finite Element mesh

I have a data extracted from Comsol on some node points and I know the coordinates of each node. Does anyone know how Comsol calculate the partial derivative from the values at each node and also ...
30 views

### FEniCS implementation of Maxwell equations for a dipole antenna

someone knows where I can find a FEniCS implementation of Maxwell equations for a dipole or other type of antenna? I mean a dipole antenna with an arbitrary geometry of every 'leg' in the dipole.
58 views

### Diagonalize a unitary matrix with orthogonal matrices using numpy

An important component of the Cartan KAK decomposition for 2 qubit operations is to diagonalize a 4x4 unitary matrix using orthogonal (not unitary, purely real orthogonal) matrices. That is to say, ...
31 views

### Predictor-Corrector vs. Deferred Difference Corrections

I want to use the Numerov method but keep higher-order terms from the Taylor expansions. In the literature, I found the term "Deferred Difference Corrections" for the procedure of first solving the ...
47 views

### Numerical integration of SDE: choice of $dt$ and algorithm

I am working on the following Stochastic Differential Equation (SDE) in the Quantum Mechanics context: $$dX_{t} = a X_{t} dt + b X_{t} dW$$ where $X_{t}$ is my stochastic varible, $dt$ is my ...
46 views

### ADMM: why does method of multipliers lose decomposability

I am trying to understand intuition of ADMM (alternating direction methods of multipliers). It combines dual ascent and method of multipliers. Downside of method of multiplier is the loss of ...
26 views

### Weighted moving variance

i have a time-series and, in analogy with exponentially weighted moving average, i would like to compute the exponentially weighted moving standard deviation or variance in an efficient, numerically ...
72 views

### ode45 with matrix initial conditions

EDIT: We have a coupled system of 10 ode each. The coupling presents in the last equation. I thought about using a matrix 10 by 2 as initial conditions. I also followed a similar question with the ...
113 views

### Eigenvalue-like problem with coupled ODEs

I am looking at the following system of ODEs: \begin{array}{r}{\left[c_{2}(k)-\partial_{\tau}^{2}\right] \varphi_{2}\left(\tau \right)=f_{21}(\tau) \varphi_{1}\left(\tau \right)} \\ {\left[c_{1}(k)-...
36 views

### The proper way to assess the error of Jacobi iteration (for 2D Poisson equation)?

Motivation: I'm using 2D regular grid (it's actually a quadtree but I can still treat it as a finite difference thing if I weight-average the solution over smaller scale cells for the purpose of ...
91 views

### simulation outputs differ across hardware platforms

We've recently ported our Python/Fortran simulation code to a new supercomputer. Some (not all) of the tests (simulations) that we've run on the new platform yield results that are significantly ...
16 views

### What is the difference between PetscSection and PetscSectionField in Petsc?

I think I have come to a pretty good understanding of what a PetscSection is meant to do in Petsc : it describe the organization of data when a possibly heterogeneous number of degrees of freedoms can ...
106 views

### Why do many people use FDM method to solve Stokes equations, i.e., saddle point matrix?

For numerical methods of the Stokes equations, with appropriate boundary: $$-\nabla^{2} \vec{u}+\nabla p=\overrightarrow{0}$$ $$\nabla \cdot \vec{u}=0$$ one may use FDM (finite difference method) ...
119 views

### Fastest algorithm for pseudoinverse of skinny matrices

For a performance-sensitive problem, I need to compute the pseudoinverse of a skinny matrix (#rows = 1000–10000, #cols= 10–20). I already employ the traditional SVD econ method. For some problem ...
96 views

### Implementation of Jacobi iteration

I have implemented the Jacobi iteration in C++ using a dense vector and a sparse matrix in CSR format. The code is as follows: ...
31 views

### Robust ways to find zeros of the Tricomi confluent hypergeometric function as a function of its parameters

I'm solving a quantum mechanical problem, and the quantization condition requires me to solve the equation $$U\left(\frac12(\ell+1-E), \ell+1, r^2\right) = 0,$$ where $U(a,b,z)$ is the confluent ...
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### Orientation of cones and transitive closures of a dmplex in Petsc

From the Petsc manual pages, I fail to understand what the orientations of cones and transitive closures mean. In particular, how can I relate these numbers to the orientation of the length/area/...
15 views

### Inconsistent potential over a cylindrical surface in COMSOL

I made the following construction in COMSOL (This is a cut): Two cylinders, the inner one in the middle is a solid cylindrical conductor. The thick outer cylindrical shell, along with the two small ...
20 views

### On using Ritz Method to solve a Mindlin–Reissner plate

I am trying to replicate the method given in the this paper. I have written a Matlab program which determines the displacement field of Mindlin–Reissner plate theory using Ritz method. The limitation ...
94 views

### Cholesky for ill-conditioned/singular covariance matrices

Can someone suggest a way to get Cholesky factorization of a singular covariance matrix? I need it to match Cholesky on full-rank matrices, ie coordinate order should be preserved. My attempt below ...
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71 views

### Number of GMRES iterations increase when stepping forward in time, using the Newton method

I am solving a system of nonlinear time-dependent equations using the Newton method in a finite-element-setting, i.e. first I create the jacobian matrix for the current time, and afterwards I try to ...

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