24
votes
What language should I use when teaching an undergraduate course in computer programming?
In 2014, I would've said Python. In 2017, I wholeheartedly believe that the language to teach undergraduates is Julia.
Teaching is always about a tradeoff. On one hand, you want to choose something ...
- 12k
18
votes
Accepted
Applying the Runge-Kutta method to second order ODEs
There seems to be quite a bit of confusion about how to apply multi-step (e.g. Runge-Kutta) methods to 2nd or higher order ODEs or systems of ODEs. The process is very simple once you understand it, ...
- 4,571
15
votes
Accepted
C++ Best practices for dealing with many constants, variables in scientific codes
If you have constants that will not change before runs, declare them in a header file:
...
- 3,586
14
votes
Accepted
Super C++ optimization of matrix multiplication with Armadillo
In fundamental C++, I find the problem here is that C++ will allocate a new object of cx_mat to store evolutionMatrix*stateMatrix, and then copy the new object to stateMatrix with operator=().
I ...
- 11.4k
14
votes
Accepted
Beating typical BLAS libraries matrix multiplication performance
Consolidating the comments:
No, you are very unlikely to beat a typical BLAS library such as Intel's MKL, AMD's Math Core Library, or OpenBLAS.1
These not only use vectorization, but also (at least ...
14
votes
C++ Best practices for dealing with many constants, variables in scientific codes
Another alternative that may be in line with your train of thought is to use a namespace (or nested namespaces) to properly group constants. An example might be:
...
- 3,788
14
votes
Accepted
What are new c++20 features that are relevant to scientific computation?
Feature test macros: HPC is generally stuck on old compilers or compilers with partially conformant implementations. This can help ease the pain of working on the custom architectures common in HPC. ...
- 2,055
13
votes
Modern C++ in scientific computing?
Two examples of libraries that use modern C++ constructs:
Both the eigen and armadillo libraries (linear algebra) use several modern C++ constructs. For instance, they use both expression templates ...
- 2,285
13
votes
Accepted
Whittaker-Shannon interpolation: Accuracy dies with speedup; can it be fixed?
I was able to reproduce the behavior reported in the question, and traced the observed inaccuracies to the following line:
...
- 1,320
12
votes
Accepted
Why do libraries need hand-vectorized code instead of compiler auto vectorization
It is true that compilers are getting better and better at auto-vectorization, and for basic coefficient-wise operations like 2*A-4*B a library like Eigen cannot do ...
- 666
12
votes
Accepted
How to document math formulations in scientific computing codes?
I prefer using doxygen that supports C++ and LaTeX comments, both inline and as separate equations.
This way, you will keep your comments, including, say, the rigorous mathematical formulation of the ...
- 8,542
11
votes
Accepted
Method to check for positive definite matrices
The standard way of approaching this is really to attempt a Cholesky factorization and check to see if such a factorization exists. This is both fast and realiable. Here it is in MATLAB notation:
A ...
- 2,169
10
votes
Modern C++ in scientific computing?
I would suggest taking a look at Deal.II. It uses the STL, it's own iterators, shared pointers, etc.
The various linear solvers can use the various matrices because of how it was designed. I ...
- 1,000
10
votes
I am searching for a C++ code implementing the complex polygamma function
I implemented a complex polygamma function in the Julia standard library (https://github.com/JuliaLang/julia/pull/7125). It is possible to call this from C++ by linking to the libjulia library.
The ...
- 221
10
votes
Are there any "light-weight" FEM packages around?
I've been developing a lightweight finite element library in Python 2.7 harnessing the power of NumPy arrays and SciPy sparse matrices. The general idea is that given a mesh and a finite element, you ...
- 2,031
9
votes
Fast, lightweight C++ tensor library for dimension-agnostic code
FTensor is a lightweight, header only, fully templated library that includes ergonomic summation notation. It has been tested extensively in 2, 3, and 4 dimensions, but should work fine for any ...
- 473
9
votes
Method to check for positive definite matrices
Mostly, I'm leaving this answer here as a cautionary tale to not use a Choleski factorization. Most of the time, this is a fine answer. However, very specifically, it can and will fail, so if this ...
- 717
9
votes
Recommended language/environment for large scale semi-continuous biological models
You should consider giving Julia a try. Let me explain what's going on in the design space right now that would be of interest to you. Full disclosure I am the lead developer of JuliaDiffEq.
...
- 12k
9
votes
Accepted
Searching for recent code source for "Parallel scientific computing in C++ and MPI "
First of all, the book you mention is very old. In fact, it misses the last two MPI standards (3 and 4), and every C++ standard from C++11 on. Secondly, know that MPI has officially no C++ bindings, ...
- 1,305
8
votes
Super C++ optimization of matrix multiplication with Armadillo
@BillGreene points to the "return value optimization" as a way around the fundamental problem, but this actually only helps for one half of it. Assume you have code of this form:
...
- 52.4k
8
votes
Accepted
Stabilizing a 3x3 real symmetric matrix eigenvalue calculation
This is trying to compute the eigenvalues by computing the roots of the characteristic polynomial. In this case, the characteristic polynomial is $p(t) = t^3-2t^2x$, $x=1.25\times 10^6$, and zero is a ...
- 11.4k
8
votes
Fastest method forfinding a solution to x*log(x)
This equation is not polynomial. Assuming both $K$ and $C$ are positive (as in your linked problem), then the solution of $C x \ln_2(x) - K = 0$ can be found in terms of the Lambert $W$ function or ...
- 763
7
votes
Modern C++ in scientific computing?
The HPX library makes heavy use of a range of C++11 features such as move constructors and is also aiming to be a complete implementation of N4409 (Working Draft, Technical Specification for C++ ...
- 171
7
votes
Accepted
A good, simple book/resource on Parallel Programming in C++ for scientific computing
One of the first things that you need to understand about parallel programming is the difference between shared memory multiprocessor computer systems and distributed memory clusters.
A shared ...
- 18.2k
7
votes
Matlab, Mathematica & LAPACK returning 3 different eigenvectors
Seems that you have a duplicate eigenvalue. Thus, you have two eigenpairs $(\lambda_1, x_1)$ and $(\lambda_2, x_2)$ where $\lambda_1 = \lambda_2$. Denote $\lambda = \lambda_1 = \lambda_2$. Let $\alpha$...
- 2,031
7
votes
Physics Simulation in C++
I think you are missing a very important and crucial step that lies exactly between the physics and simulation: the mathematical model.
In order to model any physics, one has to formulate the ...
- 8,542
7
votes
Accepted
How to justify using available code (in different language) for comparing algorithms
So, you are comparing a generally slower Matlab implementation of algorithm A to a generally faster C++ implementation of algorithm B, and still getting the advantage for A. I would say, ...
- 8,542
7
votes
Accepted
The Formula of Explicit Runge-Kutta Fourteen order
The 14th order methods due to Feagin can be found in DifferentialEquations.jl. An example using them with 128-bit floating point arithmetic is as follows:
...
- 12k
6
votes
Looking for Runge-Kutta 8th order in C/C++
summarizing some points:
If it's a long-term integration of a non-dissapative model, a symplectic integrator is what you're looking for.
Otherwise, since it's an equation of motion, Runge-Kutta ...
- 12k
6
votes
In C++, how do you calculate the analytical value of $\int_a^b \left|\sin x \right|\,dx$?
You could just go for the direct final answer of the integral:
$$\int_{a}^{b}\vert {\sin(x)}\vert dx = 2\left(\left\lfloor\frac{b}{\pi}\right\rfloor - \left\lfloor\frac{a}{\pi}\right\rfloor\right) + \...
- 61
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