Wikipedia has listed a variety of numerical methods for computing cumulative probability of a normal distribution. However, with Apache Commons Math you do not need know about any of them as the library simply does the job for you:
NormalDistribution normal = new NormalDistribution(mu, sigma);
normal.cumulativeProbability(x);
For some research project, I'm interested to know what method they use. Does anyone know what method Apache Commons Math uses to approximate the normal cumulative value? Is it from the methods listed in wikipedia or they have implemented something different?
The beauty of open source software is that you can always check the source code. The implementation of cumulativeProbability is rather simple, it just returns
0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
where Erf.erf computes the error function. It's defined here.
And no, it doesn' use any of the special methods in the mentioned Wikipedia article. It's just a straight-forward implementation of the formula
You can probably see the source code or the javadoc. See there http://commons.apache.org/proper/commons-math/source-repository.html
and
http://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math3/distribution/NormalDistribution.html
Also, there is alot of information in the user's guide. The section about distribution seems interesting: http://commons.apache.org/proper/commons-math/userguide/distribution.html
Related
I have 3 points [x0 y0], [x1 y1], [x2 y2] with strict conditional x0<x1<x2, y0<y1<y2. All this points lay on some exponentional functions y=ae^(bx)+c. I need to find a,b,c... It's not possible to solve system of 3 equations precisely, therefore I need to approximate it. Is there some math library in java that will help me solve this problem? I find something similar on mathcad
https://help.ptc.com/mathcad/en/index.html#page/PTC_Mathcad_Help/exponential_regression.html but not find in java.
Other way - how to solve system of 3 equations and 3 values approximately.
ae^(bx_0)+c=y_0
ae^(bx_1)+c=y_1
ae^(bx_2)+c=y_2
You have to solve a system of non-linear equations, for which only an approximate solution is possible but can be done using the Newton Raphson's Multivariate method.
The algorithm is, quite frankly, a notational pain but you can go through it here -
http://fourier.eng.hmc.edu/e176/lectures/NM/node21.html.
What is happening essentially is you have a function whose derivative lead you to an 'equilibrium' from an initial random point (which you guess as a possible root)
If you are not willing to write the code yourself this repo can give you a starter of sorts - https://github.com/prasser/newtonraphson.
But AFAIK, no ready library exists for this purpose. You can use Wolfram's Mathematica or MATLAB/OCTAVE for ready libraries though.
That said, here are a few other (more complicated) things you can look into
https://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm
https://www1.fpl.fs.fed.us/optimization.html
http://icl.cs.utk.edu/f2j/
http://optalgtoolkit.sourceforge.net/
http://scribblethink.org/Computer/Javanumeric/index.html
https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin_l_bfgs_b.html
Hope this helps!
div(1, sum(1, exp(sum(div(5, product(100, .1)), -5))))
I'm using this in a Solr query, and want to verify that it is the same as :
Where x is 5.
Is this language Java?
If it is, why am I getting this output here:
http://ideone.com/LWYWtU
If it isn't, what language is this and how do I test it?
Thanks in advance for your help.
EDIT: To add more of the surrounding code, here is the full boost value I'm sending to Solr:
if(exists(query({!frange l=0 u=60 v=product(geodist(),0.621371)})),div(1, sum(1, exp(sum(div(product(5), product(100, .1)), -5)))),0)
The reason I think it might be Java is because in the docs, it says Most Java Math functions are now supported, including: and then lists the math functions I ended up using for code.
Solr is Java, but that's not relevant since this is a set of functions that Solr parses and evaluate itself (and not related to Java, except that the backing functions are implemented in Java).
As far as I can say from what you've mapped the functions correctly, as long as the 5 in product(5) is the same as X. You shouldn't need product there, as the value can be included in div directly as far as I can see.
A way to validate it would be to use debugQuery in Solr and see what the value is evaluated as, and then compare it to your own value. Remember that floating point evaluation can introduce a few uncertanities.
I'm looking for a Java library to solve this problem:
We know X is sparse(most of it's entries are zero), so X can be recovered by solving this:
variable X;
minimize(norm(X,1)+norm(A*X - Y,2));
It's a MATLAB code, matrix A and vector Y are known and I want the best X.
I saw JOptimizer, but I couldn't use it. (Doesn't have good documentation or examples).
What you need is a reasonably good LP Solver.
Possible Java LP Solver Options
Apache Commons (Math) Simplex Solver.
See this blog post.
If you have access to CPLEX (not-free), its Java API would work great.
Also, you can look into SuanShu, a Java numerical and statistical library
lpSolve has a Java wrapper which can do the job.
Finally, JOptimizer is indeed a good option. Not sure if you looked at this example.
Hope at least one of those help.
As far as I can tell, you're trying to solve a binary integer program for feasibility
Ax = b, x in {0,1}.
I'm not completely sure, but it seems that you might be interested in the optimization problem
min 1'*x
s.t. Ax = b, x in {0,1}
where 1 is a vector of 1's of the same dimension as x.
The feasibility problem may be in practice much easier than the optimization problem - it all depends on a particular A and b.
If you can get a license of either CPLEX or Gurobi (if you're an academic), these are excellent integer programming solvers with good Java API's. If you don't have access to these, lpsolve may be a good option.
As far as I can tell, JOptimizer will not solve your problem since your variables are integers (although I have never used JOptimizer).
To solve convex optimization problems in java you can use the following library https://github.com/erikerlandson/gibbous
I am having a hard time understanding how to use DerivativeStructure in Apache Commons Math.
I have a Logit function for which I would like to get the first order derivative. Then I would like to get the value of that derivative on multiple distinct values.
Logit logit = new Logit(0.1, 10.0);
DerivativeStructure ds = // How to instanctiate?
DerivativeStructure dsRes = logit.value(ds);
// How to use dsRes to get the value of the derivative function applied on
// several values?
In addition, if there is any document describing how to use that DerivativeStructure, I am highly interested!
Thanks for your help.
In the Apache Commons Math User Guide, the section on Numerical analysis Differentiation, there is a reasonable introduction on how to apply the DerivativeStructure.
Are there any Java API(s) which will provide plural form of English words (e.g. cacti for cactus)?
Check Evo Inflector which implements English pluralization algorithm based on Damian Conway paper "An Algorithmic Approach to English Pluralization".
The library is tested against data from Wiktionary and reports 100% success rate for 1000 most used English words and 70% success rate for all the words listed in Wiktionary.
If you want even more accuracy you can take Wiktionary dump and parse it to create the database of singular to plural mappings. Take into account that due to the open nature of Wiktionary some data there might by incorrect.
Example Usage:
English.plural("Facility", 1)); // == "Facility"
English.plural("Facility", 2)); // == "Facilities"
jibx-tools provides a convenient pluralizer/depluralizer.
Groovy test:
NameConverter nameTools = new DefaultNameConverter();
assert nameTools.depluralize("apples") == "apple"
nameTools.pluralize("apple") == "apples"
I know there is simple pluralize() function in Ruby on Rails, maybe you could get that through JRuby. The problem really isn't easy, I saw pages of rules on how to pluralize and it wasn't even complete. Some rules are not algorithmic - they depend on stem origin etc. which isn't easily obtained. So you have to decide how perfect you want to be.
considering java, have a look at modeshapes Inflector-Class as member of the package org.modeshape.common.text. Or google for "inflector" and "randall hauch".
Its hard to find this kind of API. rather you need to find out some websservice which can serve your purpose. Check this. I am not sure if this can help you..
(I tried to put word cacti and got cactus somewhere in the response).
If you can harness javascript, I created a lightweight (7.19 KB) javascript for this. Or you could port my script over to Java. Very easy to use:
pluralizer.run('goose') --> 'geese'
pluralizer.run('deer') --> 'deer'
pluralizer.run('can') --> 'cans'
https://github.com/rhroyston/pluralizer-js
BTW: It looks like cacti to cactus is a super special conversion (most ppl are going to say '1 cactus' anyway). Easy to add that if you want to. The source code is easy to read / update.
Wolfram|Alpha return a list of inflection forms for a given word.
See this as an example:
http://www.wolframalpha.com/input/?i=word+cactus+inflected+forms
And here is their API:
http://products.wolframalpha.com/api/