Numerics - Science topic

Hi!

There is C-library "GNU Scientific Library" - chapter 29 "Numerical Differentiation". It's free software.

There is FORTRAN-C-...-Pyton-library "IMSL". Is it possible documentation will be sufficient supporting? Documentation is free.

Best regards.

Following

One simple way to make "x" n-smooth:

1) Pick a filter (IIR or FIR) with an n-smooth impulse response

2) Filter "x" with this filter

Since the result of filtering is a convolution of "x" with the impulse response of the filter, it will be at least n-smooth.

If you use an IIR filter (e.g. for computational/memory purposes), you may want to use a Bessel filter to ensure flat group delay and the smallest time-bandwidth product.

Maybe you can start reading this: http://www.tribonet.org/wiki/reynolds-equation/

You can use Legendre multiwavelets for the solution of singular integral equation with a simple Cauchy type singular part and another complex-valued part for the evaluation of the stress intensity factor at the tip of the crack with the aid of the approximate solution. You can see the article

Now, I encountered the similar problem, do you find out why? Thank you

It is better to normalize data in order to have the same range of values for each of the inputs to the ANN model. This guarantees stable convergence of network weights and biases.

thanks for answering me Mr Behnam Farid

I wish you success in your life

Hi Yajie,

You cannot indicate joint first authorship on ResearchGate unless you also add the full text. That way a reader can look at the paper and see the list of authors, plus any note indicating authorship status.

Cheers, Matt

When a researcher use a scale developed by others, then one should follow the scoring system as established the the original author. The psychometrics of the scale will be altered if handled in a different way than the original format.

Good  @Stephan

Hi Sumathi, 

I'm not sure if I understand you correctly. You're not able to run "FPGrowth" even after applying "NumericToBinary" filter. Right? If this is your case, here is my answer:

WEKA by default considers last attribute as a class attribute (which is not necessary for unsupervised learning on general, that is represented here by FPGrowth algorithm).

However, after applying "NumericToBinary" filter, you need to remove the last attribute (presuming it is not necessary in your task) either by selecting this attribute and then pressing the "Remove" button in the "Preprocess" tab, or directly by applying the "Remove" filter from "Preprocess" tab as well. Now, FPGrowth can run normally. 

Please let me know if you still have further issues.

HTH.

Samer

Actually nemerical procedure is basically the approximation technique by ABAQUS ANSYS or  LS dyna. 

As from the flow curves of stress strain we can find the material parameters of K n alpha in Hollomons  law, Ludwiks law, Swift law or Voce law. 

You should describe a little more about the data. For example, do you mean true factors or just variables? Also, what is the goal in testing the model? Are you trying to create something theoretically meaningful or are you just trying to maximize explanatory power? The answer to these q's will greatly affect the answer. I would however not recommend step wise regression. This is an often implemented technique but a very poor one. You end up with inflated type 1 error and a model that may not be very meaningful. If you are just trying to maximize explanatory power, step wise is not the worst, but you should definitely cross validate if you choose to use step wise. 

I agree with Dr.Ronald. Its argument is completely true and helpful to you.

You can typically use the Method of Manufactured Solution (MMS). Choose whatever solution you like (so long as it is appropriately differentiable) and plug it into your PDE. Whatever comes out on the right-hand side you can simply add as a forcing term. Initial and boundary conditions are directly derived from the solution you chose.

Though never tried but i think we can compute the hash of the finger print ( which is an image) and can use the hash value as the key.

There is no theorem which tells us about polynomial approximation of a BVP. However, if you choose to apply Collocation method, select polynomials which are zeros on the boundary and select roots of a  orthogonal polynomial as collocation points.

Herewith I have given link of the paper in which the form of the Landau-Lifshitz equation is given and I am try to solve the same numerically the full  Landau-Lifshitz equation  with and without spin transfer torque term...

Hi

I advice you to see these documents. You will find what you need.

Best regards

I would say you need an equation like (1- ∑| ΔV |/ (∑ |V1|+|V2|) ) * 100 .

Which if it is perfect match gives 100 and if it is anti-match (like V1=1, V2=-1) it gives 0. However, this kind of equations are not an standard way of calculating matching between two sets of numbers. The best why is to calculate the correlation function.

C=  ∑V1V2/ ∑V1 ∑V2

see

It depends entirely on your context, like whether you have a continuous or a discrete inner product. The Dirac function (or rather its action as a distribution in an integral) can be approximated in may ways. For example, as a limit of normal (Gaussian) distributions, or in a completely different setting, in terms of cardinal sine functions, i.e., the sinc functions, sinc(x) = sin(pi*x)/(pi*x). Check out the Wikipedia article on sinc functions to see whether it might be of use to you.

But without further knowledge of your context, it's impossible to answer the question. 

You are right: essentially, I offered you almost singular matrix, which is due to numerics indefinite. The simplest way of generating numerically difficult problems is to introduce deterministic linear dependence between entries of modeled multivariate variable.    

we can use fuzzy logic or other classification method as SVM

use mathematical modeling to solve poisson's  equation   

Hello,

another software also is Plot digitizer. This program will allow you to take a scanned image of a plot (in GIF, JPEG, or PNG format) and digitize values off the plot just by clicking the mouse on each data point.

Hi, Aliakbar.

I suppose you mean let t = k*n,  then ending time tf = k*N, where N is the total number of steps.  Thus the total number N can be fixed, while k is a variable time scale factor (depending on ending time tf). Do I get it right?

Regards

Hi. Their differences are in coupling of the pressure and velocity terms. it will be useful in running time and CPU calculations. It depends on the physic of the problem under investigation

I suggest you read the article: http://www.researchgate.net/publication/278403191_Numerical_Coding_of_Nominal_Data

Perhaps there you will find the answer.

There is another book with title 'Feedback Control Theory' by Doyle and Francis. There are also very good examples in that book.

Please send me your email address, I can forward you some other important papers and books.

Dear Zhi Lin

The iterative process converges when the function in its definition domain is Lipschitzian i.e. the absolute value of its derivative is less than 1. This means that if this condition is not fullfilled you cannot stabilise the iteration process, since de function diverges. The function must absolutely converge!

Regards,

G.C.

InsyAllah I will explain in detail soon.

Hi,

You can try topic model to convert the text into a probabilistic combination of different topics.

Best regards.

Fortran is the favorite whipping boy of the programming world.  People feel completely comfortable making condescending statements about the language and those who use it.  I've been coding since I was 12, taught myself three languages by 10th grade (including 6502 machine language coded in hex), and learned several more by the time I finished grad school.  Fortran has become my language of choice for many reasons, but being "stuck" isn't one of them.  Expressiveness is part of it.  Support for mathematical calculations is another. And performance is very high on the list.  But the number one reason from which most of my other reasons flow is that Fortran is the only language with an international standards body that sees scientific programmers as its target audience

On performance, take a look at this comparison of Fortran, C++, and Python in a domain of broad interest in physics (solving PDEs):

Python isn't even in the running and C++ only comes close on the largest problems.  And on the performance question, I think it's important to note that, in the multi-core/many-core world, high performance necessitates parallelism.  Fortran is the only  standardized language with its own high-performing and scalable parallel programming model in the form of Fortran 2008 coarray parallel programming.  If you download OpenCoarrays (www.opencoarrys.org), the test suite contains multiple PDE solvers, including

(1) an object-oriented, parallel Burgers equation solver that has been shown to scale 16,384 cores with 87% parallel efficiency using nothing but Fortran 2008 with no need to embed any compiler directives or calls to libraries external to the language (I'll be glad to provide references if desired), and 

(2) a spectral Navier-Stokes solver for which the coarray Fortran version outperforms the MPI version even when the compiler uses MPI under the hood to support coarray communication and synchronization.

While I think Python is wonderful and is great for scripting purposes, I'm more likely to move to something like Julia if and when I finally switch away from Fortran for production code.  Like Fortran, Julia was conceived with numerical computation and high performance in mind.   For a great perspective on languages for scientific computing, including Fortran, Python, and Julia, see http://arstechnica.com/science/2014/05/scientific-computings-future-can-any-coding-language-top-a-1950s-behemoth/. 

Use pinv function - Moore-Penrose pseudoinverse of matrix.

Consider an example:

A = [1 2 3 4; 5 4 3 2; 0 0 0 1; 0 0 0 2]

x = [1;3;5;7]

b = A*x

Matrix A is singular, so solution by means of mldivide is not satisfactory:

A\b

Warning: Matrix is singular to working precision.

ans =

NaN

NaN

NaN

7

If you use pinv:

pinv(A)*b

ans =

1.0000

3.0000

5.0000

7.0000

Which is equal to the original x.

You can also solve your set of equations by means of least squares method.

Read more:

Take a look at this YouTube WEKA discretization tutorial:

When performing discretization you must pay attention to overfitting and missing data problems.

It is wrong to divide a numerical scale into many small discrete classes or bins because it will lead to overfitting. Such small intervals are usually over trained on the learning dataset and not universal. This can be solved by setting the least number of individuals for each class. Actually, this first proposed way back by Robert Holte. The optimal choice for cut off (i.e. discrete class boundary) is where the target class is changing. If you are really sure that value is "50" in your dataset than there's no problem, but this is entirely your judgment ("expert opinion") not necessarily what the data is saying. You have to be aware of that.

Missing data is another huge problem in discretization because it can lead to wrong cut offs. Missing values can be interpreted as a specific attribute values. However, this can be problematic if a large number of attributes with missing values relatively accurately predict the target class.

Hope this helps,

Marko

thank you... Dr.Linyong Song

From experiments, one can estimate the mass of fuel consumed by the engine from the fuel gauge.  The useful heat converted to mechanical work from the power developed by the engine, the energy associated with the exhaust gases, and water through accurate measurement of mass flow and temperatures over a period of time can be estimated using relevant equations.  Following a suitable method one can determine the power associated with friction. Making a balance between the energy associated with the combustion of fuel and the heat transformations, the quantity of drain fuel can be determined.

For numerical calculations, an iterative approach may be resorted from the quantity of fuel supplied and the energy released by combustion.  Alternately, one can assume a a certain percent of fuel to be drained from injector.  Depending on the modeling undertaken, suitable approach in numerical modeling may be resorted.

Very generally speaking, the Method of Lines approach is to first spatially discretize the PDEs (in this case, the Boussinesq equations) and then use a time-integrator to advance the resulting system of ODEs. The choice of discretization method depends on the geometry and the Prandtl number of the Boussinesq equations. For example, people use finite differences and even Chebyshev pseudospectral methods for this purpose. However, the equations may have complicated boundary conditions, in which case people use things like the Influence Matrix method.

For solving Boussinesq equations with an infinite Prandtl number in a spherical shell, see Yoshida, M., and A. Kageyama (2004), Application of the Yin‐Yang grid to a thermal convection of a Boussinesq fluid

with infinite Prandtl number in a three-dimensional spherical shell. See also this paper by Wright, Flyer and Yuen which combines RBF-PS and Chebyshev-PS to accomplish this (http://scholarworks.boisestate.edu/cgi/viewcontent.cgi?article=1027&context=math_facpubs)

Dear Naven, you can find a rational function to approximate tanh:

tanh(z)= Tanh[z] == z/(1 + z^2/(3 + z^2/(5 + z^2/(7 + z^2/(9 + z^2/(11+z^2/(13 )))))))

just look at  the web link:    

   http://functions.wolfram.com/ElementaryFunctions/Tanh/10/0001/ 

but may be this is more complicate than the standart polynomial  interpolation function described by Guy Caniaux from CNRM center.

regards

hubert

Dear Behnam Farid, thank you for the pointers.  The first paper refers to distance in the plane, while I need graph distance.  The Frish and Hammersley paper looks more general, and I am trying to get a copy... Thanks a lot.

Tommaso

(u_xy)_{ij  =}[ (u_y)_i+1,j - (u_y)_{i - 1,j} ] / (2hx)

            = [ ( u_i+1,j+1 - u_{i+1, j -1})/ (2hy)  - ( u_i-1,j+1 - u_{i-1, j-1})/ (2hy) ] /(2hx)

            =( ui+1,j+1 - ui+1, j -1 -  ui-1,j+1 + ui-1, j-1)/ (2hy)(2hx)

Dear @Hakeem, you can try the least squares method if you have both values at the same points(times).