Understanding the Order() Function

Understanding the order() function

This seems to explain it.

The definition of order is that a[order(a)] is in
increasing order. This works with your example, where the correct
order is the fourth, second, first, then third element.

You may have been looking for rank, which returns the rank of the
elements

R> a <- c(4.1, 3.2, 6.1, 3.1)

R> order(a)

[1] 4 2 1 3

R> rank(a)

[1] 3 2 4 1

so rank tells you what order the numbers are in,
order tells you how to get them in ascending order.

plot(a, rank(a)/length(a)) will give a graph of the CDF. To see why
order is useful, though, try plot(a, rank(a)/length(a),type="S")
which gives a mess, because the data are not in increasing order

If you did

oo<-order(a)

plot(a[oo],rank(a[oo])/length(a),type="S")

or simply

oo<-order(a)

plot(a[oo],(1:length(a))/length(a)),type="S")

you get a line graph of the CDF.

I'll bet you're thinking of rank.

Understanding function execution order in Recursion

When you do:

child(parent()); 

It has to execute parent() to know what value to send to child. So it keeps calling parent until it gets to the else return 1;, then keeps passing the return value to child

Including 0s in the increasing order function in R

Order returns the index values of the elements in a vector in a sorted order, so that, for example:

x<-c(5,3,0,7)
order(x)
[1] 3 2 1 4

x[order(x)]
[1] 0 3 5 7

This is useful if, for example, you want to sort one vector by the order of another.

If you want the response to be the actual vector values sorted in order, use sort:

sort(x)
[1] 0 3 5 7

Difference between sort(), rank(), and order()

sort() sorts the vector in an ascending order.

rank() gives the respective rank of the numbers present in the vector, the smallest number receiving the rank 1.

order() returns the indices of the vector in a sorted order.

for example: if we apply these functions are applied to the vector - c (3, 1, 2, 5, 4)

sort(c (3, 1, 2, 5, 4)) will give c(1,2,3,4,5)

rank(c (3, 1, 2, 5, 4)) will give c(3,1,2,5,4)

order(c (3, 1, 2, 5, 4)) will give c(2,3,1,5,4).
if you put these indices in this order, you will get the sorted vector. Notice how v[2] = 1, v[3] = 2, v[1] = 3, v[5] = 4 and v[4] = 5

also there is a tie handling method in R. If you run rank(c (3, 1, 2, 5, 4, 2)) it will give Rank 1 to 1, since there are two 2 present R will rank them on 2 and 3 but assign Rank 2.5 to each of them, next 3 will get Rank 4.0, so

rank(c (3, 1, 2, 5, 4, 2)) will give you output [4.0 1.0 2.5 6.0 5.0 2.5]

Hope this is helpful.

how does the order function break ties in R?

Let's take a look at

idx <- order(x <- c(1,1,3:1,1:4,3), y <- c(9,9:1), z <- c(2,1:9))
idx;
#[1]  6  5  2  1  7  4 10  8  3  9

First thing to note is that

x[idx]
# [1] 1 1 1 1 2 2 3 3 3 4

So idx orders entries in x from smallest to largest values.

Values in y and z affect how order treats ties in x.

Take entries x[5] = 1 and x[6] = 1. Since there is a tie here, order looks up entries at the corresponding positions in y, i.e. y[5] = 6 and y[6] = 5. Since y[6] < y[5], the entries in x are sorted x[6] < x[5].

If there is a tie in y as well, order will look up entries in the next vector z. This happens for x[1] = 1 and x[2] = 2, where both y[1] = 9 and y[2] = 9. Here z breaks the tie because z[2] = 1 < z[1] = 2 and therefore x[2] < x[1].

Does the order of functions in a Python script matter?

The only thing that Python cares about is that the name is defined when it is actually looked up. That's all.

In your case, this is just fine, order doesn't really matter since you are just defining two functions. That is, you are just introducing two new names, no look-ups.

Now, if you called one of these (in effect, performed a look-up) and switched the order around:

def print_sum(a, b):
    print(sum_numbers(a, b))

print_sum(2, 4)

def sum_numbers(a, b):
    return a + b

you'd be in trouble (NameError) because it will try to find a name (sum_numbers) that just doesn't exist yet.

So in general, yes, the order does matter; there's no hoisting of names in Python like there is in other languages (e.g JavaScript).

rank and order in R

set.seed(1)
x <- sample(1:50, 30)    
x
# [1] 14 19 28 43 10 41 42 29 27  3  9  7 44 15 48 18 25 33 13 34 47 39 49  4 30 46  1 40 20  8
rank(x)
# [1]  9 12 16 25  7 23 24 17 15  2  6  4 26 10 29 11 14 19  8 20 28 21 30  3 18 27  1 22 13  5
order(x)
# [1] 27 10 24 12 30 11  5 19  1 14 16  2 29 17  9  3  8 25 18 20 22 28  6  7  4 13 26 21 15 23

rank returns a vector with the "rank" of each value. the number in the first position is the 9th lowest. order returns the indices that would put the initial vector x in order.

The 27th value of x is the lowest, so 27 is the first element of order(x) - and if you look at rank(x), the 27th element is 1.

x[order(x)]
# [1]  1  3  4  7  8  9 10 13 14 15 18 19 20 25 27 28 29 30 33 34 39 40 41 42 43 44 46 47 48 49

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