This is essentially a question on fundamentals, and whether or not there is a more efficient way to achieve what I am looking for. I have built a working fluid dynamics calculator in Excel to find the flow rates required for a target pressure loss, the optimisation is handled using Solver but it's very clunky and not user friendly.
I'm trying to replicate the function in Octave since it's widely used here, but I am a complete beginner; I'm probably missing something obvious. I can easily enter all of the math for a single iteration via a series of functions, but my excel file required using the 'Solver' macro, and I'm unsure how to efficiently replicate this in Octave.
I am aware that linprog (in matlab) and glpk (octave) can be used to solve systems of linear equations.
I have a series of nested equations which are all dependant on a single matrix, Q (flow rates at various locations). Many other inputs are required, but they either remain constant throughout calculation (e.g. system geometry) or are dictated by Q (e.g. Reynolds number and loss coefficients). In trying to simplify my problem I have settled on two steps:
Write code to solve my problem, input: Q matrix, output: pressure loss matrix
Create a loop that iterates different Q matrices until some conditions for the pressure loss matrix are met.
I don't think it will be practical to get my expressions into the form of A*x = B (in order to use glpk) given the complexity. In excel, I can point solver at a Q value that drives a multitude of equations that impact pressure loss, and it will find the value I need to achieve a target. How can I most efficiently replicate this functionality in Octave?
First off all Solver is not a macro. Pretty far from.
So, you're going to replicate a comprehensive "What-If" Analysis Plug-in -- so complex in fact, that Microsoft chose to contract a 3rd Party company of experts to develop the tool and provide support for it (successfully based on the 1.2 Billion copies they've distributed).
And you're going to this an inferior coding language that you're a complete beginner with? Cool. I'd like to see this!
Cool. Here's a checklist of Solver's features, so you don't miss anything:
Good Luck!
More Information:
Wikipedia : Solver
Office.com : Define and Solve a Problem by using Solver
Frontline: Official Solver Page: http://solver.com
AppSource.Microsoft.com : Solver (with Video)
Frontline:L Solver International Manazine
Related
There are a number of guides I've seen on using LSTMs for time series in tensorflow, but I am still unsure about the current best practices in terms of reading and processing data - in particular, when one is supposed to use the tf.data.Dataset API.
In my situation I have a file data.csv with my features, and would like to do the following two tasks:
Compute targets - the target at time t is the percent change of
some column at some horizon, i.e.,
labels[i] = features[i + h, -1] / features[i, -1] - 1
I would like h to be a parameter here, so I can experiment with different horizons.
Get rolling windows - for training purposes, I need to roll my features into windows of length window:
train_features[i] = features[i: i + window]
I am perfectly comfortable constructing these objects using pandas or numpy, so I'm not asking how to achieve this in general - my question is specifically what such a pipeline ought to look like in tensorflow.
Edit: I guess that I'd also like to know whether the 2 tasks I listed are suited for the dataset api, or if i'm better off using other libraries to deal with them?
First off, note that you can use dataset API with pandas or numpy arrays as described in the tutorial:
If all of your input data fit in memory, the simplest way to create a
Dataset from them is to convert them to tf.Tensor objects and use
Dataset.from_tensor_slices()
A more interesting question is whether you should organize data pipeline with session feed_dict or via Dataset methods. As already stated in the comments, Dataset API is more efficient, because the data flows directly to the device, bypassing the client. From "Performance Guide":
While feeding data using a feed_dict offers a high level of
flexibility, in most instances using feed_dict does not scale
optimally. However, in instances where only a single GPU is being used
the difference can be negligible. Using the Dataset API is still
strongly recommended. Try to avoid the following:
# feed_dict often results in suboptimal performance when using large inputs
sess.run(train_step, feed_dict={x: batch_xs, y_: batch_ys})
But, as they say themselves, the difference may be negligible and the GPU can still be fully utilized with ordinary feed_dict input. When the training speed is not critical, there's no difference, use any pipeline you feel comfortable with. When the speed is important and you have a large training set, the Dataset API seems a better choice, especially you plan distributed computation.
The Dataset API works nicely with text data, such as CSV files, checkout this section of the dataset tutorial.
So, I'm wondering how to implement a STFT in Julia, possibly using a Hamming window. I can't find anything on the internet.
What is the best way to do it? I'd prefer not to use Python libraries, but pure native Julia if possible. Maybe it's a feature still being developed in Juila...?
Thanks!
I'm not aware of any native STFT implementation in Julia. As David stated in his comment, you will have to implement this yourself. This is fairly straightforward:
1) Break up your signal into short time sections
2) Apply your window of choice (in your case, Hamming)
3) Take the FFT using Julia's fft function.
All of the above are fairly standard mathematical operations and you will find a lot of references online. The below code generates a Hamming window if you don't have one already (watch out for Julia's 1-indexing when using online references as a lot of the signal processing reference material likes to use 0-indexing when describing window generation).
Wb = Array(Float64, N)
## Hamming Window Generation
for n in 1:N
Wb[n] = 0.54-0.46cos(2pi*(n-1)/N)
end
You could also use the Hamming window function from DSP.jl.
P.S If you are running Julia on OS X, check out the Julia interface to Apple's Accelerate framework. This provides a very fast Hamming window implementation, as well as convolution and elementwise multiplication functions that might be helpful.
So I have been making a simple HTML5 tuner using the Web Audio API. I have it all set up to respond to the correct frequencies, the problem seems to be with getting the actual frequencies. Using the input, I create an array of the spectrum where I look for the highest value and use that frequency as the one to feed into the tuner. The problem is that when creating an analyser in Web Audio it can not become more specific than an FFT value of 2048. When using this if i play a 440hz note, the closest note in the array is something like 430hz and the next value seems to be higher than 440. Therefor the tuner will think I am playing these notes when infact the loudest frequency should be 440hz and not 430hz. Since this frequency does not exist in the analyser array I am trying to figure out a way around this or if I am missing something very obvious.
I am very new at this so any help would be very appreciated.
Thanks
There are a number of approaches to implementing pitch detection. This paper provides a review of them. Their conclusion is that using FFTs may not be the best way to go - however, it's unclear quite what their FFT-based algorithm actually did.
If you're simply tuning guitar strings to fixed frequencies, much simpler approaches exist. Building a fully chromatic tuner that does not know a-priori the frequency to expect is hard.
The FFT approach you're using is entirely possible (I've built a robust musical instrument tuner using this approach that is being used white-label by a number of 3rd parties). However you need a significant amount of post-processing of the FFT data.
To start, you solve the resolution problem using the Short Timer FFT (STFT) - or more precisely - a succession of them. The process is described nicely in this article.
If you intend building a tuner for guitar and bass guitar (and let's face it, everyone who asks the question here is), you'll need t least a 4092-point DFT with overlapping windows in order not to violate the nyquist rate on the bottom E1 string at ~41Hz.
You have a bunch of other algorithmic and usability hurdles to overcome. Not least, perceived pitch and the spectral peak aren't always the same. Taking the spectral peak from the STFT doesn't work reliably (this is also why the basic auto-correlation approach is also broken).
I was reading the CURAND Library API and I am a newbie in CUDA and I wanted to see if someone could actually show me a simple code that uses the CURAND Library to generate random numbers. I am looking into generating a large amount of number to use with Discrete Event Simulation. My task is just to develop the algorithms to use GPGPU's to speed up the random number generation. I have implemented the LCG, Multiplicative, and Fibonacci methods in standard C Language Programming. However I want to "port" those codes into CUDA and take advantage of threads and blocks to speed up the process of generating random numbers.
Link 1: http://adnanboz.wordpress.com/tag/nvidia-curand/
That person has two of the methods I will need (LCG and Mersenne Twister) but the codes do not provide much detail. I was wondering if anyone could expand on those initial implementations to actually point me in the right direction on how to use them properly.
Thanks!
Your question is misleading - you say "Use the cuRAND Library for Dummies" but you don't actually want to use cuRAND. If I understand correctly, you actually want to implement your own RNG from scratch rather than use the optimised RNGs available in cuRAND.
First recommendation is to revisit your decision to use your own RNG, why not use cuRAND? If the statistical properties are suitable for your application then you would be much better off using cuRAND in the knowledge that it is tuned for all generations of the GPU. It includes Marsaglia's XORWOW, l'Ecuyer's MRG32k3a, and the MTGP32 Mersenne Twister (as well as Sobol' for Quasi-RNG).
You could also look at Thrust, which has some simple RNGs, for an example see the Monte Carlo sample.
If you really need to create your own generator, then there's some useful techniques in GPU Computing Gems (Emerald Edition, Chapter 16: Parallelization Techniques for Random Number Generators).
As a side note, remember that while a simple LCG is fast and easy to skip-ahead, they typically have fairly poor statistical properties especially when using large quantities of draws. When you say you will need "Mersenne Twister" I assume you mean MT19937. The referenced Gems book talks about parallelising MT19937 but the original developers created the MTGP generators (also referenced above) since MT19937 is fairly complex to implement skip-ahead.
Also as another side note, just using a different seed to achieve parallelisation is usually a bad idea, statistically you are not assured of the independence. You either need to skip-ahead or leap-frog, or else use some other technique (e.g. DCMT) for ensuring there is no correlation between sequences.
I don't have much experience in machine learning, pattern recognition, data mining, etc. and in their underlying theory and systems.
I would like to develop an artificial model of the time it takes a human to make a move in a given Sudoku puzzle.
So what I'm looking for as an output from the machine learning process is a model that can give predictions on how long does it take for a target human to make a move in a given Sudoku situation.
Same input doesn't always map to same outcome. It takes different times for the human to make a move with the same situation, but my hypothesis is that there's a tendency in the resulting probability distribution. (My educated guess is that it is ~normal.)
I have ideas about the factors that influence the distribution (like #empty slots) but would preferably leave it to the system to figure these patterns out. Please notice, that I'm not interested in the patterns, just the model.
I can generate sample and test data easily by running sudoku puzzles and measuring the times it takes to make the moves.
What kind of learning algorithm would you suggest to use for this?
I was thinking NNs, but I'm not sure if they can have the desired property of giving weighted random outcomes for the same input.
If I understand this correctly you have an input vector of length 81, which contains 1 if the square is filled in and 0 otherwise. You want to learn a function which returns a probability distribution which models the response time of a human to that board position.
My first response would be that this is a regression problem and you should try straightforward linear regression. This will not provide you with a distribution of response times, but a single 'best-guess' response time.
I'm not clear on why you want to model a distribution of response times. However, if you really want to do want to output a distribution then it sounds like you want to look at Bayesian methods. I'm not really an expert on Bayesian inference, so I can't help you much further here.
However, I don't really think your approach is going to work because I agree with your intuition about features such as the number of empty slots being important. There are also other obvious features, such as the number of empty slots per row/column that are likely to be important. Explicitly putting these features in your representation will probably be much more successful than expecting that the learning algorithm will infer something similar on its own.
The monte carlo method seems like it would work well here but would require a stack of solutions the size of the moon to really do it. And it wouldn't give you the time per person, just the time on average.
My understanding of it, tenuous as it is, is that you have a database with a board position and the time it took a human to make the next move. At the very least you have a starting point for most moves. Even if it's not in the database you could start to calculate how long it would take to make a move based on some algorithm. Though I know you had specified you wanted machine learning to do this it might be worth segmenting the problem into something a little smaller then building on it.
If you have some guesstimate as to what influences the function (# of empty cell, etc), try to train a classifier on a vector of features, and not on the 81 cells vector (0/1 or 0..9, doesn't really matter for my argument).
I think that your claim:
we wouldn't have to necessary know the underlying patterns, the "trained patterns" in a learning system automatically encodes these sometimes quite delicate and subtle patterns inside them -- that's one of their great power
is wrong. you do have to give the network the right domain. for example, when trying to detect object in an image, working in the pixel domain is pointless. you'll only get results if you first run some feature detection to detect edges, corners, etc.
Theoretically, with enough non-linearity (in NN - enough layers in the network) it can detect such things, but in practice, I have never seen that work, without giving the classifier the right features to work with.
I was thinking NNs, but I'm not sure if they can have the desired property of giving weighted random outcomes for the same input.
You're just trying to learn a function from 2^81 or 10^81 (or a much smaller feature space as I suggest) to R (response time between 0 and Inf) or some discretization of that. So NN and other classifiers can do that.