The "for a=SomeArray" code template works well for iterating through arrays (e.g. number, characters, cells). It doesn't work for an array of axes e.g.,
faxes=get(gcf,'Children')
class(faxes)
for a=faxes
class(a)
size(a)
end
You bascially need to explicitly index into faxes using a counter. If that was not the case, you'd be able to avoid faxes and the indexing variable, leading to much simpler code. Is there some coding detail that I'm missing that prevents this?
I've posted this to:
Usenet
Stack Overflow
According to Usenet, the array faxes needs to be a row vector. Since get(gcf,'Children') is a column vector, it needs to be transposed:
faxes=get(gcf,'Children')
class(faxes)
for a=faxes'
class(a)
size(a)
end
Related
Based on my earlier question, I understand the benefit of using stack allocation. Suppose I have an array of arrays. For example, A is a list of matrices and each element A[i] is a 1x3 matrix. The length of A and the dimension of A[i] are known at run time (given by the user). Each A[i] is a matrix of Float64 and this is also known at run time. However, through out the program, I will be modifying the values of A[i] element by element. What data structure can also allow me to use stack allocation? I tried StaticArrays but it doesn't allow me to modify a static array.
StaticArrays defines MArray (MVector, MMatrix) types that are fixed-size and mutable. If you use these there's a higher chance of the compiler determining that they can be stack-allocated, but it's not guaranteed. Moreover, since the pattern you're using is that you're passing the mutable state vector into a function which presumably modifies it, it's not going to be valid or helpful to stack allocate that anyway. If you're going to allocate state once and modify it throughout the program, it doesn't really matter if it is heap or stack allocated—stack allocation is only a big win for objects that are allocated, used locally and then don't escape the local scope, so they can be “freed” simply by popping the stack.
From the code snippet you showed in the linked question, the state vector is allocated in the outer function, test_for_loop, which shouldn't be a big deal since it's done once at the beginning of execution. Using a variably sized state vector to index into an array with a splat (...) might be an issue, however, and that's done in test_function. Using something with fixed size like MVector might be better for that. It might, however, be better still, to use a state tuple and return a new rather than mutated state tuple at the end. The compiler is very good at turning that kind of thing into very efficient code because of immutability.
Note that by convention test_function should be called test_function! since it modifies its M argument and even more so if it modifies the state vector.
I would also note that this isn't a great question/answer pair since it's not standalone at all and really just a continuation of your other question. StackOverflow isn't very good for this kind of iterative question/discussion interaction, I'm afraid.
In Maple, I have a matrix N and its elements N[i,j], If I modify the elements of this matrix as follows for example
>for j from 1 to 4 do
>print(F[i,j]=(diff(N[i,j],x)));
>od;od;
where the matrix elements are functions of x.
I've wanted to define new matrix elements
>BA[i,j]:=(diff(N[i,j],x)));
but I can't do this with Maple, through the above command. Can someone help me ?
Better than using a loop is simply BA:= diff~(N,x). The ~ can be appended to any operator to mean "apply the operator to each member of the container and return a new container containing the modified members."
Also, be careful about using print. Its only purpose is to print stuff on the screen from the middle (not the end) of a computation. It can't be used to change any stored values. Good programs use print very sparingly, if at all. The end result of a computation is displayed automatically, without needing a print command.
I know i will look like a total noob, but there's something I can't wrap my head around. Let me emphasize that i DID google this thing, but i didn't find what I was looking for.
I'm going through the learnrubythehardway course, and for ex39 this is one of the functions we have defined:
def Dict.hash_key(aDict, key)
return key.hash % aDict.length
end
The author gives this explanation:
hash_key
This deceptively simple function is the core of how a hash works. What it does is uses the built-in Ruby hash function to convert a
string to a number. Ruby uses this function for its own hash data
structure, and I'm just reusing it. You should fire up a Ruby console
to see how it works. Once I have a number for the key, I then use the
% (modulus) operator and the aDict.length to get a bucket where this
key can go. As you should know, the % (modulus) operator will divide
any number and give me the remainder. I can also use this as a way of
limiting giant numbers to a fixed smaller set of other numbers. If you
don't get this then use Ruby to explore it
I like this course, but the above paragraph was no help.
Ok, you call the function passing it two arguments (aDict is an array) and it returns something.
(My questions are not totally independent of one another.)
What and how does it do that? (ok, it returns a bucket index, but how do we "get there"?)
What does the key.hash do/what is it?
How does using the % help me get what I need? (What is the use of "modding" the key.hash by the aDict.length?)
"Use Ruby to explore it." - ok, but my question No.2. kinda already suggests that I wouldn't know how to go about doing that.
Thanks in advance.
key.hash is calling Object#hash, which is not to be confused with Hash.
Object#hash converts a string into a number consistently (the same string will always result in the same number, in the same running instance of Ruby).
pry(main)> "abc".hash
=> -1672853150
So now we have a number, but it's way too large for the number of buckets in our Dict structure, which defaults to 256 buckets. So we modulus it to get a number within our bucket range.
pry(main)> "abc".hash % 256
=> 98
This essentially allows us to translate Dict["abc"] into aDict[98].
RE: This example in particular
I'm going to change the order of things in a way that I hope makes more sense:
#2. You can think of a hash as a sort of 'fingerprint' of something. The .hash method will create a (generally) unique output for any given input.
#3. In this case, we know that the hash is a number, so we take the modulo of the generated number by the backing array's length in order to find a (hopefully empty) index that is within our storage's bounds.
#1. That's how. A hashing algorithm will return the same output for any given input. The modulo takes this output and turns it into something we can actually use in an array to find something reliably.
#4. Call hash on something. Call it on a string and then modulo it by the length of an array. Try again on another string. Do that again, and use your result to assign something to that array. Do it again to see that the hash and modulo thing will find that value again.
Further Notes:
By itself, the modulo function is not a good way to pick unique indexes for keys. This example is the first step, but especially in a small array, there is still a relatively large chance for the hashes of different keys to modulo into the same number. That's called a collision, and handling those seems to be outside the scope of this question.
I'm trying to create a 2d array where, when I access an index, will return the value. However, if an undefined index is accessed, it calls a callback and fills the index with that value, and then returns the value.
The array will have negative indexes, too, but I can overcome that by using 4 arrays (one for each quadrant around 0,0).
You can create a Matrix class that relies on tuples and dictionary, with the following behavior :
from collections import namedtuple
2DMatrixEntry = namedtuple("2DMatrixEntry", "x", "y", "value")
matrix = new dict()
defaultValue = 0
# add entry at 0;1
matrix[2DMatrixEntry(0,1)] = 10.0
# get value at 0;1
key = 2DMatrixEntry(0,1)
value = {defaultValue,matrix[key]}[key in matrix]
Cheers
This question is probably too broad for stackoverflow. - There is not a generic "one size fits all" solution for this, and the results depend a lot on the language used (and standard library).
There are several problems in this question. First of all let us consider a 2d array, we say this is simply already part of the language and that such an array grows dynamically on access. If this isn't the case, the question becomes really language dependent.
Now often when allocating memory the language automatically initializes the spots (again language dependent on how this happens and what the best method is, look into RAII). Though I can foresee that actual calculation of the specific cell might be costly (compared to allocation). In that case an interesting thing might be so called "two-phase construction". The array has to be filled with tuples/objects. The default construction of an object sets a bit/boolean to false - indicating that the value is not ready. Then on acces (ie a get() method or a operator() - language dependent) if this bit is false it constructs, else it just reads.
Another method is to use a dictionary/key-value map. Where the key would be the coordinates and the value the value. This has the advantage that the problem of construct-on-access is inherit to the datastructure (though again language dependent). The drawback of using maps however is that lookup speed of a value changes from O(1) to O(logn). (The actual time is widely different depending on the language though).
At last I hope you understand that how to do this depends on more specific requirements, the language you used and other libraries. In the end there is only a single data structure that is in each language: a long sequence of unallocated values. Anything more advanced than that depends on the language.
I'm looking for an algorithm that can do a one-to-one mapping of a string onto another string.
I want an algorithm that given an alphabet I can perform a symmetric mapping function.
For example:
Let's consider that I have the alphabet "A","B","C","D","E","F". I want something like F("ABC") = "CEA" and F("CEA") = "ABC" for every N letter permutation.
Surely, an algorithm like this exists. If you know of an algorithm, please post the name of it and I can research it. If I haven't been clear enough in my request, please let me know.
Thanks in advance.
Edit 1:
I should clarify that I want enough entropy so that F("ABC") would equal "CEA" and F("CEA") = "ABC" but then I do NOT want F("ABD") to equal "CEF". Notice how two input letters stayed the same and the two corresponding output letters stayed the same?
So a Caesar Cipher/ROT13 or shuffling the array would not be sufficient. However, I don't need any "real" security. Just enough entropy for the output of the function to appear random. Weak encryption algorithms welcome.
Just create an array of objects that contain 2 fields -- a letter, and a random number. Sort the array. By the random numbers. This creates a mapping where the i-th letter of the alphabet now maps to the i-th letter in the array.
If simple transposition or substitution isn't quite enough, it sounds like you want to advance to a polyalphabetic cipher. The Vigenère cipher is extremely easy to implement in code, but is still difficult to break without using a computer.
I suggest the following.
Perform a dense coding of the input to positive integers - with an alphabet size of n and string length of m you can code the string into integers between zero and n^m - 1. In your example this would be the range [0,215]. Now perform a fixed involution on the encoded number and decode it again.
Take RC4, settle for some password, and you're done. (Not that this would be very safe.)
Take the set of all permutations of your alphabet, shuffle it, and map the first half of the set onto the second half. Bad for large alphabets, of course. :)
Nah, thought that over, I forgot about character repetitions. Maybe divide the input into chunks without repeating chars and apply my suggestion to all of those chunks.
I would restate your problem thus, and give you a strategy for that restatement:
"A substitution cypher where a change in input leads to a larger change in output".
The blocking of characters is irrelevant-- in the end, it's just mappings between numbers. I'll speak of letters here, but you can extend it to any block of n characters.
One of the easiest routes for this is a rotating substitution based on input. Since you already looked at the Vigenere cipher, it should be easy to understand. Instead of making the key be static, have it be dependent on the previous letter. That is, rotate through substitutions a different amount per each input.
The variable rotation satisfies the condition of making each small change push out to a larger change. Note that the algorithm will only push changes in one direction such that changes towards the end have smaller effects. You could run the algorithm both ways (front-to-back, then back-to-front) so that every letter of cleartext changed has the possibility of changing the entire string.
The internal rotation strategy elides the need for keys, while of course losing of most of the cryptographic security. It makes sense in context, though, as you are aiming for entropy rather than security.
You can solve this problem with Format-preserving encryption.
One Java-Library can be found under https://github.com/EVGStudents/FPE.git. There you can define a Regex and encrypt/decrypt string values matching this regex.