Let's say I have a vector V, and I want to either turn this vector into multiple m x n matrices, or get multiple m x n matrices from this Vector V.
For the most basic example: Turn V = collect(1:75) into 3 5x5 matrices.
As far as I am aware this can be done by first using reshape reshape(V, 5, :) and then looping through it. Is there a better way in Julia without using a loop?
If possible, a solution that can easily change between row-major and column-major results is preferrable.
TL:DR
m, n, n_matrices = 4, 2, 5
V = collect(1:m*n*n_matrices)
V = reshape(V, m, n, :)
V = permutedims(V, [2,1,3])
display(V)
From my limited knowledge about Julia:
When doing V = collect(1:m*n), you initialize a contiguous array in memory. From V you wish to create a container of m by n matrices. You can achieve this by doing reshape(V, m, n, :), then you can access the first matrix with V[:,:,1]. The "container" in this case is just another array (thus you have a three dimensional array), which in this case we interpret as "an array of matrices" (but you could also interpret it as a box). You can then transpose every matrix in your array by swapping the first two dimensions like this: permutedims(V, [2,1,3]).
How this works
From what I understand; n-dimensional arrays in Julia are contiguous arrays in memory when you don't do any "skipping" (e.g. V[1:2:end]). For example the 2 x 4 matrix A:
1 3 5 7
2 4 6 8
is in memory just 1 2 3 4 5 6 7 8. You simply interpret the data in a specific way, where the first two numbers makes up the first column, then the second two numbers makes the next column so on so forth. The reshape function simply specifies how you want to interpret the data in memory. So if we did reshape(A, 4, 2) we basically interpret the numbers in memory as "the first four values makes the first column, the second four values makes the second column", and we would get:
1 5
2 6
3 7
4 8
We are basically doing the same thing here, but with an extra dimension.
From my observations it also seems to be that permutedims in this case reallocates memory. Also, feel free to correct me if I am wrong.
Old answer:
I don't know much about Julia, but in Python using NumPy I would have done something like this:
reshape(V, :, m, n)
EDIT: As #BatWannaBe states, the result is technically one array (but three dimensional). You can always interpret a three dimensional array as a container of 2D arrays, which from my understanding is what you ask for.
I can create a recursive formula from recurrences where it only passes down one argument (something like $T(n/2)$). However, for a case like this where the value of $u$ and $v$ are different, how do I put them together? This is the problem:
The call to recursive function RecursiveFunction(n, n) for some n > 2
RecursiveFunction(a, b)
if a >= 2 and b >= 2
u=a/2
v=b-1
RecursiveFunction(u, v)
The end goal is to find the tight asymptotic bounds for the worst-case running time, but I just need a formula to start first.
There are in fact two different answers to this, depending on the relative sizes of a and b.
The function can be written as follows:
Where C is some constant work done per call (if statement, pushing u, v onto the call stack etc.). Since the two variables evolve independently, we can analyse their evolution separately.
a - consider the following function:
Expanding the iterative case by m times:
The stopping condition a < 2 is such that:
b - as before:
The complexity of T(a, b) thus depends on which variable reaches its stopping condition first, i.e. the smallest between m and n:
I am trying to create a function that takes the sum of the first n odd integers, i.e the summation from i=1 to n of (2i-1).
If n = 1 it should output 1
If n = 2 it should output 4
I'm having problems using a for loop which only outputs the nth term
n <-2
for (i in 1:n)
{
y<-((2*i)-1)
}
y
In R programming we try avoiding for loops
cumsum ( seq(1,2*n, by=2) )
Or just use 'sum' if you don't want the series of partial sums.
There's actually no need to use a loop or to construct the sequence of the first n odd numbers here -- this is an arithmetic series so we know the sum of the first n elements in closed form:
sum.first.n.odd <- function(n) n^2
sum.first.n.odd(1)
[1] 1
sum.first.n.odd(2)
[1] 4
sum.first.n.odd(100)
[1] 10000
This should be a good deal more efficient than any solution based on for or sum because it never computes the elements of the sequence.
[[Just seeing the title -- the OP apparently knows the analytic result and wanted something else...]]
Try this:
sum=0
n=2
for(i in seq(1,2*n,2)){
sum=sum+i
}
But, of course, R is rather slow when working with loops. That's why one should avoid them.
Closed. This question needs debugging details. It is not currently accepting answers.
Edit the question to include desired behavior, a specific problem or error, and the shortest code necessary to reproduce the problem. This will help others answer the question.
Closed 7 years ago.
Improve this question
my question is simple... every reference I find in books and on the internet for learning R programming is presented in a very linear way with no context. When I try and learn things like functions, I see the code and my brain just freezes because it's looking for something to relate these R terms to and I have no frame of reference. I have a PhD and did a lot of statistics for my dissertation but that was years ago when we were using different programming languages and when it comes to R, I don't know why I can't get this into my head. Is there someone who can explain in plain english an example of this simple code? So for example:
above <- function(x, n){
use <- x > n
x[use]
}
x <- 1:20
above(x, 12)
## [1] 13 14 15 16 17 18 19 20
I'm trying to understand what's going on in this code but simply don't. As a result, I could never just write this code on my own because I don't have the language in my head that explains what is happening with this. I get stuck at the first line:
above <- function(x, n) {
Can someone just explain this code sample in plain English so I have some kind of context for understanding what I'm looking at and why I'm doing what I'm doing in this code? And what I mean by plain English is, walking through the code, step by step and not just repeating the official terms from R like vector and function and array and all these other things, but telling me, in a common sense way, what this means.
Since your background ( phd in statsitics) the best way to understand this
is in mathematics words.
Mathematically speaking , you are defining a parametric function named above that extracts all element from a vector x above a certain value n. You are just filtering the set or the vector x.
In sets notation you can write something like :
above:{x,n} --> {y in x ; y>n}
Now, Going through the code and paraphrasing it (in the left the Math side , in the right its equivalent in R):
Math R
---------------- ---------------------
above: (x,n) <---> above <- function(x, n)
{y in x ; y>n} <---> x[x > n]
So to wrap all the statments together within a function you should respect a syntax :
function_name <- function(arg1,arg2) { statements}
Applying the above to this example (we have one statement here) :
above <- function(x,n) { x[x>n]}
Finally calling this function is exactly the same thing as calling a mathematical function.
above(x,2)
ok I will try, if this is too detailed let me know, but I tried to go really slowly:
above <- function(x, n)
this defines a function, which is just some procedure which produces some output given some input, the <- means assign what is on the right hand side to what is on the left hand side, or in other words put everything on the right into the object on the left, so for example container <- 1 puts 1 into the container, in this case we put a function inside the object above,
function(x, n) everything in the paranthesis specifys what inputs the function takes, so this one takes two variables x and n,
now we come to the body of the function which defines what it does with the inputs x and n, the body of the function is everything inside the curley braces:
{
use <- x > n
x[use]
}
so let's explain that piece by piece:
use <- x > n
this part again puts whats on the right side into the object on the left, and what is happening on the right hand side? a comparison returning TRUE if x is bigger than n and FALSE if x is equal to or smaller then n, so if x is 5 and n is 3 the result will be TRUE, and this value will get stored inside use, so use contains TRUE now, now if we have more than one value inside x than every value inside x will get compared to n, so for example if x = [1, 2, 3] and n = 2
than we have
1 > 2 FALSE
2 > 2 FALSE
3 > 2 TRUE
, so use will contain FALSE, FALSE, TRUE
x[use]
now we are taking a part of x, the square brackets specify which parts of x we want, so in my example case x has 3 elements and use has 3 elements if we combine them we have:
x use
1 FALSE
2 FALSE
3 TRUE
so now we say I dont want 1,2 but i want 3 and the result is 3
so now we have defined the function, now we call it, or in normal words we use it:
x <- 1:20
above(x, 12)
first we assign the numbers 1 through 20 to x, and then we tell the function above to execute (do everything inside its curley braces with the inputs x = 1:20 and n = 12, so in other words we do the following:
above(x, 12)
execute the function above with the inputs x = 1:20 and n = 12
use <- 1:20 > 12
compare 12 to every number from 1:20 and return for each comparison TRUE if the number is in fact bigger than 12 and FALSE if otherwise, than store all the results inside use
x[use]
now give me the corresponding elements of x for which the vector use contains TRUE
so:
x use
1 FALSE
2 FALSE
3 FALSE
4 FALSE
5 FALSE
6 FALSE
7 FALSE
8 FALSE
9 FALSE
10 FALSE
11 FALSE
12 FALSE
13 TRUE
14 TRUE
15 TRUE
16 TRUE
17 TRUE
18 TRUE
19 TRUE
20 TRUE
so we get the numbers 13:20 back as a result
I'll give it a crack too. A few basic points that should get you going in the right direction.
1) The idea of a function. Basically, a function is reusable code. Say I know that in my analysis for some bizarre reason I will often want to add two numbers, multiply them by a third, and divide them by a fourth. (Just suspend disbelief here.) So one way I could do that would just be to write the operation over and over, as follows:
(75 + 93)*4/18
(847 + 3)*3.1415/2.7182
(999 + 380302)*-6901834529/2.5
But that's tedious and error-prone. (What happens if I forget a parenthesis?) Alternatively, I can just define a function that takes whatever numbers I feed into it and carries out the operation. In R:
stupidMath <- function(a, b, c, d){
result <- (a + b)*c/d
}
That code says "I'd like to store this series of commands and attach them to the name "stupidMath." That's called defining a function, and when you define a function, the series of commands is just stored in memory---it doesn't actually do anything until you "call" it. "Calling" it is just ordering it to run, and when you do so, you give it "arguments" ---the stuff in the parentheses in the first line are the arguments it expects, i.e., in my example, it wants four distinct pieces of data, which will be called 'a', 'b', 'c', and 'd'.
Then it'll do the things it's supposed to do with whatever you give it. "The things it's supposed to do" is the stuff in the curly brackets {} --- that's the "body" of the function, which describes what to do with the arguments you give it. So now, whenever you want to carry that mathematical operation you can just "call" the function. To do the first computation, for example, you'd just write stupidMath(75, 93, 4, 18) Then the function gets executed, treating 75 as 'a', 83 as 'b', and so forth.
In your example, the function is named "above" and it takes two arguments, denoted 'x' and 'n'.
2) The "assignment operator": R is unique among major programming languages in using <- -- that's equivalent to = in most other languages, i.e., it says "the name on the left has the value on the right." Conceptually, it's just like how a variable in algebra works.
3) so the "body" of the function (the stuff in the curly brackets) first assigns the name "use" to the expression x > n. What's going on there. Well, an expression is something that the computer evaluates to get data. So remember that when you call the function, you give it values for x and n. The first thing this function does is figures out whether x is greater than n or less than n. If it's greater than n, it evaluates the expression x > n as TRUE. Otherwise, FALSE.
So if you were to define the function in your example and then call it with above(10, 5), then the first line of the body would set the local variable (don't worry right now about what a 'local' variable is) 'use' to be 'TRUE'. This is a boolean value.
Then the next line of the function is a "filter." Filtering is a long topic in R, but basically, R things of everything as a "vector," that is, a bunch of pieces of data in a row. A vector in R can be like a vector in linear algebra, i.e., (1, 2, 3, 4, 5, 99) is a vector, but it can also be of stuff other than numbers. For now let's just focus on numbers.
The wacky thing about R (one of the many wacky things about R) is that it treats a single number (a "scalar" in linear algebra terms) just as a vector with only one item in it.
Ok, so why did I just go into that? Because in lots of places in R, a vector and a scalar are interchangable.
So in your example code, instead of giving a scalar for the first argument, when we call the function we've given 'above' a vector for its first argument. R likes vectors. R really likes vectors. (Just talk to R people for a while. They're all obsessed with doing every goddmamn thing in terms of a vector.) So it's no problem to pass a vector for the first argument. But what that means is that the variable 'use' is going to be a vector too. Specifically, 'use' is going to be a vector of booleans, i.e., of TRUE or FALSE for each individual value of X.
To take a simpler version: suppose you said:
mynums <- c(5, 10)
myresult <- above(mynums, 7)
when the code runs, the first thing it's going to do is define that 'use' variable. But x is a vector now, not a scalar (the c(5,10) code said "make a vector with two elements, and fill them with the numbers '5' and '10'), so R's going to go ahead and carry out the comparison for each element of x. Since 5 is less than 7 and 10 is greater than 7, use becomes the two item-vector of boolean values (FALSE, TRUE)
Ok, now we can talk about filtering. So a vector of boolean values is called a 'logical vector.' And the code x[use] says "filter x by the stuff in the variable use." When you tell R to filter something by a logical vector, it spits back out the elements of the thing being filtered which correspond to the values of 'TRUE'
So in the example just given:
mynums <- c(5, 10)
myresult <- above(mynums, 7)
the value of myresult will just be 10. Why? Because the function filtered 'x' by the logical vector 'use,' 'x' was (5, 10), and 'use' was (FALSE, TRUE); since the second element of the logical was the only true, you only got the second element of x.
And that gets assigned to the variable myresult because myresult <- above(mynums, 7) means "assign the name myresult to the value of above(mynums, 7)"
voila.
I have created two vectors in R, using statistical distributions to build the vectors.
The first is a vector of locations on a string of length 1000. That vector has around 10 values and is called mu.
The second vector is a list of numbers, each one representing the number of features at each location mentioned above. This vector is called N.
What I need to do is generate a random distribution for all features (N) at each location (mu)
After some fiddling around, I found that this code works correctly:
for (i in 1:length(mu)){
a <- rnorm(N[i],mu[i],20)
feature.location <- c(feature.location,a)
}
This produces the right output - a list of numbers of length sum(N), and each number is a location figure which correlates with the data in mu.
I found that this only worked when I used concatenate to get the values into a vector.
My question is; why does this code work? How does R know to loop sum(N) times but for each position in mu? What role does concatenate play here?
Thanks in advance.
To try and answer your question directly, c(...) is not "concatenate", it's "combine". That is, it combines it's argument list into a vector. So c(1,2,3) is a vector with 3 elements.
Also, rnorm(n,mu,sigma) is a function that returns a vector of n random numbers sampled from the normal distribution. So at each iteration, i,
a <- rnorm(N[i],mu[i],20)
creates a vector a containing N[i] random numbers sampled from Normal(mu[i],20). Then
feature.location <- c(feature.location,a)
adds the elements of that vector to the vector from the previous iteration. So at the end, you have a vector with sum(N[i]) elements.
I guess you're sampling from a series of locations, each a variable no. of times.
I'm guessing your data looks something like this:
set.seed(1) # make reproducible
N <- ceiling(10*runif(10))
mu <- sample(seq(1000), 10)
> N;mu
[1] 3 4 6 10 3 9 10 7 7 1
[1] 206 177 686 383 767 496 714 985 377 771
Now you want to take a sample from rnorm of length N(i), with mean mu(i) and sd=20 and store all the results in a vector.
The method you're using (growing the vector) is not recommended as it will be re-copied in memory each time an element is added. (See Circle 2, although for small examples like this, it's not so important.)
First, initialize the storage vector:
f.l <- NULL
for (i in 1:length(mu)){
a <- rnorm(n=N[i], mean=mu[i], sd=20)
f.l <- c(f.l, a)
}
Then, each time, a stores your sample of length N[i] and c() combines it with the existing f.l by adding it to the end.
A more efficient approach is
unlist(mapply(rnorm, N, mu, MoreArgs=list(sd=20)))
Which vectorizes the loop. Unlist is used as mapply returns a list of vectors of varying lengths.