I am trying to create a vector dynamically in dependence of n (for example 1 or 4). If my n is bigger I need to have more values in my vector.
for i=1:(N-n)
yvecT(i)=y(n+i); % Achtung, Zeilenvektor
for k=n:-1:1
F(i-1+n,:)=[-y(i) -y(i-k) u(i) u(i-k)];
end
end
%n=1 F(i,:)=[-y(i) u(i)];
%n=2 F(i,:)=[-y(i) -y(i-1) u(i) u(i-1)];
%n=4 F(i,:)=[-y(i) -y(i-1) -y(i-2) -y(i-3) u(i) u(i-1) u(i-2) u(i-3)];
it is a function used to identify a System....
You should have posted the for-loop (with the if-statements) from the link in the question and stated that you wanted it to work for an arbitary n. That would have made everyone understand your problem. I think the easiest way to do what you do is to use subreferencing. So in case n==2 we do not have
F(i-1,:)=[-y(i) -y(i-1) u(i) u(i-1)];
but rather,
F(i-(n-1),:)=[-y(i:-1:(n-1)) u(i:-1:(n-1))];
This looks messier, but it works for any arbitary n. Some other comments about the code. The variable i is also a function returning the imaginary unit. By naming a variable i you overload this function. The recommended way is to use 1i as an imaginary unit, so it is not critical, but in case you do not necessarily need i as a variable you should consider another name. Also it is easier for us to understand in case you write in english. So in general, prefer comments in english when posting here.
Related
I have some specially-defined arrays in Julia which you can think of being just a composition of many arrays. For example:
type CompositeArray{T}
x::Vector{T}
y::Vector{T}
end
with an indexing scheme
getindex(c::CompositeArray,i::Int) = i <= length(c) ? c.x[i] : c.y[i-length(c.x)]
I do have one caveat: the higher indexing scheme just goes to x itself:
getindex(c::CompositeArray,i::Int...) = c.x[i...]
Now the iterator through these can easily be made as the chain of the iterator on x and then on y. This makes iterating through the values have almost no extra cost. However, can something similar be done for iteration to setindex!?
I was thinking of having a separate dispatch on CartesianIndex{2} just for indexing x vs y and the index, and building an eachindex iterator for that, similar to what CatViews.jl does. However, I'm not certain how that will interact with the i... dispatch, or whether it will be useful in this case.
In addition, will broadcasting automatically use this fast iteration scheme if it's built on eachindex?
Edits:
length(c::CompositeArray) = length(c.x) + length(c.y)
In the real case, x can be any AbstractArray (and thus has a linear index), but since only the linear indexing is used (except for that one user-facing getindex function), the problem really boils down to finding out how to do this with x a Vector.
Making X[CartesianIndex(2,1)] mean something different from X[2,1] is certainly not going to end well. And I would expect similar troubles from the fact that X[100,1] may mean something different from X[100] or if length(X) != prod(size(X)). You're free to break the rules, but you shouldn't be surprised when functions in Base and other packages expect you to follow them.
The safe way to do this would be to make eachindex(::CompositeArray) return a custom iterator over objects that you control entirely. Maybe just throw a wrapper around and forward methods to CartesianRange and CartesianIndex{2} if that data structure is helpful. Then when you get one of these custom index types, you know that SplitIndex(CartesianIndex(1,2)) is indeed intending to refer to the first element in the second array.
For example (in JavaScript):
//Not that I would ever add a method to a base JavaScript prototype...
//(*wink nudge*)...
Array.prototype.lastIndex = function() {
return this.length - 1;
}
console.log(array[array.lastIndex()]);
vs
console.log(array[array.length - 1]);
Technically speaking, the latter method uses one less character, but also utilizes a magic number. Granted, the readability may not really be affected in this case, but magic numbers suck. Which is better practice to use?
I'm of the opinion that 1 and 0 don't really count as "magic numbers" in many cases. When you're referring to the index of the last item (i.e. length - 1), that would definitely be one time where I would not consider 1 a magic number.
Different languages have their own idiomatic ways of accessing the last element of an array, and that should be used. For example, in Groovy that would be:
myArray.last()
While in C, one would very likely do:
my_array[len - 1]
and in Common Lisp, something like:
(first (last my_list))
i agree with #DragoonWraith that 1 is not a magic number. however it's not about magic numbers but about readability. if you need last index use myArray.lastIndex(), if you need last element use myArray.last() or myArray.lastElement(). it's way easier to read and understand than myArray[myArray.length - 1]
My take is that we should be looking for the style which the most programmers will be familiar with. Given that anyone who's been programming for more than a couple weeks in a language with this sort of array syntax (i.e., C-influenced imperative languages) will be comfortable with the idea that arrays use 0-based indexing, I suspect that anyone reading your code will understand what array[array.length-1] means.
The method calls are a bit less standard, and are language-specific, so you'll spend a bit more time understanding that if you're not totally familiar with the language. This alone makes me prefer the length-1 style.
Is there an elegant way to express
val a = Array.fill(2,10) {1}
def do_to_elt(i:Int,j:Int) {
if (a.isDefinedAt(i) && a(i).isDefinedAt(j)) f(a(i)(j))
}
in scala?
I recommend that you not use arrays of arrays for 2D arrays, for three main reasons. First, it allows inconsistency: not all columns (or rows, take your pick) need to be the same size. Second, it is inefficient--you have to follow two pointers instead of one. Third, very few library functions exist that work transparently and usefully on arrays of arrays as 2D arrays.
Given these things, you should either use a library that supports 2D arrays, like scalala, or you should write your own. If you do the latter, among other things, this problem magically goes away.
So in terms of elegance: no, there isn't a way. But beyond that, the path you're starting on contains lots of inelegance; you would probably do best to step off of it quickly.
You just need to check the array at index i with isDefinedAt if it exists:
def do_to_elt(i:Int, j:Int): Unit =
if (a.isDefinedAt(i) && a(i).isDefinedAt(j)) f(a(i)(j))
EDIT: Missed that part about the elegant solution as I focused on the error in the code before your edit.
Concerning elegance: no, per se there is no way to express it in a more elegant way. Some might tell you to use the pimp-my-library-Pattern to make it look more elegant but in fact it does not in this case.
If your only use case is to execute a function with an element of a multidimensional array when the indices are valid then this code does that and you should use it. You could generalize the method by changing the signature of to take the function to apply to the element and maybe a value if the indices are invalid like this:
def do_to_elt[A](i: Int, j: Int)(f: Int => A, g: => A = ()) =
if (a.isDefinedAt(i) && a(i).isDefinedAt(j)) f(a(i)(j)) else g
but I would not change anything beyond this. This also does not look more elegant but widens your use case.
(Also: If you are working with arrays you mostly do that for performance reasons and in that case it might even be better to not use isDefinedAt but perform validity checks based on the length of the arrays.)
An Example
Suppose we have a text to write and could be converted to "uppercase or lowercase", and can be printed "at left, center or right".
Specific case implementation (too many functions)
writeInUpperCaseAndCentered(char *str){//..}
writeInLowerCaseAndCentered(char *str){//..}
writeInUpperCaseAndLeft(char *str){//..}
and so on...
vs
Many Argument function (bad readability and even hard to code without a nice autocompletion IDE)
write( char *str , int toUpper, int centered ){//..}
vs
Context dependent (hard to reuse, hard to code, use of ugly globals, and sometimes even impossible to "detect" a context)
writeComplex (char *str)
{
// analize str and perhaps some global variables and
// (under who knows what rules) put it center/left/right and upper/lowercase
}
And perhaps there are others options..(and are welcome)
The question is:
Is there is any good practice or experience/academic advice for this (recurrent) trilemma ?
EDIT:
What I usually do is to combine "specific case" implementation, with an internal (I mean not in header) general common many-argument function, implementing only used cases, and hiding the ugly code, but I don't know if there is a better way that I don't know. This kind of things make me realize of why OOP was invented.
I'd avoid your first option because as you say the number of function you end up having to implement (though possibly only as macros) can grow out of control. The count doubles when you decide to add italic support, and doubles again for underline.
I'd probably avoid the second option as well. Againg consider what happens when you find it necessary to add support for italics or underlines. Now you need to add another parameter to the function, find all of the cases where you called the function and updated those calls. In short, anoying, though once again you could probably simplify the process with appropriate use of macros.
That leaves the third option. You can actually get some of the benefits of the other alternatives with this using bitflags. For example
#define WRITE_FORMAT_LEFT 1
#define WRITE_FORMAT_RIGHT 2
#define WRITE_FORMAT_CENTER 4
#define WRITE_FORMAT_BOLD 8
#define WRITE_FORMAT_ITALIC 16
....
write(char *string, unsigned int format)
{
if (format & WRITE_FORMAT_LEFT)
{
// write left
}
...
}
EDIT: To answer Greg S.
I think that the biggest improvement is that it means that if I decide, at this point, to add support for underlined text I it takes two steps
Add #define WRITE_FORMAT_UNDERLINE 32 to the header
Add the support for underlines in write().
At this point it can call write(..., ... | WRITE_FORMAT_UNLDERINE) where ever I like. More to the point I don't need to modify pre-existing calls to write, which I would have to do if I added a parameter to its signature.
Another potential benefit is that it allows you do something like the following:
#define WRITE_ALERT_FORMAT (WRITE_FORMAT_CENTER | \
WRITE_FORMAT_BOLD | \
WRITE_FORMAT_ITALIC)
I prefer the argument way.
Because there's going to be some code that all the different scenarios need to use. Making a function out of each scenario will produce code duplication, which is bad.
Instead of using an argument for each different case (toUpper, centered etc..), use a struct. If you need to add more cases then you only need to alter the struct:
typedef struct {
int toUpper;
int centered;
// etc...
} cases;
write( char *str , cases c ){//..}
I'd go for a combination of methods 1 and 2.
Code a method (A) that has all the arguments you need/can think of right now and a "bare" version (B) with no extra arguments. This version can call the first method with the default values. If your language supports it add default arguments. I'd also recommend that you use meaningful names for your arguments and, where possible, enumerations rather than magic numbers or a series of true/false flags. This will make it far easier to read your code and what values are actually being passed without having to look up the method definition.
This gives you a limited set of methods to maintain and 90% of your usages will be the basic method.
If you need to extend the functionality later add a new method with the new arguments and modify (A) to call this. You might want to modify (B) to call this as well, but it's not necessary.
I've run into exactly this situation a number of times -- my preference is none of the above, but instead to use a single formatter object. I can supply it with the number of arguments necessary to specify a particular format.
One major advantage of this is that I can create objects that specify logical formats instead of physical formats. This allows, for example, something like:
Format title = {upper_case, centered, bold};
Format body = {lower_case, left, normal};
write(title, "This is the title");
write(body, "This is some plain text");
Decoupling the logical format from the physical format gives you roughly the same kind of capabilities as a style sheet. If you want to change all your titles from italic to bold-face, change your body style from left justified to fully justified, etc., it becomes relatively easy to do that. With your current code, you're likely to end up searching through all your code and examining "by hand" to figure out whether a particular lower-case, left-justified item is body-text that you want to re-format, or a foot-note that you want to leave alone...
As you already mentioned, one striking point is readability: writeInUpperCaseAndCentered("Foobar!") is much easier to understand than write("Foobar!", true, true), although you could eliminate that problem by using enumerations. On the other hand, having arguments avoids awkward constructions like:
if(foo)
writeInUpperCaseAndCentered("Foobar!");
else if(bar)
writeInLowerCaseAndCentered("Foobar!");
else
...
In my humble opinion, this is a very strong argument (no pun intended) for the argument way.
I suggest more cohesive functions as opposed to superfunctions that can do all kinds of things unless a superfunction is really called for (printf would have been quite awkward if it only printed one type at a time). Signature redundancy should generally not be considered redundant code. Technically speaking it is more code, but you should focus more on eliminating logical redundancies in your code. The result is code that's much easier to maintain with very concise, well-defined behavior. Think of this as the ideal when it seems redundant to write/use multiple functions.
I was thinking to implement MD5 as a code kata and wanted to use BDD to drive the design (I am a BDD newb).
However, the only test I can think of starting with is to pass in an empty string, and the simplest thing that will work is embedding the hash in my program and returning that.
The logical extension of this is that I end up embedding the hash in my solution for every test and switching on the input to decide what to return. Which of course will not result in a working MD5 program.
One of my difficulties is that there should only be one public function:
public static string MD5(input byte[])
And I don't see how to test the internals.
Is my approach completely flawed or is MD5 unsuitable for BDD?
I believe you chose a pretty hard exercise for a BDD code-kata. The thing about code-kata, or what I've understood about it so far, is that you somehow have to see the problem in small incremental steps, so that you can perform these steps in red, green, refactor iterations.
For example, an exercise of finding an element position inside an array, might be like this:
If array is empty, then position is 0, no matter the needle element
Write test. Implementation. Refactor
If array is not empty, and element does not exist, position is -1
Write test. Implementation. Refactor
If array is not empty, and element is the first in list, position is 1
Write test. Implementation. Refactor
I don't really see how to break the MD5 algorithm in that kind of steps. But that may be because I'm not really an algorithm guy. If you better understand the steps involved in the MD5 algorithm, then you may have better chances.
It depends on what you mean with unsuitable... :-) It is suitable if you want to document a few examples that describes your implementation. It should also be possible to have the algorithm emerge from your specifciation if you add one more character for each test.
By just adding a switch statement you're just trying to "cheat the system". Using BDD/TDD does not mean you have to implement stupid things. Also the fact that you have hardcoded hash values as well as a switch statement in your code are clear code smells and should be refactored and removed. That is how your algorithm should emerge because when you see the hard coded values you first remove them (by calculating the value) and then you see that they are all the same so you remove the switch statement.
Also if your question is about finding good katas I would recommend lokking in the Kata catalogue.