Questions tagged [scaling]
For questions about the effect of scaling on a computation (e.g. changing units, normalizing). For questions about the "scaling" of an approach with input size/time, use [tag:complexity]
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optimization scaling techniques
Consider a convex QP of the form
$$
\min_x \bigl\{\tfrac12 x^\top Q x + q^\top x : Ax\leq b\bigr\}\tag{P}
$$
with dual
$$
\min_y \bigl\{\tfrac12 (A^\top y + q)^\top Q^{\dagger} (A^\top y+q) + b^\top y ...
- 325
1
vote
0
answers
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How to scale gradients in a gradient descent algorithm?
I am training a neural network with the multiobjective steepest gradient descent algorithm. The want to steer the direction of the gradient descent so that I land up at a point slightly above where I ...
- 113
3
votes
1
answer
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Nondimensionalization of a multi-component chemical diffusion equation
Edit I've modified the equations because they were wrong and I added the whole system, as asked by @Wolfgang
I am trying to nondimensionalize a system of partial differential equations similar to 2nd ...
- 319
2
votes
0
answers
63
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N-body correct scaling
I realized an usual way to scale an N-body problem for an N-body simulation is by choosing units such that gravitational constant $G = 1$, but I'm probably doing it the wrong way. Suppose I simply ...
- 31
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1
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If I rescale the time in a differential equation, do I need to adjust the parameters?
Imagine I have a differential equation and I have some data and the model is supposed to fit the data. If I now rescale the time in the range 0 to 1, do I need to adjust the parameters of the ...
- 35
2
votes
0
answers
38
views
Scaling tensor approximation by symmetric tensor decomposition with SciPy's L-BFGS-B
I am trying to approximate a symmetric tensor of which the values are in the range of [1e-7,1e-4], by a symmetric tensor decomposition of lower rank. For this I am using the L-BFGS-B method in SciPy's ...
- 21
3
votes
1
answer
597
views
Is there any reason to scale a matrix before (sparse) Cholesky decomposition?
I have a sparse symmetric positive-definite matrix $M$ and I expect the entries in some rows/columns to have very different orders of magnitude (up to a factor of $10^8$) than the entries in others.
...
- 273
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0
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How to achieve (approx) unit scaling of a non-linear diffusion (heat) equation with a wildly varying diffusion coefficient?
I have numerical issues with a poorly scaled one-dimensional non-linear diffusion equation in physical co-ordinates
$$ \frac{\partial{u}}{\partial{t}}(x,t) = \frac{\partial}{\partial{x}}\left(D(u) \...
1
vote
1
answer
99
views
Weak scaling for N-body simulations
I'm going to be doing some weak scaling of an $N$-body integrator on AWS. In the past when I've done weak scaling for this integrator I've fixed the number of particles per core ($N/n = {\rm const}$). ...
- 111
0
votes
1
answer
49
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Time iteration no longer smooth after using scaled units
I have a time iteration function looked on a 2D surface like this.
Since the numbers wee very small i.e. hbar=6.6260700404e-34./(2*pi), my professor told me to use our own "scaled unites" during the ...
- 153
3
votes
1
answer
622
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Scaling/nondimensionalization for numerical optimization
I have a numerical optimization problem that I am trying to scale appropriately, in order to allow for the solver to achieve faster and more accurate results. I found a paper here that had a short ...
2
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0
answers
72
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Best way to conduct parallel scaling tests?
I have just finished a new version of a parallel code that I have been working on. I would like to do a strong scaling test, but I am always bothered by how much monotonous work scaling tests seem to ...
1
vote
1
answer
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Strong scalability plot, HPC
I have to create a strong scalability plot, which measures the execution time for a numberOfThreads =1,2,4,8,16 with size=1024. ...
- 13
2
votes
1
answer
164
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Parallel processing ability of popular commercial software
I recently scaled my dynamic model based on an open source FEM solver, to run a mesh containing nearly 34 million cells successfully on 800 cores. I have very limited experience using commercial ...
- 347
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0
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77
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Does scaling factor affect discretization?
Suppose I want to solve the below equation numerically.
$$
\frac{dy}{dx}=y
$$
I'd like to normalize the space discretization by choosing
$$
a\bar{x}=x
$$
where I assume $\bar{x}$ is unity.
Then the ...
- 319
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0
answers
166
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Scaling a vector-valued non-linear function for numerical optimization/minimization [closed]
I am trying to minimize a non-linear vector-valued function in MATLAB. As a test case for my code, I try to minimize a function whose solution I know apriori.
The problem is that one of the ...
2
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1
answer
554
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I need to scale variables to solve a 2D PDE. What are the physical considerations of scaling?
I am solving a boundary value problem in 2D via an implicit finite difference scheme. Unfortunately, although the problem is well-posed and should have a unique solution, the condition number of the ...
- 263
1
vote
1
answer
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What is the cost of factorization for one-dimensional sparse problems?
In Golub and Van Loan's book, Matrix Computations, page 606, it is stated that:
With standard discretizations, 2-dimensional problems can be solved with $O(n^{3/2})$ work and $O(n \log{n})$ fill-...
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votes
3
answers
432
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Are scaled equations still needed?
If one wants to solve a problem in physics, one often has to deal with very small numbers because of the units, e.g. the energy range of interest of semiconductors lies in the region $eV \approx 10^{-...
- 267
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2
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397
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How gracefully does scalapack/pblas revert to lapack/blas in serial
If I use scalapack and pblas, and the code is run in serial (1x1 blacs process grid), how well does scalapack and pblas revert to the performance of lapack/blas?
I am particularly interested in the ...
- 3,081
2
votes
2
answers
938
views
Re-scaling array of floats so that all items are approximately integer
I have an array of floating point values $F$. I want to input my array into an algorithm that only takes integer values. How can I efficiently determine the smallest multiplier $m$ such that all ...
16
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3
answers
2k
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Is variable scaling essential when solving some PDE problems numerically?
In semiconductor simulation, it is common that the equations are scaled so they have normalised values. For example, in extreme cases electron density in semiconductors can vary over 18 order of ...
- 5,429
8
votes
1
answer
91
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Bad scaling versus collinearity
I was trying to solve a linear system:
$$
\mathbf{A}\mathbf{x} = \mathbf{y}
$$
but the conditioning number was quite bad (around $10^{17}$).
I thought that the system was singular, but after scaling ...
- 707
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votes
3
answers
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Log-log parallel scaling/efficiency plots
A lot of my own work revolves around making algorithms scale better, and one of the preferred ways of showing parallel scaling and/or parallel efficiency is to plot the performance of an algorithm/...
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