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I need to use the equivalent of Excel's TINV function in a C++ code with no statistics library linked to it.
The problem is I don't know the maths behind Student's law.
Do you think it will be reasonable to reimplement this function from scratch without using a statistics library?
I don't have access to C++11, in that case I would use std::student_t_distribution.
If yes, please provide me references to code it.
If no, do you know a lightweight library that provides it?
Thank you.
Boost has a math library with statistics functions. Here is an example on how to use it for the student's t-test
http://www.boost.org/doc/libs/1_43_0/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html
Given the lack to this tool means you may have to write one. I'm already assuming that you looked and could not find one. The math isn't that bad though. It's just testing to see if two observed distributions have the same mean. www.r-tutor.com has a good tutorial on this distribution. Math World shows the deeper context. Happy hunting.
It's too much work without using a statistics library.
What I am gonna do is generate numeric values in Excel for the range of values I need and copy it in an array in my code.
Hardcore style.
I have 3 main questions:
Let's say I have a large text file. (1)Is replacing the words with their rank an effective way to compress the file? (Got answer to this question. This is a bad idea.)
Also, I have come up with a new compression algorithm. I read some existing compression models that are used widely and I found out they use some pretty advanced concepts like statistical redundancy and probabilistic prediction. My algorithm does not use all these concepts and is a rather simple set of rules that need to be followed while compressing and decompressing. (2)My question is am I wasting my time trying to come up with a new compression algorithm without having enough knowledge about existing compression schemes?
(3)Furthermore, if I manage to successfully compress a string can I extend my algorithm to other content like videos, images etc.?
(I understand that the third question is difficult to answer without knowledge about the compression algorithm. But I am afraid the algorithm is so rudimentary and nascent I feel ashamed about sharing it. Please feel free to ignore the third question if you have to)
Your question doesn't make sense as it stands (see answer #2), but I'll try to rephrase and you can let me know if I capture your question. Would modeling text using the probability of individual words make for a good text compression algorithm? Answer: No. That would be a zeroth order model, and would not be able to take advantage of higher order correlations, such as the conditional probability of a given word following the previous word. Simple existing text compressors that look for matching strings and varied character probabilities would perform better.
Yes, you are wasting your time trying to come up with a new compression algorithm without having enough knowledge about existing compression schemes. You should first learn about the techniques that have been applied over time to model data, textual and others, and the approaches to use the modeled information to compress the data. You need to study what has already been researched for decades before developing a new approach.
The compression part may extend, but the modeling part won't.
Do you mean like having a ranking table of words sorted by frequency and assign smaller "symbols" to those words that are repeated the most, therefore reducing the amount of information that needs to be transmitted?
That's basically how Huffman Coding works, the problem with compression is that you always hit a limit somewhere along the road, of course, if the set of things that you try to compress follows a particular pattern/distribution then it's possible to be really efficient about it, but for general purposes (audio/video/text/encrypted data that appears to be random) there is no (and I believe that there can't be) "best" compression technique.
Huffman Coding uses frequency on letters. You can do the same with words or with letter frequency in more dimensions, i.e. combinations of letters and their frequency.
So I'm new to C++ and am trying to learn some things. As such I am trying to make a Random Number Generator (RNG or PRNG if you will). I have basic knowledge of RNGs, like you have to start with a seed and then send the seed through the algorithm. What I'm stuck at is how people come up with said algorithms.
Here is the code I have to get the seed.
int getSeed()
{
time_t randSeed;
randSeed = time(NULL);
return randSeed;
}
Now I know that there is are prebuilt RNGs in C++ but I'm looking to learn not just copy other people's work and try to figure it out.
So if anyone could lead me to where I could read or show me examples of how to come up with algorithms for this I would be greatly appreciative.
First, just to clarify, any algorithm you come up with will be a pseudo random number generator and not a true random number generator. Since you would be making an algorithm (i.e. writing a function, i.e. making a set of rules), the random number generator would have to eventually repeat itself or do something similar which would be non-random.
Examples of truly random number generators are one's that capture random noise from nature and digitize it. These include:
http://www.fourmilab.ch/hotbits/
http://www.random.org/
You can also buy physical equipment that generate white noise (or some other means on randomness) and digitally capture it:
http://www.lavarnd.org/
http://www.idquantique.com/true-random-number-generator/products-overview.html
http://www.araneus.fi/products-alea-eng.html
In terms of pseudo random number generators, the easiest ones to learn (and ones that an average lay person could probably make on their own) are the linear congruential generators. Unfortunately, these are also some of the worst PRNGs there are.
Some guidelines for determining what is a good PRNG include:
Periodicity (what is the range of available numbers?)
Consecutive numbers (what is the probability that the same number will be repeated twice in a row)
Uniformity (Is it just as likely to pick numbers from a certain sub range as another sub range)
Difficulty in reverse engineering it (If it is close to truly random then someone should not be able to figure out the next number it generates based on the last few numbers it generated)
Speed (how fast can I generate a new number? Does it take 5 or 500 arithmetic operations)
I'm sure there are others I am missing
One of the more popular ones right now that is considered good in most applications (ie not crptography) is the Mersenne Twister. As you can see from the link, it is a simple algorithm, perhaps only 30 lines of code. However trying to come up with those 20 or 30 lines of code from scratch takes a lot of brainpower and study of PRNGs. Usually the most famous algorithms are designed by a professor or industry professional that has studied PRNGs for decades.
I hope you do study PRNGs and try to roll your own (try Knuth's Art of Computer Programming or Numerical Recipes as a starting place), but I just wanted to lay this all out so at the end of the day (unless PRNGs will be your life's work) its much better to just use something someone else has come up with. Also, along those lines, I'd like to point out that historically compilers, spreadsheets, etc. don't use what most mathematicians consider good PRNGs so if you have a need for a high quality PRNGs don't use the standard library one in C++, Excel, .NET, Java, etc. until you have research what they are implementing it with.
A linear congruential generator is commonly used and the Wiki article explains it pretty well.
To quote John von Neumann:
Anyone who considers arithmetical
methods of producing random digits is
of course in a state of sin.
This is taken from Chapter 3 Random Numbers of Knuth's book "The Art of Computer Programming", which must be the most exhaustive overview of the subject available. And once you have read it, you will be exhausted. You will also know why you don't want to write your own random number generator.
The correct solution best fulfills the requirements and the requirements of every situation will be unique. This is probably the simplest way to go about it:
Create a large one dimensional array
populated with "real" random values.
"seed" your pseudo-random generator by
calculating the starting index with
system time.
Iterate through the array and return
the value for each call to your
function.
Wrap around when it reaches the end.
I'm looking for a (space) efficient implementation of an LCS algorithm for use in a C++ program. Inputs are two random access sequences of integers.
I'm currently using the dynamic programming approach from the wikipedia page about LCS. However, that has O(mn) behaviour in memory and time and dies on me with out of memory errors for larger inputs.
I have read about Hirschberg's algorithm, which improves memory usage considerably, Hunt-Szymanski and Masek and Paterson. Since it isn't trivial to implement these I'd prefer to try them on my data with an existing implementation. Does anyone know of such a library? I'd imagine since text diff tools are pretty common, there ought to be some open source libraries around?
When searching for things like that, try scholar.google.com. It is much better for finding scholarly works. It turned up
http://www.biotec.icb.ufmg.br/cabi/artigos/seminarios2/subsequence_algorithm.pdf
this document, a "survey of longest common subsequences algorithms".
Not C++ but Python but I think usable.
http://wordaligned.org/articles/longest-common-subsequence
Hirschberg's Algorithm embeds a javascript implementation : almost C.
this is a follow up to my recent question ( Code for identifying programming language in a text file ). I'm really thankful for all the answers I got, it helped me very much. My code for this task is complete and it works fairly well - quick and reasonably accurate.
The method i used is the following: i have a "learning" perl script that identifies most frequently used words in a language by doing a word histogram over a set of sample files. These data are then loaded by the c++ program which then checks the given text and accumulates score for each language based on found words and then simply checks which language accumulated the highest score.
Now i would like to make it even better and work a bit on the quality of identification. The problem is I often get "unknown" as result (many languages accumulate a small score, but none anything bigger than my threshold). After some debugging, research etc i found out that this is probably due to the fact, that all words are considered equal. This means that seeing a "#include" for example has the same effect as seeing a "while" - both of which indicate that it might be c/c++ (i'm now ignoring the fact that "while" is used in many other languages), but of course in larger .cpp files there might be a ton of "while" but most of the time only a few "#include".
So the fact that a "#include" is more important is ignored, because i could not come up with a good way how to identify if a word is more important than another. Now bear in mind that the script which creates the data is fairly stupid, its only a word histogram and for every chosen word it assigns a score of 1. It does not even look at the words (so if there is a "#&|?/" in a file very often it might get chosen as a good word).
Also i would like to have the data creation part fully automated, so nobody should have to look at the data and alter them, change scores, change words etc. All the "brainz" should be in the script and the cpp program.
Does somebody have a suggestion how to identify keywords, or more generally, important words? Some things that might help: i have the number of occurences of each word and the number of total words (so a ratio may be calculated). I have also thought about wiping out characters like ;, etc. since the histogram script often puts for example "continue;" in the result, but the important word is "continue". Last note: all checks for equality are done for exact match - no substrings, case sensitive. This is mainly because of speed, but substrings might help (or hurt, i dont know)...
NOTE: thanks all who bothered to answer, you helped me a lot.
My work with this is almost finished so i will describe what i did to get good results.
1) Get a decent training set, about 30-50 files per language from various sources to avoid coding style bias
2) Write a perl script that does a word histogram. Implement blacklist and whitelist (more about it below)
3) add bogus words to blacklist, like "license", "the" etc. These are often found at the start of file in license information.
4) add about five most important words per language to the whitelist. These are words that are found in most source code of a given language, but are not frequent enough to get into the histogram. For example for C/C++ i had: #include, #define, #ifdef, #ifndef and #endif in the whitelist.
5) Emphasize the start of a file, so give more points to words found in the first 50-100 lines
6) when doing the word histogram, tokenize the file using #words = split(/[\s\(\){}\[\];.,=]+/, $_); This should be ok for most languages i think (gives me the best results). For each language, have about 10-20 most frequent words in the final results.
7) When the histogram is complete, remove all words that are found in the blacklist and add all those that are found in the whitelist
8) Write a program which processes a text file in the same way as the script - tokenize using the same rules. If a word is found in the histogram data, add points to the right language. Words in the histogram which correspond to only one language should add more points, those which belong to multiple languages should add less.
Comments are welcome. Currently on about 1000 text files i get 80 unknowns (mostly on extremely short files - mainly javascript with just one or two lines). About 20 files are recognized wrong. Size of the files is about 11kB ranging from 100 bytes to 100 kBytes (almost 11MB total). It takes one second to process them all, which is good enough for me.
I think you're approaching this from the wrong viewpoint. From your description, it sounds like you are building a classifier. A good classifier needs to discriminate between different classes; it doesn't need to precisely estimate the correspondence between the input and the most likely class.
Practically: your classifier doesn't need to assess precisely how close to C++ a certain input is; it merely needs to determine if the input is more like C than C++. This makes your work a lot easier - most of your current "unknown" cases will be close to one or two languages, even though they don't exceed your basic threshold.
Now, once you realize this, you will also see what training your classifier needs: not some random aspect of the sample files, but what sets two languages apart. Hence, when you have parsed your C samples, and your C++ samples, you will see that #include does not set them apart. However, class and template will be far more common in C++. On the other hand, #include does distinguish between C++ and Java.
There are of course other aspects besides keywords that you can use. For instance, the most obvious would be the frequency of {, and ; is similarly distinguishing. Another very useful feature for your classifier would be the comment tokens for the different languages. The basic problem of course would be automatically identifying them. Again, hardcoding //, /*, ', --, # and ! as pseudo-keywords would help.
This also identifies another classification rule: SQL will often have -- at the beginning of a line, whereas in C it will often appear somewhere else. Thus it may be useful for your classifier to take the context into account as well.
Use Google Code Search to learn weights for the set of keywords: #include in C++ gets 672.000 hits, in Python only ~5000.
You can normalize the results by looking at the number of results for the language in total:
C++ gives about 770.000 files whereas Python returns 120.000.
Thus "#include" is extremely rare in Python files, but exists in almost every C++ file. (Now you still have to learn to distinguish C++ and C of course.) All that is left is to do the correct reasoning about probabilities.
You need to get some exclusiveness into your lookup data.
When teaching the programming languages you expect, you should search for words typical for one or few language(s). If a word appears in several code files of the same language but appears in few or none of the other language files, it's a strong suggestion to that language.
So the score of a word could be calculated at the lookup side by selecting the words that are exclusive to a language or a group of languages. Find several of these words and get the intersection of these by adding the scores, and found your language you will have.
In an answer to your other question, someone recommended a naïve Bayes classifier. You should implement this suggestion because the technique is good at separating according to distinguishing features. You mentioned the while keyword, but that's not likely to be useful because so many languages use it—and a Bayes classifier won't treat it as useful.
An interesting part of your problem is how to tokenize an unknown program. Whitespace-separated chunks is a decent rough start, but going meaningfully beyond that will be tricky.