The function apply() is certainly one of the most useful function. I was scared of it during a while and refused to use it. But it makes the code so much faster to write and so efficient that we can't afford not using it. If you are like me, that you refuse to use apply because it is scary, read the following lines, it will help you. You want to know how to use apply() in general, with a home-made function or with several parameters ? Then, go to see the following examples.




The function apply() is known as extremely useful to improve the speed of our code when we want to operate some functions on a matrix or a vector. I use it, but I do not really know how to use it.

What is it?

apply() is a R function which enables to make quick operations on matrix, vector or array. The operations can be done on the lines, the columns or even both of them.

How does it work?

The pattern is really simple : apply(variable, margin, function).
-variable is the variable you want to apply the function to.
-margin specifies if you want to apply by row (margin = 1), by column (margin = 2), or for each element (margin = 1:2). Margin can be even greater than 2, if we work with variables of dimension greater than two.
-function is the function you want to apply to the elements of your variable.

Because I think example is clearer than anything else, here is the most important example to understand the function apply().


Introduction:

#the matrix we will work on:
a = matrix(c(1:15), nrow = 5 , ncol = 3)

#will apply the function mean to all the elements of each row
apply(a, 1, mean)
# [1]  6  7  8  9 10

#will apply the function mean to all the elements of each column
apply(a, 2, mean)
# [1]  3  8 13

#will apply the function mean to all the elements of each column and of each row, ie each element
apply(a, 1:2, mean)
#     [,1] [,2] [,3]
# [1,]    1    6   11
# [2,]    2    7   12
# [3,]    3    8   13
# [4,]    4    9   14
# [5,]    5   10   15

We have just worked on the different margins to show the basic possibilities. But as I said we can also work on other variables such as an array of dimension 3:

#apply() for array of other dimension :
a = array(1:8, dim = c(2,2,2))
apply(a, 3, sum)

# , , 1
#
#       [,1] [,2]
# [1,]    1    3
# [2,]    2    4
#
# , , 2
#
#        [,1] [,2]
# [1,]    5    7
# [2,]    6    8


Use a home-made function:

We can also use our own function. For example, we reproduce the function sum (absolutely useless but let's keep it simple!).

f1 = function(x){
  return(sum(x))
}

apply(a, 1, f1)

Several parameters:
A function with several parameters. Here is the main reason why I was never using apply(), I did not know how to do when I had several parameters in a function. This is quite simple, we just have to specifiy in the parameter the variable which is constant.


f2 = function(x1,x2){
  x1-x2
}
b = 2

#with the second parameter as an option
apply(a,1,f2,x2=b)

#       [,1] [,2] [,3] [,4] [,5]
# [1,]   -1    0    1    2    3
# [2,]    4    5    6    7    8
# [3,]    9   10   11   12   13
# [3,]   22   24   26   28   30

#with the first parameter as an option
apply(a,1,f2,x1=b)

# [,1] [,2] [,3] [,4] [,5]
# [1,]    1    0   -1   -2   -3
# [2,]   -4   -5   -6   -7   -8
# [3,]   -9  -10  -11  -12  -13

I hope these examples will help you. Personally I use the function apply() since I went through these few examples. Of course there are many other details which can be useful, but these first examples deal with the main useful possibilities of apply().
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The financial market is not only made of stock options. Other financial products enable market actors to target specific aims. For example, an oil buyer like a flight company may want to cover the risk of increase in the price of oil. In this case it is possible to buy on the financial market what is known as a "Call" or a "Call Option".

A Call Option is a contract between two counterparties (the flight company and a financial actor). The buyer of the Call has the opportunity but not the obligation to buy a certain  quantity of a certain product (called the underlying) at a certain date (the maturity) for a certain price (the strike).

I found a golden website. The blog of Esteban Moro. He uses R to work on networks. In particular he has done a really nice code to make some great videos of networks. This post is purely a copy of his code. I just changed a few arguments to change colors and to do my own network.

To create the network, I used the  Barabási-Albert algorithm that you can find at the end of the post on the different algorithms for networks. Igraph is the library which has been used.
3

As you have certainly seen now, I like working on artificial neural networks. I have written a few posts about models with neural networks (Models to generate networks, Want to win to Guess Who and Study of spatial segregation).

Unfortunately, I missed so far a nice and pleasant aspect of networks : its graphical approach. Indeed, plots of neural networks are often really nice and really useful to understand the network.

Sometimes such a graph can point out some characteristics of the network.
1

I already talked about networks a few times in this blog. In particular, I had this approach to explain spatial segregation in a city or to solve the Guess Who? problem. However, one of the question is how to generate a good network. Indeed, I aim to study strategy to split a network, but I need first to work with a realistic neural network. I could have downloaded data of a network, but I'd rather study the different models proposed to generate neural networks.

The function apply() is certainly one of the most useful function. I was scared of it during a while and refused to use it. But it makes the code so much faster to write and so efficient that we can't afford not using it. If you are like me, that you refuse to use apply because it is scary, read the following lines, it will help you. You want to know how to use apply() in general, with a home-made function or with several parameters ? Then, go to see the following examples.
1

Have you ever played the board game "Guess who?". For those who have not experienced childhood (because it might be the only reason to ignore this board game), this is a game consisting in trying to guess who the opponent player is thinking of among a list of characters - we will call the one he chooses the "chosen character". These characters have several characteristics such as gender, having brown hair or wearing glasses.

If you want to choose randomly your next holidays destination, you are likely to process in a way which is certainly biased. Especially if you choose randomly the latitude and the longitude. A bit like they do in this lovely advertising (For those of you who do not speak French, this is about a couple who have won the national gamble prize and have to decide their next travel. The husband randomly picks Australia and the wife is complaining : "Not again!").
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My previous post is about a method to simulate a Brownian motion. A friend of mine emailed me yesterday to tell me that this is useless if we do not know how to simulate a normally distributed variable.

My first remark is: use the rnorm() function if the quality of your simulation is not too important (Later, I'll try to explain you why the R "default random generation" functions are not perfect). However, it may be fun to generate a normal distribution from a simple uniform distribution.

The Brownian motion is certainly the most famous stochastic process (a random variable evolving in the time). It has been the first way to model a stock option price (Louis Bachelier's thesis in 1900).

The reason why is easy to understand, a Brownian motion is graphically very similar to the historical price of a stock option.
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The merge of two insurance companies enables to curb the probability of ruin by sharing the risk and the capital of the two companies.

For example, we can consider two insurance companies, A and B. A is a well known insurance company with a big capital and is dealing with a risk with a low variance. We will assume that the global risk of all its customers follow a chi-square distribution with one degree of freedom.
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