From 0f91e33b5ba29f6a51d060a5c3a9f1ae6a6d793a Mon Sep 17 00:00:00 2001 From: Arnab Chakraborty Date: Mon, 16 Oct 2023 13:47:16 +0530 Subject: [PATCH] florence --- sm1/Rfun.html | 490 +++++++++++++++++++++++++++++++++++++++++++++++++ sm1/Rfun.rb | 245 +++++++++++++++++++++++++ sm1/Rfun.rb~ | 44 +++++ sm1/index.html | 7 + sm1/index.rb | 6 + sm1/news.html | 5 + 6 files changed, 797 insertions(+) create mode 100644 sm1/Rfun.html create mode 100644 sm1/Rfun.rb create mode 100644 sm1/Rfun.rb~ diff --git a/sm1/Rfun.html b/sm1/Rfun.html new file mode 100644 index 00000000..f15c38c5 --- /dev/null +++ b/sm1/Rfun.html @@ -0,0 +1,490 @@ + + + + + + + + + + + + + + + + + + + +
+[Home] +

Table of contents

+ +
+ +

Functions in R

+Functions play a very important role in R. In this page we shall +summarise some of the important points regarding them. + +

The basic structure

+A function is like a machine. It has + +Here is a simple function in R: + +
+myfun = function(x,y) {
+  z = x+y
+  cat("The difference = ',x-y,'\n')
+  sin(z)
+}
+
+ +The name of the function is myfun (any name of your +choice, as long as it does not clash with any keyword of R). The +word function is a keyword. The inputs to the +function are listed (comma-separated) inside the ( +... ). The parentheses are complulsory wven if there +are no inputs. The input names are dummy variables (has nothing +to do with other variables with the same name). More on this +later. The inputs are called the arguments or +the parameters of the function. +

+The body of the function comes next, inside a pairs of braces +(optional if the body consists of a single statement). + +

+In body of the function consists of one or more statements, each +of which serve one or more of the these three purposes: + + + +

Visibility of a variable

+The variables outside a function, and those inside a function are +linked only via the arguments and returned value. The following example illustrates +this: + +
+f = function(x) {
+  y = x+1
+  x = x-1
+  2*x+y
+}
+
+x = 25
+y = 34
+z = 4
+val = f(z)
+x #prints 25
+y #prints 34
+z #prints 4
+val #prints 10
+
+ + +If you are in a desperate need of a function that modifies a variable value +outside, then use the <<- assignment instead +of = as in the following example. + + +
+f = function(x) {
+  y = x+1
+  x <<- x-1  #The RHS x is the argument x, the LHS x is the global x. 
+  2*x+y
+}
+
+x = 25
+y = 34
+z = 4
+val = f(z)
+x #prints 5 (modified)
+y #prints 34 (unmodified)
+z #prints 4 (unmodified)
+val #prints 10
+
+ +But use the <<- assignment very sparingly, as its +careless use generally leads to bugs that are hard to detect. + +

Returning multiple values

+Functions in R can return only one object. In order to return +multiple objects, you first need to pack them into a single +object. Such a composite object is called a list. + + +
+f = function(n) {
+  list(1:n, sum(1:n), sum((1:n)^2))
+}
+
+ +This function takes a positive integer as input, and returns +three things: + + +The function is used like this: + +
+val = f(10)
+val\frac 1
+val\frac 2
+val\frac 3
+
+ +Notice the use of \frac ... to unpack +a list. However, this is cumbersome. An easier way +is to use names for the different fields in a list: + +
+f = function(n) {
+  list(all=1:n, sum=sum(1:n), sumOfSq=sum((1:n)^2))
+}
+
+ +Then you can use: + +
+val = f(10)
+val$all
+val$sum
+val$sumOfSq
+
+ + +

Passing arguments by position or name

+Consider this example: + +
+f = function(x,y,z) {
+  cat('x = ',x,'y = ','z = ',z)
+}
+
+ +Here are two different ways to call this function: + +
+f(3,4,5) #Output: x = 3 y = 4 z = 5
+f(y=3,x=4,z=5) #Output: x = 4 y = 5 z = 5
+
+ +The second form uses names of the arguments, and is useful when +there are many parameters and it is difficult to remember their +order. Its usefulness increases even further when used along with +defaut values: + +
+f = function(x,y,z=3) {
+  cat('x = ',x,'y = ','z = ',z)
+}
+
+ +Consider the following calls to this function: + +
+f(3,4,5) #Output: x = 3 y = 4 z = 5
+f(y=3,x=4) #Output: x = 4 y = 5 z = 3 (default value)
+
+ +Most standard functions in R is of this type: they have +m..a..n..y arguments (may be even more than 50), of which most +have default values. We care to remember the positions of only +yhe first few (th most important ones), and names of the next few +(of secondary importance), and just use the defaults for the +rest. An example is the plot function: + +
+u = 1:10
+v = 2*x+4
+plot(u,v) #Passing by position (the first along horizontal axis,
+          #the second along vertical)
+plot(u,v,ty='l', col='red') #Using names of arguments. 
+                            #Many other arguments, like line
+                            #types, line width etc are at their default values.
+
+ + + +

R as a functional programming language

+Notice the similarity of the following two R snippets: + +
+x = c(3,4,6,1)
+
+ +and + +
+x = function(t) t^2
+
+ +The first makes x an object, while the second makes +it a function. The same assignment operation = is +used in both the cases. This points at a deep truth about R: it +treats objects and functions on an equal footing. You can do with +functions pretty much whatever you can do with objects, e.g., you +can pass a function as an input to another function, or return a +function from a function, you can have arrays of functions, you +can create functions on the fly. + +

Passing functions as an input to another function

+ + +
+fsq = function(g,x) {
+  g(g(x))
+}
+
+ + +

Returning a function from a function

+ + +
+compose = function(f,g) {
+  function(x) {
+    f(g(x))
+  }
+}
+
+ +Here is how you use it: + +
+sinOfCos = compose(sin,cos)
+sinOfCos(1) #returns sin(cos(1))
+
+ +This is of course of limited value. Here is a really useful one: + +
+iter(f,n) {
+  function(x) {
+    for(i in 1:n) x = f(x)
+    x
+  }
+}
+
+ +You can numerically solve the equation $x = \cos x$ using +this function as: + +
+iter(cos,100)
+
+ + + +

apply function">The apply function

+R allows multidimensional arrays (their modern popular name +being tensor). +The following line produces a $3\times4\times10$ array +consisting of the integers 1 to 120: + +
+x = matrix(1:12, 3,4)
+
+ +Now suppose we want to find row sums. Then you apply +the sum function to the first dimension (i.e., +rows): + +
+apply(x,1,sum)
+
+ +If you want to find column sums, then: + +
+apply(x,2,sum)
+
+ +You may replace sum by prod or any +function that takes a vector in and produces a single number. +
+ + + +
+ +
+
+ + diff --git a/sm1/Rfun.rb b/sm1/Rfun.rb new file mode 100644 index 00000000..2143f940 --- /dev/null +++ b/sm1/Rfun.rb @@ -0,0 +1,245 @@ +@{ +Functions in R +Functions play a very important role in R. In this page we shall +summarise some of the important points regarding them. + +The basic structure +A function is like a machine. It has + +Here is a simple function in R: + +myfun = function(x,y) { + z = x+y + cat("The difference = ',x-y,'\n') + sin(z) +} + +The name of the function is myfun (any name of your +choice, as long as it does not clash with any keyword of R). The +word function is a keyword. The inputs to the +function are listed (comma-separated) inside the ( +... ). The parentheses are complulsory wven if there +are no inputs. The input names are dummy variables (has nothing +to do with other variables with the same name). More on this +later. The inputs are called the arguments or +the parameters of the function. +

+The body of the function comes next, inside a pairs of braces +(optional if the body consists of a single statement). + +

+In body of the function consists of one or more statements, each +of which serve one or more of the these three purposes: +

+ +Visibility of a variable +The variables outside a function, and those inside a function are +linked only via the arguments and returned value. The following example illustrates +this: + +f = function(x) { + y = x+1 + x = x-1 + 2*x+y +} + +x = 25 +y = 34 +z = 4 +val = f(z) +x #prints 25 +y #prints 34 +z #prints 4 +val #prints 10 + + +If you are in a desperate need of a function that modifies a variable value +outside, then use the <<- assignment instead +of = as in the following example. + + +f = function(x) { + y = x+1 + x <<- x-1 #The RHS x is the argument x, the LHS x is the global x. + 2*x+y +} + +x = 25 +y = 34 +z = 4 +val = f(z) +x #prints 5 (modified) +y #prints 34 (unmodified) +z #prints 4 (unmodified) +val #prints 10 + +But use the <<- assignment very sparingly, as its +careless use generally leads to bugs that are hard to detect. + +Returning multiple values +Functions in R can return only one object. In order to return +multiple objects, you first need to pack them into a single +object. Such a composite object is called a list. + + +f = function(n) { + list(1:n, sum(1:n), sum((1:n)^2)) +} + +This function takes a positive integer as input, and returns +three things: + + +The function is used like this: + +val = f(10) +val[[1]] +val[[2]] +val[[3]] + +Notice the use of [[...]] to unpack +a list. However, this is cumbersome. An easier way +is to use names for the different fields in a list: + +f = function(n) { + list(all=1:n, sum=sum(1:n), sumOfSq=sum((1:n)^2)) +} + +Then you can use: + +val = f(10) +val$all +val$sum +val$sumOfSq + +Passing arguments by position or name +Consider this example: + +f = function(x,y,z) { + cat('x = ',x,'y = ','z = ',z) +} + +Here are two different ways to call this function: + +f(3,4,5) #Output: x = 3 y = 4 z = 5 +f(y=3,x=4,z=5) #Output: x = 4 y = 5 z = 5 + +The second form uses names of the arguments, and is useful when +there are many parameters and it is difficult to remember their +order. Its usefulness increases even further when used along with +defaut values: + +f = function(x,y,z=3) { + cat('x = ',x,'y = ','z = ',z) +} + +Consider the following calls to this function: + +f(3,4,5) #Output: x = 3 y = 4 z = 5 +f(y=3,x=4) #Output: x = 4 y = 5 z = 3 (default value) + +Most standard functions in R is of this type: they have +m..a..n..y arguments (may be even more than 50), of which most +have default values. We care to remember the positions of only +yhe first few (th most important ones), and names of the next few +(of secondary importance), and just use the defaults for the +rest. An example is the plot function: + +u = 1:10 +v = 2*x+4 +plot(u,v) #Passing by position (the first along horizontal axis, + #the second along vertical) +plot(u,v,ty='l', col='red') #Using names of arguments. + #Many other arguments, like line + #types, line width etc are at their default values. + + +R as a functional programming language +Notice the similarity of the following two R snippets: + +x = c(3,4,6,1) + +and + +x = function(t) t^2 + +The first makes x an object, while the second makes +it a function. The same assignment operation = is +used in both the cases. This points at a deep truth about R: it +treats objects and functions on an equal footing. You can do with +functions pretty much whatever you can do with objects, e.g., you +can pass a function as an input to another function, or return a +function from a function, you can have arrays of functions, you +can create functions on the fly. + +Passing functions as an input to another function + +fsq = function(g,x) { + g(g(x)) +} + +Returning a function from a function + +compose = function(f,g) { + function(x) { + f(g(x)) + } +} + +Here is how you use it: + +sinOfCos = compose(sin,cos) +sinOfCos(1) #returns sin(cos(1)) + +This is of course of limited value. Here is a really useful one: + +iter(f,n) { + function(x) { + for(i in 1:n) x = f(x) + x + } +} + +You can numerically solve the equation x = \cos x using +this function as: + +iter(cos,100) + + +The apply function +R allows multidimensional arrays (their modern popular name +being tensor). +The following line produces a 3\times4\times10 array +consisting of the integers 1 to 120: + +x = matrix(1:12, 3,4) + +Now suppose we want to find row sums. Then you apply +the sum function to the first dimension (i.e., +rows): + +apply(x,1,sum) + +If you want to find column sums, then: + +apply(x,2,sum) + +You may replace sum by prod or any +function that takes a vector in and produces a single number. +@} diff --git a/sm1/Rfun.rb~ b/sm1/Rfun.rb~ new file mode 100644 index 00000000..f1d839cb --- /dev/null +++ b/sm1/Rfun.rb~ @@ -0,0 +1,44 @@ +@{ +Functions in R +Functions play a very important role in R. In this page we shall +summarise some of the important points regarding them. + +The basic structure +A function is like a machine. It has + +Here is a simple function in R: + +myfun = function(x,y) { + z = x+y + cat("The difference = ',x-y,'\n') + sin(z) +} + +The name of the function is myfun (any name of your +choice, as long as it does not clash with any keyword of R). The +word function is a keyword. The inputs to the +function are listed (comma-separated) inside the ( +... ). The parentheses are complulsory wven if there +are no inputs. The input names are dummy variables (has nothing +to do with other variables with the same name). More on this +later. The inputs are called the arguments or +the parameters of the function. +

+The body of the function comes next, inside a pairs of braces +(optional if the body consists of a single statement). + +

+In body of the function consists of one or more statements, each +of which serve one or more of the these three purposes: +

+@} diff --git a/sm1/index.html b/sm1/index.html index ed48275e..7d2aebce 100644 --- a/sm1/index.html +++ b/sm1/index.html @@ -377,6 +377,13 @@

+ +
  • Oct 12, 2023: +[Florence +Nightingale video] +[R functions] +
    • + diff --git a/sm1/index.rb b/sm1/index.rb index 81e7a835..36dc6fd8 100644 --- a/sm1/index.rb +++ b/sm1/index.rb @@ -159,6 +159,12 @@ topics taught so far. The rest of the course will primarily deal with chapter 3, 4 and 5. + +
  • Oct 12, 2023: +[Florence +Nightingale video] +[R functions] +
    • Survival tips diff --git a/sm1/news.html b/sm1/news.html index 627c9f12..dd492ff8 100755 --- a/sm1/news.html +++ b/sm1/news.html @@ -2,6 +2,11 @@ + +
    Oct 16, 2023 +
    Oct 09, 2023