Hey I thought I would enter my answer to this even though its late. I think there are some important things to consider first with how strong you wish to have the linking between java and python.
Firstly Do you only want to call functions or do you actually want python code to change the data in your java objects? This is very important. If you only want to call some python code with or without arguments, then that is not very difficult. If your arguments are primitives it makes it even more easy. However if you want to have java class implement member functions in python, which change the data of the java object, then this is not so easy or straight forward.
Secondly are we talking cpython or will jython do? I would say cpython is where its at! I would advocate this is why python is so kool! Having such high abstractions however access to c,c++ when needed. Imagine if you could have that in java. This question is not even worth asking if jython is ok because then it is easy anyway.
So I have played with the following methods, and listed them from easy to difficult:
Java to Jython
Advantages: Trivially easy. Have actual references to java objects
Disadvantages: No CPython, Extremely Slow!
Jython from java is so easy, and if this is really enough then great. However it is very slow and no cpython! Is life worth living without cpython I don't think so! You can easily have python code implementing your member functions for you java objects.
Java to Jython to CPython via Pyro
Pyro is the remote object module for python. You have some object on a cpython interpreter, and you can send it objects which are transferred via serialization and it can also return objects via this method. Note that if you send a serialized python object from jython and then call some functions which change the data in its members, then you will not see those changes in java. You just need to remember to send back the data which you want from pyro. This I believe is the easiest way to get to cpython! You do not need any jni or jna or swig or .... You don't need to know any c, or c++. kool huh?
Advantages: Access to cpython, not as difficult as following methods
Disadvantages: Cannot change the member data of java objects directly from python. Is somewhat indirect, (jython is middle man).
Java to C/C++ via JNI/JNA/SWIG to Python via Embedded interpreter (maybe using BOOST Libraries?)
OMG this method is not for the faint of heart. And I can tell you it has taken me very long to achieve this in with a decent method. Main reason you would want to do this is so that you can run cpython code which as full rein over you java object. There are major major things to consider before deciding to try and bread java (which is like a chimp) with python (which is like a horse). Firstly if you crash the interpreter that's lights out for you program! And don't get me started on concurrency issues! In addition, there is allot allot of boiler, I believe I have found the best configuration to minimize this boiler but still it is allot! So how to go about this: Consider that C++ is your middle man, your objects are actually c++ objects! Good that you know that now. Just write your object as if your program as in cpp not java, with the data you want to access from both worlds. Then you can use the wrapper generator called swig (http://www.swig.org/Doc1.3/Java.html) to make this accessible to java and compile a dll which you call System.load(dll name here) in java. Get this working first, then move on to the hard part! To get to python you need to embed an interpreter. Firstly I suggest doing some hello interpreter programs or this tutorial Embedding python in C/C. Once you have that working, its time to make the horse and the monkey dance! You can send you c++ object to python via [boost][3] . I know I have not given you the fish, merely told you where to find the fish. Some pointers to note for this when compiling.
When you compile boost you will need to compile a shared library. And you need to include and link to the stuff you need from jdk, ie jawt.lib, jvm.lib, (you will also need the client jvm.dll in your path when launching the application) As well as the python27.lib or whatever and the boost_python-vc100-mt-1_55.lib. Then include Python/include, jdk/include, boost and only use shared libraries (dlls) otherwise boost has a teary. And yeah full on I know. There are so many ways in which this can go sour. So make sure you get each thing done block by block. Then put them together.
Jython has some limitations:
There are a number of differences. First, Jython programs cannot use CPython extension modules written in C. These modules usually have files with the extension .so, .pyd or .dll. If you want to use such a module, you should look for an equivalent written in pure Python or Java. Although it is technically feasible to support such extensions - IronPython does so - there are no plans to do so in Jython.
Distributing my Python scripts as JAR files with Jython?
you can simply call python scripts (or bash or Perl scripts) from Java using Runtime or ProcessBuilder and pass output back to Java:
Running a bash shell script in java
java runtime.getruntime() getting output from executing a command line program
This gives a pretty good overview over the current options. Some of which are named in other answers. Jython is not usable until they decide to implement Python 3.x and many of the other projects are coming form the python side and want to access java. But there are a few options still, to name something which has not been named yet: gRPC
It's not smart to have python code inside java. Wrap your python code with flask or other web framework to make it as a microservice. Make your java program able to call this microservice (e.g. via REST).
Beleive me, this is much simple and will save you tons of issues. And the codes are loosely coupled so they are scalable.
Updated on Mar 24th 2020: According to @stx's comment, the above approach is not suitable for massive data transfer between client and server. Here is another approach I recommended: Connecting Python and Java with Rust(C/C++ also ok). https://medium.com/@shmulikamar/https-medium-com-shmulikamar-connecting-python-and-java-with-rust-11c256a1dfb0
Here a library that lets you write your python scripts once and decide which integration method (Jython, CPython/PyPy via Jep and Py4j) to use at runtime:
https://github.com/subes/invesdwin-context-python
Since each method has its own benefits/drawbacks as explained in the link.
It depends on what do you mean by python functions? if they were written in cpython you can not directly call them you will have to use JNI, but if they were written in Jython you can easily call them from java, as jython ultimately generates java byte code.
Now when I say written in cpython or jython it doesn't make much sense because python is python and most code will run on both implementations unless you are using specific libraries which relies on cpython or java.
GraalVM is a good choice. I've done Java+Javascript combination with GraalVM for microservice design (Java with Javascript reflection). They recently added support for python, I'd give it a try especially with how big its community has grown over the years.
Depending on your requirements, options like XML-RPC could be useful, which can be used to remotely call functions virtually in any language supporting the protocol.
You can call any language from java using Java Native Interface
Source: Stackoverflow.com