I know that tan(angle) gets me the tangent. But how do I do the "reverse tangent" so that I can get the angle given the length of both sides of the right triangle?
I'm assuming there is a method for this in math.h?
As others have mentioned, atan() is what you're looking for. Generally, the operation is referred to as "inverse tangent" or "arc tangent", not "reverse tangent". The name "atan" comes from "arc tangent". There's also an atan2() function which takes both the X and the Y coordinates as separate paramters and will give you an angle relative to the 0 mark whereas atan() will leave figuring out the quadrant as an exercise for the developer. Beware, however, that the atan2() function on certain older MS environments (or maybe visual studio libraries?) doesn't work quite right...
There should be an atan() function.
For example: http://www.acm.uiuc.edu/webmonkeys/book/c_guide/2.7.html
use atan()
Related
I've recently encountered these two variables in some Velocity code:
$!variable1
!$variable2
I was surprised by the similarity of these so I became suspicious about the correctness of the code and become interested in finding the difference between two.
Is it possible that velocity allows any order of these two symbols or do they have different purpose? Do you know the answer?
#Jr. Here is the guide I followed when doing VM R&D: http://velocity.apache.org/engine/1.7/user-guide.html
Velocity uses the !$ and $! annotations for different things. If you use !$ it will basically be the same as a normal "!" operator, but the $! is used as a basic check to see if the variable is blank and if so it prints it out as an empty string. If your variable is empty or null and you don't use the $! annotation it will print the actual variable name as a string.
I googled and stackoverflowed a lot before I finally found the answer at people.apache.org.
According to that:
It is very easy to confuse the quiet reference notation with the
boolean not-Operator. Using the not-Operator, you use !${foo}, while
the quiet reference notation is $!{foo}. And yes, you will end up
sometimes with !$!{foo}...
Easy after all, shame it didn't struck me immediately. Hope this helps someone.
I am trying to solve a problem involving the equating of sums of exponentials.
This is how I would do it hardcoded:
#NLconstraint(m, exp(x[25])==exp(x[14])+exp(x[18]))
This works fine with the rest of the code. However, when I try to do it for an arbitrary set of equations like the above I get an error. Here's my code:
#NLconstraint(m,[k=1:length(LHSSum)],sum(exp.(LHSSum[k][i]) for i=1:length(LHSSum[k]))==sum(exp.(RHSSum[k][i]) for i=1:length(RHSSum[k])))
where LHSSum and RHSSum are arrays containing arrays of the elements that need to be exponentiated and then summed over. That is LHSSum[1]=[x[1],x[2],x[3],...,x[n]]. Where x[i] are variables of type JuMP.Variable. Note that length(LHSSum)=length(RHSSum).
The error returned is:
LoadError: exp is not defined for type Variable. Are you trying to build a nonlinear problem? Make sure you use #NLconstraint/#NLobjective.
So a simple solution would be to simply do all the exponentiating and summing outside of the #NLconstraint function, so the input would be a scalar. However, this too presents a problem since exp(x) is not defined since x is of type JuMP.variable, whereas exp expects something of type real. This is strange since I am able to calculate exponentials just fine when the function is called within an #NLconstraint(). I.e. when I code this line#NLconstraint(m,exp(x)==exp(z)+exp(y)) instead of the earlier line, no errors are thrown.
Another thing I thought to do would be a Taylor Series expansion, but this too presents a problem since it goes into #NLconstraint land for powers greater than 2, and then I get stuck with the same vectorization problem.
So I feel stuck, I feel like if JuMP would allow for the vectorized evaluation of #NLconstraint like it does for #constraint, this would not even be an issue. Another fix would be if JuMP implements it's own exp function to allow for the exponentiation of JuMP.Variable type. However, as it is I don't see a way to solve this problem in general using the JuMP framework. Do any of you have any solutions to this problem? Any clever workarounds that I am missing?
I'm confused why i isn't used in the expressions you wrote. Do you mean:
#NLconstraint(m, [k = 1:length(LHSSum)],
sum(exp(LHSSum[k][i]) for i in 1:length(LHSSum[k]))
==
sum(exp(RHSSum[k][i]) for i in 1:length(RHSSum[k])))
Do you think x, y, z are good variable names? How will you explain a new programmer to write readable code?
Readable code means some combination of comments and variable and function naming that allows me to read the code once and understand it. If I have to read it more than once, or spend my time working through complicated loops or functions, there's room for improvement.
Good summary descriptions at the top of files and classes are useful to give the reader context and background information.
Clear names are important. Verbose names make it much easier to write readable code with far fewer comments.
Writing readable code is a skill that takes some time to learn. I personally like overly verbose names because they create self documenting code.
As already stated x, y, and z are good variables for 3D coordinates but probably bad for anything else...
If someone does not believe that names are important, just use a code obfuscator on some code then ask them to debug it :-).
(BTW that's the only situation where a code obfuscator can be useful IMHO)
There seems to be slightly different conventions per progamming language; however, the consensus these days is to...
use pascal case
make the name meaningful
end with a noun
Here is a decent recap of what Microsoft publishes as standard naming conventions for .NET
The inventor of python has published a style guide which includes naming conventions.
There was a time when Microsoft VC++ developers (myself included) actually rallied around what was known as Hungarian Notation
Certainly there are multiple schools of thought on this, but I would only use these for counters, and advise far more descriptive names for any other variables.
x, y and z can be perfectly good variable names. For example you might be writing code that refers to them in reference to a 3D cartesian coordinate system. These names are often used for the three axes in such a system and as such they would be well suited.
I would give them some maintenance work on some code with variables called x, y, z and let them realise for themselves that readability is vital...
95% of code viewing is not by the author, but by the customer that everyone forgets about - the next programmer. You owe it to her to make her life easy.
Good variable names describe exactly what they are without being overly complex. I always use descriptive names, even in loops (for instance, index instead of i). It helps keep track of what's going on, especially when I'm working on rewriting a particularly complex piece of code.
Well give them a chunk of bad code and ask them to debug it.
Take the following code (simple example)
<?php $a = fopen('/path/to/file.ext', 'w');$b = "NEW LINE\n";fwrite($a, $b);fclose($a);?>
The bug is: File only ever contains 1 line when it should be a log
Problem: 'w' in fopen should be 'a'
This obviously is a super easy example, if you want to give them a bigger more complicated example give them the WMD source and ask them to give you readable code in 2 hours, it will get your point across.
As long as x, y and z are (3D) Cartesian co-ordinates, then they're great names.
In a similar vein, i, j and k would be OK for loop variables.
In all cases, the variable names should relate to the data
x,y and z are acceptable variable names if they represent 3d coordinates, or if they're used for iterating over 2 or 3 dimensional arrays.
This code is fine as far as I'm concerned:
for(int x = 0; x < xsize ; x++)
{
for(int y = 0; y < ysize ; y++)
{
for(int z = 0; z < zsize ; z++)
{
DoSomething(data[x][y][z]);
...
This one is a short answer, but it works very well for me:
If it would need a code comment to describe it, then rethink the variable name.
So if it's obvious, why "x" was choosen, then they are good names. E.g. "i" as variable name in a loop is (often) pretty obvious.
An ideal variable name is both short (to make the code more compact) and descriptive (to help understanding the code).
Opinions differ on which of the two is more important. Personally, I'd say it depends on the scope of the variable. A variable used only inside a 3 line loop can get away with being single letter. A class field in a 500 line class better be pretty damn descriptive. The Spartan Programming philosophy says that as far as possible, all units of code should be small enough that variable names can be very short.
Readable code and good naming conventions are not the same thing!
A good name for a variable is one that allows you to understand (or reasonably guess) the purpose and type of the variable WITHOUT seeing the context in which it is used. Thus, "x" "y" and "z" say coordinates because that is a reasonable guess. Conversely, a bad name is one that leads you to a wrong likely guess. For example, if "x" "y" and "z" represent people.
A good name for a function is one that conveys everything you would need to know about it without having to consult its documentation. That is not always possible.
Readable code is first of all code whose structured could be understood even if you obfuscated all variable and function names. If you do that and can't figure out the control structure easily, you're screwed.
Once you have readable code and good naming, then maybe you'll have truly readable code.
In algebra if I make the statement x + y = 3, the variables I used will hold the values either 2 and 1 or 1 and 2. I know that assignment in programming is not the same thing, but I got to wondering. If I wanted to represent the value of, say, a quantumly weird particle, I would want my variable to have two values at the same time and to have it resolve into one or the other later. Or maybe I'm just dreaming?
Is it possible to say something like i = 3 or 2;?
This is one of the features planned for Perl 6 (junctions), with syntax that should look like my $a = 1|2|3;
If ever implemented, it would work intuitively, like $a==1 being true at the same time as $a==2. Also, for example, $a+1 would give you a value of 2|3|4.
This feature is actually available in Perl5 as well through Perl6::Junction and Quantum::Superpositions modules, but without the syntax sugar (through 'functions' all and any).
At least for comparison (b < any(1,2,3)) it was also available in Microsoft Cω experimental language, however it was not documented anywhere (I just tried it when I was looking at Cω and it just worked).
You can't do this with native types, but there's nothing stopping you from creating a variable object (presuming you are using an OO language) which has a range of values or even a probability density function rather than an actual value.
You will also need to define all the mathematical operators between your variables and your variables and native scalars. Same goes for the equality and assignment operators.
numpy arrays do something similar for vectors and matrices.
That's also the kind of thing you can do in Prolog. You define rules that constraint your variables and then let Prolog resolve them ...
It takes some time to get used to it, but it is wonderful for certain problems once you know how to use it ...
Damien Conways Quantum::Superpositions might do what you want,
https://metacpan.org/pod/Quantum::Superpositions
You might need your crack-pipe however.
What you're asking seems to be how to implement a Fuzzy Logic system. These have been around for some time and you can undoubtedly pick up a library for the common programming languages quite easily.
You could use a struct and handle the operations manualy. Otherwise, no a variable only has 1 value at a time.
A variable is nothing more than an address into memory. That means a variable describes exactly one place in memory (length depending on the type). So as long as we have no "quantum memory" (and we dont have it, and it doesnt look like we will have it in near future), the answer is a NO.
If you want to program and to modell this behaviour, your way would be to use a an array (with length equal to the number of max. multiple values). With this comes the increased runtime, hence the computations must be done on each of the values (e.g. x+y, must compute with 2 different values x1+y1, x2+y2, x1+y2 and x2+y1).
In Perl , you can .
If you use Scalar::Util , you can have a var take 2 values . One if it's used in string context , and another if it's used in a numerical context .
In this question, a user commented to never use the With block in VB. Why?
"Never" is a strong word.
I think it fine as long as you don't abuse it (like nesting)
IMHO - this is better:
With MyCommand.Parameters
.Count = 1
.Item(0).ParameterName = "#baz"
.Item(0).Value = fuz
End With
Than:
MyCommand.Parameters.Count = 1
MyCommand.Parameters.Item(0).ParameterName = "#baz"
MyCommand.Parameters.Item(0).Value = fuz
There is nothing wrong about the With keyword. It's true that it may reduce readibility when nested but the solution is simply don't use nested With.
There may be namespace problems in Delphi, which doesn't enforce a leading dot but that issue simply doesn't exist in VB.NET so the people that are posting rants about Delphi are losing their time in this question.
I think the real reason many people don't like the With keyword is that is not included in C* languages and many programmers automatically think that every feature not included in his/her favourite language is bad.
It's just not helpful compared to other options.
If you really miss it you can create a one or two character alias for your object instead. The alias only takes one line to setup, rather than two for the With block (With + End With lines).
The alias also gives you a quick mouse-over reference for the type of the variable. It provides a hook for the IDE to help you jump back to the top of the block if you want (though if the block is that large you have other problems). It can be passed as an argument to functions. And you can use it to reference an index property.
So we have an alternative that gives more function with less code.
Also see this question:
Why is the with() construct not included in C#, when it is really cool in VB.NET?
The with keyword is only sideswiped in a passing reference here in an hilarious article by the wonderful Verity Stob, but it's worth it for the vitriol: See the paragraph that starts
While we are on identifier confusion. The with keyword...
Worth reading the entire article!
The With keyword also provides another benefit - the object(s) in the With statement only need to be "qualified" once, which can improve performance. Check out the information on MSDN here:
http://msdn.microsoft.com/en-us/library/wc500chb(VS.80).aspx
So by all means, use it.