Mathematical functions on Python 3 - python

I have a work to do on numerical analysis that consists on implementing algorithms for root-finding problems. Among them are the Newton method which calculates values for a function f(x) and it's first derivative on each iteraction.
For that method I need a way to the user of my application enter a (mathematical) function and save it as a variable and use that information to give values of that function on different points. I know just the very basic of Python programming and maybe this is pretty easy, but how can I do it?

If you trust the user, you could input a string, the complete function expression as it would be done in Python, then call eval() on that string. Python itself evaluates the expression. However, the user could use that string to do many things in your program, many of them very nasty such as taking over your computer or deleting files.
If you do not trust the user, you have much more work to do. You could program a "function builder", much like the equation editor in Microsoft Word and similar programs. If you "know just the very basic of Python programming" this is beyond you. You might be able to use a search engine to find one for Python.
One more possibility is to write your own evaluator. That would also be beyond you, and you also might be able to find one you can use.
If you need more detail, show some more work of your own then ask.

Related

Numpy argmax source

I can't seem to find the code for numpy argmax.
The source link in the docs lead me to here, which doesn't have any actual code.
I went through every function that mentions argmax using the github search tool and still no luck. I'm sure I'm missing something.
Can someone lead me in the right direction?
Thanks
Numpy is written in C. It uses a template engine that parsing some comments to generate many versions of the same generic function (typically for many different types). This tool is very helpful to generate fast code since the C language does not provide (proper) templates unlike C++ for example. However, it also make the code more cryptic than necessary since the name of the function is often generated. For example, generic functions names can look like #TYPE#_#OP# where #TYPE# and #OP# are two macros that can take different values each. On top of all of this, the CPython binding also make the code more complex since C functions have to be wrapped to be called from a CPython code with complex arrays (possibly with a high amount of dimensions and custom user types) and CPython arguments to decode.
_PyArray_ArgMinMaxCommon is a quite good entry point but it is only a wrapping function and not the main computing one. It is only useful if you plan to change the prototype of the Numpy function from Python.
The main computational function can be found here. The comment just above the function is the one used to generate the variants of the functions (eg. CDOUBLE_argmax). Note that there are some alternative specific implementation for alternative type below the main one like OBJECT_argmax since CPython objects and strings must be computed a bit differently. Thank you for contributing to Numpy.
As mentioned in the comments, you'll likely find what you are searching in the C code implementation (here under _PyArray_ArgMinMaxCommon). The code itself can be very convoluted, so if your intent was to open an issue on numpy with a broad idea, I would do it on the page you linked anyway.

Visualize Python function flow (e.g. as tree or concept map)

I have taught myself python in quite a haphazard way. So my question perhaps won't be very pythonic.
When I write functions in classes, I often lose overview of what each function does. I do try to name them properly. But still, they are sometimes smaller parts of code where it seems arbitrary in which functions to put them. So whenever I want to make changes, I still need to go through the entire code in order to figure out how my functions actually flow.
From what I understand, we have objects and we have functions, and these are our units for structuring our code. But this only gives you a flat structure. It doesn't allow you to do any kind of nesting, like in a tree diagram, over multiple levels. Especially, the code in my file doesn't automatically water itself so that the functions that are called first and more often automatically further up on the top, whereas helper functions would be automatically further down in the document, or even nested.
In fact, even being able to visually nest lower-order subroutines "inside" a higher-order function that calls it would seem helpful. But it's not something that would be supported by Python's syntax. (Plus, it wouldn't quite suffice, because a sub-routine might be used by several higher-order functions.)
I imagine it would be useful to see all functions in my code visualized as a tree, or as a concept map:
Where each function is a dot. And calling order visualized by arrows. This way, I would also easily see which functions are more central, and which are more outliers, or even orphaned.
Yet perhaps this isn't even a case for another tool. Perhaps this is more a case of me not understanding proper coding. Perhaps there is something I can do differently in order to get the kind of intuitive overview over how my program works, without needing another tool.
Firstly, I am not quite sure why this isn't asked more often. Reading code is not intuitive, at all! We should be able to visualize the evolution of a process or function so well that close to every one will be able to understand its behavior. In the 60s and so, people had to be reasonably sure their programs would run, because getting access to the computer would take time; today we execute or compile our program, run tests if we have them, and get to know immediately whether it works. What happened is there is less mental effort now, we execute a bit less code in our heads, and the computer a bit more. But we must still think of how the program behaves midst execution in order to debug. For the future, it would be nice if the computer could just tell us how the program behaves.
You propose looking at a sort of tree of the program as a resolute, and after all, the abstract syntax tree is literally a tree, but I don't think this is what we ought to spend our efforts on when it comes to visualizing systems. What would be preferable is if we could look at an interactive view of how the problem changes its intermediate data-structures as a function of time.
Currently, we have debuggers--but that's akin to looking at the issue by asking what a function is at many values, when we would much rather look at its graph. A lot of programming is done by doing something you feel is right, observing if the behavior correct, if it's not correct then we make modifications by reacting and correcting said behavior.
Bret Victor in his essay, Learnable Programming, discusses this topic. I highly recommend it, even though it won't help you right now, maybe you can help others in the future by making these ideas more prevalent.
Onwards, then to where I tell you what you can do right now. In his book Clean Code, Robert C. Martin proposes structuring code much like how a newspaper is laid out.
Think of a well-written newspaper article. You read it vertically. At the top you expect a headline that will tell you what the story is about and allows you to decide whether it is something you want to read. The first paragraph gives you a synopsis of the whole story, hiding all the details while giving you the broad-brush concepts. As you continue downward, the details increase until you have all the dates, names, quotes, claims, and other minutia.
What is proposed, is to organize your program top-down, with higher level procedures that call mid-level procedures, which in turn call the lower level procedures. At any place, it should be obvious that (1) you are at the appropriate level of abstraction, and (2) you are looking at the part of the program implementing the behavior you seek to modify.
This means storing state at the level where it belongs, and exposing it anywhere else. Procedures should take only the parameters they need, because more parameters means you must also think about more parameters when reasoning about the code.
This is the primary reason for decomposing procedures into smaller procedures. For example, here some code I've written previously. It's not perfect, but you can see very clearly which part of the program you need to go to if you want to change anything.
Of course, higher order procedures are listed before any other. I'm telling you what I'm going to do, before I show you how I do it.
function formatLinks(matches, stripped) {
let formatted_links = []
for (match of matches) {
let diff = difference(match, stripped)
if (isSimpleLink(diff)) {
formatted_links.push(formatAsSimpleLink(diff))
} else if (hasPrefix(diff)) {
formatted_links.push(formatAsPrefixedLink(diff))
} else if (hasSuffix(diff)) {
formatted_links.push(formatAsSuffixedLink(diff))
}
}
// There might be multiple links within a word
// in which case we join them and strip any duplicated parts
// (which are otherwise interpreted as suffixes)
if (formatted_links.length > 1) {
return combineLinks(formatted_links)
}
// Default case
return formatted_links[0]
}
If JavaScript was a typed language, and if we could see an image of the decisions made in the code, as a factor of input and time, this could be even better.
I think Quokka.js and VS Code Debug Visualizer are both doing interesting work in this sector.

Sympy thinks the same variable is two different variables

Sorry for the messy title, but let me explain. I have a long code doing a bunch of manipulations on an expressions including (among others) a function f=sp.Function('f')(x,y). My end result is some huge expression, but I noted that there are terms that look like
f^3(x,y)f(x,y)-f^4(x,y)
and it completely fails to simplify this to zero. This makes the expressions much longer than they should be and thus very had to handle. Does anyone recognize this problem? How can I force sympy to know that f and f are the same function?
I can not provide a working example since the code is very long, and I was not able to identify a small subcode that gives the same problem. If you need the output or have some idea how I can manipulate the output to identify what the problem is, please tell me.
Thanks.
Try using simplify function on the end result.

alternative to sympy's simplify function

I've been using the simplify function in Sympy to simplify some long complicated equations, but it's not proving sufficient, as it frequently does not simplify things as much as possible, giving my program numerical errors when it comes to solving the equations.
Does anyone know of any other symbolic engines with a simplify function that can be used instead?
Many thanks.
Maybe you use python's subprocess module to run maxima on behalf of your python program? This is what maxima-mode on Emacs does, just do something similar. Start maxima, keep file handles to it's input/output, feed it with equations and let it mangle them to your desire (Maxima has lots of equation-changing functions), and read back the result from the output file handle.
Sympy vs. Maxima
pyMaxima

Syntax recognizer in python

I need a module or strategy for detecting that a piece of data is written in a programming language, not syntax highlighting where the user specifically chooses a syntax to highlight. My question has two levels, I would greatly appreciate any help, so:
Is there any package in python that receives a string(piece of data) and returns if it belongs to any programming language syntax ?
I don't necessarily need to recognize the syntax, but know if the string is source code or not at all.
Any clues are deeply appreciated.
Maybe you can use existing multi-language syntax highlighters. Many of them can detect language a file is written in.
You could have a look at methods around baysian filtering.
My answer somewhat depends on the amount of code you're going to be given. If you're going to be given 30+ lines of code, it should be fairly easy to identify some unique features of each language that are fairly common. For example, tell the program that if anything matches an expression like from * import * then it's Python (I'm not 100% sure that phrasing is unique to Python, but you get the gist). Other things you could look at that are usually slightly different would be class definition (i.e. Python always starts with 'class', C will start with a definition of the return so you could check to see if there is a line that starts with a data type and has the formatting of a method declaration), conditionals are usually formatted slightly differently, etc, etc. If you wanted to make it more accurate, you could introduce some sort of weighting system, features that are more unique and less likely to be the result of a mismatched regexp get a higher weight, things that are commonly mismatched get a lower weight for the language, and just calculate which language has the highest composite score at the end. You could also define features that you feel are 100% unique, and tell it that as soon as it hits one of those, to stop parsing because it knows the answer (things like the shebang line).
This would, of course, involve you knowing enough about the languages you want to identify to find unique features to look for, or being able to find people that do know unique structures that would help.
If you're given less than 30 or so lines of code, your answers from parsing like that are going to be far less accurate, in that case the easiest best way to do it would probably be to take an appliance similar to Travis, and just run the code in each language (in a VM of course). If the code runs successfully in a language, you have your answer. If not, you would need a list of errors that are "acceptable" (as in they are errors in the way the code was written, not in the interpreter). It's not a great solution, but at some point your code sample will just be too short to give an accurate answer.

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