Difference between revisions of "RPR-OBJECTS-Vectors"

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<section begin=abstract />
 
<section begin=abstract />
 
<!-- included from "../components/RPR-Objects-Vectors.components.wtxt", section: "abstract" -->
 
<!-- included from "../components/RPR-Objects-Vectors.components.wtxt", section: "abstract" -->
...
+
Introduction to vector objects in R: what are they, how are they created, how can they be subset?
 
<section end=abstract />
 
<section end=abstract />
  
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=== Objectives ===
 
=== Objectives ===
 
<!-- included from "../components/RPR-Objects-Vectors.components.wtxt", section: "objectives" -->
 
<!-- included from "../components/RPR-Objects-Vectors.components.wtxt", section: "objectives" -->
...
+
This unit will ...
 +
* ... introduce scalars, vectors and matrices;
 +
* ... demonstrate vectorized operations;
 +
* ... teach various ways of subsetting;
  
 
{{Vspace}}
 
{{Vspace}}
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=== Outcomes ===
 
=== Outcomes ===
 
<!-- included from "../components/RPR-Objects-Vectors.components.wtxt", section: "outcomes" -->
 
<!-- included from "../components/RPR-Objects-Vectors.components.wtxt", section: "outcomes" -->
...
+
After working through this unit you ...
 +
* ... can create vectors by assignment from sequences or using the <code>c()</code>;
 +
* ... are familar with subsetting by index, name, and boolean vectors;
 +
* ... can subset elements, ranges, and slices from vectors and matrices;
 +
* ... can combine objects with <code>c()</code>, <code>rbind()</code>, or <code>cbind()</code>.
  
 
{{Vspace}}
 
{{Vspace}}
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'''R''' objects can be composed from different kinds of data according to the type and number of "atomic" values they contain:
+
'''R''' objects can be composed of different kinds of data according to the type and number of "atomic" values they contain:
* Scalar data are single values;
+
* Scalar items are single values;
 
* Vectors are ordered sequences of scalars, they must all have the same "data type" (e.g. numeric, logical, character ...);
 
* Vectors are ordered sequences of scalars, they must all have the same "data type" (e.g. numeric, logical, character ...);
 
* Matrices are vectors for which one or more "dimension(s)" have been defined;
 
* Matrices are vectors for which one or more "dimension(s)" have been defined;
* Data frames are spreadsheet-like objects, columns are like vectors and all columns must have the same length, but within one data frame, columns can have different data types;
+
* [[RPR-Objects-Dataframes|"Dataframes""]] are spreadsheet-like objects, their columns are like vectors and all columns must have the same length, but within one dataframe, columns can have different data types;
* Lists are the most general collection of data items, the can contain items of any type and kind, including matrices and lists.
+
* [[RPR-Objects-Lists|Lists]] are the most general collection of data items, the can contain items of any type and kind, including matrices, functions, dataframes, and lists.
  
 
{{Vspace}}
 
{{Vspace}}
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''Scalars'' are single numbers, the "atomic" parts of more complex datatypes. Of course we can work with single numbers in '''R''', but under the hood they are actually vectors of length 1. (More on vectors in the next section). We have encountered scalars above, e.g. with the use of constants and their assignment to variables. To round this off, here are some remarks on the types of scalars '''R''' uses, and on ''coercion'' between types, i.e. casting one datatype into another. The following scalar types are supported:
+
''Scalars'' are single numbers, the "atomic" parts of more complex datatypes. Of course we can work with single numbers in '''R''', but under the hood they are actually vectors of length 1. (More on vectors in the next section). To create a scalar object, simply assign some value to its name.
 +
 
 +
<source lang="rsplus">
 +
x <- pi      # define a scalar by assignment
 +
x            # its value is ...
 +
length(x)    # its length is ...
 +
x[1]          # it is actually a vector, and its first element is ...
 +
x[2]          # a second element does not exist NA: Not Available
 +
</source>
 +
 
 +
 
 +
Here are some remarks on the types of scalars '''R''' uses, and on ''coercion'' between types, i.e. casting one datatype into another. The following scalar types are supported:
  
 
* Boolean constants: <code>TRUE</code> and <code>FALSE</code>. This type has the "mode" ''logical";
 
* Boolean constants: <code>TRUE</code> and <code>FALSE</code>. This type has the "mode" ''logical";
Line 117: Line 135:
 
</source>
 
</source>
  
I have combined these information functions into a single function, <code>objectInfo()</code> which gets loaded and defined with the <code>BasicSetup</code> script so you can experiment with it. We can use {{c|objectInfo()}} to explore how R objects are made up, by handing various expressions as arguments to the function. Many of these you may not yet recognize ... bear with it though:
+
I have combined these information functions into a single function, <code>objectInfo()</code> which gets loaded and defined when you execute the <code>init()</code> function of the <code>BasicSetup</code> project, so you can explore objects in more detail. We can use {{c|objectInfo()}} to explore how R objects are made up, by handing various expressions as arguments to the function. Many of these you may not yet recognize ... bear with it though:
 +
 
 +
{{task| 1=
 +
* Load the <code>R-Exercise_BasicSetup</code> project in R studio if you don't still have it open.
 +
* Type <code>init()</code> as instructed when the project loads.
 +
* Continue below.
 +
}}
  
  
 
<source lang="rsplus">
 
<source lang="rsplus">
 +
  
 
#Let's have a brief look at the function itself: typing a function name without its parentheses returns the source code for the function:
 
#Let's have a brief look at the function itself: typing a function name without its parentheses returns the source code for the function:
Line 161: Line 186:
  
 
# NULL
 
# NULL
objectInfo( NULL )     # NULL is nothing. Not 0, not NaN,
+
objectInfo( NULL ) # NULL is nothing. Not 0, not NaN,
                      # not FALSE - nothing. NULL is the value that is
+
                    # not FALSE - nothing. NULL is the value that is returned
                      # returned by expressions or
+
                    # by expressions or functions when the result is
                      # functions when the result is undefined.
+
                    # undefined and nothing more can be said about it.
  
 
objectInfo( as.factor("M") )    # factor
 
objectInfo( as.factor("M") )    # factor
Line 184: Line 209:
  
 
objectInfo( a ~ b )              # a formula
 
objectInfo( a ~ b )              # a formula
objectInfo( objectInfo )        # this function itself
+
objectInfo( objectInfo )        # the function itself
 
</source>
 
</source>
  
Line 213: Line 238:
 
===Vectors===
 
===Vectors===
  
 
+
Since we (almost) never do statistics on scalars, '''R''' obviously needs ways to handle collections of data items. In its simplest form such a collection is a '''vector''': an ordered list of items of the same type. Vectors are created from scratch with the <code>c()</code> function which '''c'''oncatenates individual items into a list, or with various sequencing functions. Vectors have properties, such as length; individual items in vectors can be combined in useful ways. All elements of a vector must be of the same type. If they are not, they are coerced silently to the most general type (which is often {{c|character}}). (The actual hierarchy for coercion is raw < logical < integer < double < complex < character < list ).
Since we (almost) never do statistics on scalars, '''R''' obviously needs ways to handle collections of data items. In its simplest form such a collection is a '''vector''': an ordered list of items of the same type. Vectors are created from scratch with the <code>c()</code> function which '''c'''oncatenates individual items into a list, or with various sequencing functions. Vectors have properties, such as length; individual items in vectors can be combined in useful ways. All elements of a vector must be of the same type. If they are not, they are coerced silently to the most general type (which is often {{c|character}}). (The actual hierarchy for coercion is raw < logical < integer < double < complex < character < list ).
 
  
 
<source lang="rsplus">
 
<source lang="rsplus">
Line 246: Line 270:
 
# to character mode. The emphasis is on _silently_. This might
 
# to character mode. The emphasis is on _silently_. This might
 
# be unexpected, for example if you are reading numeric data
 
# be unexpected, for example if you are reading numeric data
# from a text-file but someone has entered a " " for a missing
+
# from a text-file into a vector but someone has entered a " " for a missing
# value...
+
# value ... then everything is characterified. Nasty.
 +
</source>
  
  
 +
There are various ways to '''subset''' (retrieve) specific values from a vector; this is important.
  
# Various ways to retrieve values from the vector:
+
===Subsetting by index===
 +
<source lang="rsplus">
 +
# Extracting by index ...
 +
f[1]        # "1" is first element, not 0.
 +
head(f, 1)  # same thing
  
# Extracting by index ...
 
f[1] # "1" is first element.
 
 
f[length(f)] # length() is the index of the last element.
 
f[length(f)] # length() is the index of the last element.
 +
tail(f, 1)  # same thing
 +
  
 
# With a vector of indices ...
 
# With a vector of indices ...
Line 274: Line 304:
 
                   # The index vector can be of any length.
 
                   # The index vector can be of any length.
 
f[a] # In this case, four elements are retrieved from f[]
 
f[a] # In this case, four elements are retrieved from f[]
 +
</source>
 +
 +
{{Vspace}}
  
 +
====Excluding itwms with negative indexes====
 +
<source lang="rsplus">
 
# Negative indices omit elements ...
 
# Negative indices omit elements ...
 
# ...using an index vector with negative indices
 
# ...using an index vector with negative indices
Line 283: Line 318:
  
 
f[a] # Here, the first four elements are omitted from f[]
 
f[a] # Here, the first four elements are omitted from f[]
f[-((length(f)-3):length(f))] # Here, the last four elements are omitted from f[]
 
  
# Extracting with a logical vector...
+
f[-((length(f)-3):length(f))] # Here, the last four elements are omitted
 +
 
 +
</source>
 +
 
 +
{{Vspace}}
 +
 
 +
===Subsetting by boolean vectors===
 +
<source lang="rsplus">
 
f > 4 # A logical expression operating on the target vector
 
f > 4 # A logical expression operating on the target vector
 
       # returns a vector of logical elements. It has the
 
       # returns a vector of logical elements. It has the
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f[f > 4]; # We can use this logical vector to extract only
 
f[f > 4]; # We can use this logical vector to extract only
 
           # elements for which the logical expression evaluates as TRUE.
 
           # elements for which the logical expression evaluates as TRUE.
           # This is sometimes called "filtering".
+
           # This is also called "filtering".
 
# Note: the logical vector is aligned with the elements of the original
 
# Note: the logical vector is aligned with the elements of the original
 
# vector. You can't retrieve elements more than once, as you could
 
# vector. You can't retrieve elements more than once, as you could
 
# with index vectors. If the logical vector is shorter than its target
 
# with index vectors. If the logical vector is shorter than its target
 
# it is "recycled" to the full length.
 
# it is "recycled" to the full length.
 +
 +
(1:20)[c(TRUE, FALSE)]  # odd numbers, but how and why?
 +
 +
 +
</source>
 +
 +
{{Vspace}}
 +
 +
 +
===Subsetting by name===
 +
<source lang="rsplus">
 +
 +
# If the vector has named elements, vectors of names can be used exactly like
 +
# index vectors:
 +
 +
summary(f)["Median"]
 +
summary(f)[c("Max", "Min")]  # Oooops - I mistyped. But you can fix the expression, right?
  
  
 +
</source>
  
# Example: extending the Fibonacci series for three steps.
+
{{Vspace}}
# Think: How does this work? What numbers are we adding here and why does the result end up in the vector?
 
( f <- c(f, f[length(f)-1] + f[length(f)]) )
 
( f <- c(f, f[length(f)-1] + f[length(f)]) )
 
( f <- c(f, f[length(f)-1] + f[length(f)]) )
 
  
 +
==="[" is an operator===
 +
<source lang="rsplus">
  
 
# Some more thoughts about "["
 
# Some more thoughts about "["
 
# "[" is not just a special character, it is an operator. It
 
# "[" is not just a special character, it is an operator. It
# operates on whatever it is attached to on the left. We have attached it
+
# operates on whatever it is attached to on the left.
# to vectors above, but we can also attach it directly to function
+
 
# expressions, if the function returns a vector. For example, the
+
?"["  # help is available ...
# summary() function returns some basic statistics on a vector:
+
 
 +
# We have attached "[" to vectors above,
 +
# but we can also attach it directly to functions or other expressions.
 +
# For example, the summary() function returns some basic statistics of a vector:
 +
 
 
summary(f)
 
summary(f)
 
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
 
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
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# ... which brings us to yet another way to extract elements from Vectors:
 
# ... which brings us to yet another way to extract elements from Vectors:
 +
# subsetting by name:
 +
 +
</source>
 +
 +
{{Vspace}}
 +
 +
===Extending vectors===
 +
<source lang="rsplus">
  
# Extracting named elements...
+
# Vectors are not immutable. They can grow and shrink as required.
# If the vector has named elements, vectors of names can be used exactly like
+
( x <- 1:3 )
# index vectors:
+
length(x)
 +
x[4] <- 4; x
 +
length(x)
 +
x[7] <- 7; x
 +
length(x)
 +
( x <- x[-(5:6)] )
 +
length(x)
  
summary(f)["Median"]
+
# Example: extending the Fibonacci series for three steps.
summary(f)[c("Max", "Min")] # Oooops - I mistyped. But you can fix the expression, right?
+
# Think: How does this work? What numbers are we adding here and why does the result end up in the vector?
 +
( f <- c(f, f[length(f)-1] + f[length(f)]) )
 +
( f <- c(f, f[length(f)-1] + f[length(f)]) )
 +
( f <- c(f, f[length(f)-1] + f[length(f)]) )
  
  
 
</source>
 
</source>
  
Many operations on scalars can be simply extended to vectors and '''R''' computes them '''very''' efficiently by iterating over the elements in the vector.
+
{{Vspace}}
 +
 
 +
===Vectorized operations===
 +
<source lang="rsplus">
 +
 
 +
Many operations on vectors are by default performed for every element of the vector, and '''R''' computes them '''very''' efficiently. These are called "vectorized" operations and definitely should be used whenever possible, rather than loops or other explicit iterations.
  
 
<source lang="rsplus">
 
<source lang="rsplus">
 
f
 
f
f+1
+
f + 1
f*2
+
f * 2
  
 
# computing with two vectors of same length
 
# computing with two vectors of same length
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safeSample <- function(x, size, ...) {
 
safeSample <- function(x, size, ...) {
 
# Replace the sample() function to ensure sampling from a single
 
# Replace the sample() function to ensure sampling from a single
# value gives that value with probability p == 1.
+
# value returns that value.
        # Respect additional arguments if present.
+
  # Respect additional arguments if present.
 
     if (length(x) == 1 && is.numeric(x) && x > 0) {
 
     if (length(x) == 1 && is.numeric(x) && x > 0) {
 
     if (missing(size)) size <- 1
 
     if (missing(size)) size <- 1
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:Don't be discouraged though: such warts are rare in '''R'''.
 
:Don't be discouraged though: such warts are rare in '''R'''.
&nbsp;
 
 
  
 
</div>
 
</div>
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{{Vspace}}
 
{{Vspace}}
  
===Matrices===
+
===Matrices and higher-dimensional objects===
  
  
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( a <- 1:12 )
 
( a <- 1:12 )
 
dim(a) <- c(2,6)
 
dim(a) <- c(2,6)
 +
a
 +
dim(a) <- c(4,3)
 
a
 
a
 
dim(a) <- c(2,2,3)
 
dim(a) <- c(2,2,3)
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</source>
 
</source>
  
<code>dim()</code> also allows you to retrieve the number of rows resp. columns a matrix has. For example:
+
<code>dim()</code> also tells you the number of rows resp. columns a matrix has. For example:
 
<source lang="rsplus">
 
<source lang="rsplus">
dim(a)    # returns a vector
+
dim(a)    # returns the dimensions of a in a vector
dim(a)[3]  # only the third value of the vector
+
dim(a)[3]  # only the size of the third dimension of a
 
</source>
 
</source>
  
 
If you have a two-dimensional matrix, the function <code>nrow()</code> and <code>ncol()</code> will also give you the number of rows and columns, respectively. Obviously, <code>dim(a)[1]</code> is the same as <code>nrow(a)</code>.
 
If you have a two-dimensional matrix, the function <code>nrow()</code> and <code>ncol()</code> will also give you the number of rows and columns, respectively. Obviously, <code>dim(a)[1]</code> is the same as <code>nrow(a)</code>.
  
As an alternative to <code>dim()</code>, matrices can be defined using the <code>matrix()</code> or <code>array()</code> functions (see there), or "glued" together from vectors by rows or columns, using the  <code>rbind()</code> or <code>cbind()</code> functions respectively:
+
As an alternative to <code>dim()</code>, matrices can be defined using the <code>matrix()</code> or <code>array()</code> functions (see there), or "glued" together from vectors by rows or columns, using the  <code>rbind()</code> or <code>cbind()</code> functions respectively:
  
 
<source lang="rsplus">
 
<source lang="rsplus">
Line 440: Line 523:
 
( m1 <- rbind(a, b) )
 
( m1 <- rbind(a, b) )
 
( m2 <- cbind(a, b) )
 
( m2 <- cbind(a, b) )
( m  <- cbind(m2, c = 9:12) )  # naming a column :c" while cbind()'ing it
+
( m  <- cbind(m2, c = 9:12) )  # naming a column "c" while cbind()'ing it
  
 
</source>
 
</source>
  
Addressing (retrieving) individual elements or slices from matrices is simply done by specifying the appropriate indices, where a missing index indicates that the entire row or column is to be retrieved. '''This is called "subsetting" or "subscripting" and is one of the most important and powerful aspects of working with R.'''
+
"Subsetting" (retrieving) individual elements or slices from matrices is simply done by specifying the appropriate indices, where a missing index indicates that the entire row or column is to be retrieved.
  
Explore how you extract rows or columns from a matrix by specifying them. Within the square brackets the order is '''[rows, columns]'''
+
Explore how you extract rows or columns from a matrix by specifying them. Within the square brackets the order is '''<code>[&lt;rows&gt;, &lt;columns&lt;]</code>'''
  
 
<source lang="rsplus">
 
<source lang="rsplus">
Line 455: Line 538:
 
</source>
 
</source>
  
More on subsetting below.
+
Note that '''R''' has numerous functions to compute with matrices, such as transposition, multiplication, inversion, calculating eigenvalues and eigenvectors and much more.
 
 
Note that '''R''' has numerous functions to compute with matrices, such as transposition, multiplication, inversion, calculating eigenvalues and eigenvectors and more.
 
  
 
{{Vspace}}
 
{{Vspace}}
Line 501: Line 582:
  
 
-->
 
-->
 +
=== Question 1===
 +
 +
Within the square brackets of a matrix the order is '''<code>[&lt;rows&gt;, &lt;columns&lt;]</code>''', but what about slices of a 3D matrix? Is it '''<code>[&lt;slices&gt;, &lt;rows&gt;, &lt;columns&lt;]</code>''' or '''<code>[&lt;rows&gt;, &lt;columns&lt;, &lt;slices&gt;]</code>'''?
 +
 +
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
 +
Answer ...
 +
<div class="mw-collapsible-content">
 +
Just try:
 +
<source lang="rsplus">
 +
x <- 1:27
 +
dim(x) <- c(3, 3, 3)
 +
x
 +
x[2, 1, 1]  # 2
 +
x[1, 1, 2]  # 10
 +
 +
</source>
 +
 +
... and this means <code>[&lt;rows&gt;, &lt;columns&lt;, &lt;slices&gt;]</code> is correct.
 +
 +
</div>
 +
  </div>
 +
 +
  {{Vspace}}
  
 
{{Vspace}}
 
{{Vspace}}
Line 529: Line 633:
 
:2017-08-05
 
:2017-08-05
 
<b>Modified:</b><br />
 
<b>Modified:</b><br />
:2017-08-05
+
:2017-09-10
 
<b>Version:</b><br />
 
<b>Version:</b><br />
:0.1
+
:1.0
 
<b>Version history:</b><br />
 
<b>Version history:</b><br />
*0.1 First stub
+
*1.0 Completed to first live version
 +
*0.1 Material collected from previous tutorial
 
</div>
 
</div>
 
[[Category:ABC-units]]
 
[[Category:ABC-units]]

Revision as of 15:57, 10 September 2017

Abstract

Introduction to vector objects in R: what are they, how are they created, how can they be subset?


 


This unit ...

Prerequisites

You need to complete the following units before beginning this one:


 


Objectives

This unit will ...

  • ... introduce scalars, vectors and matrices;
  • ... demonstrate vectorized operations;
  • ... teach various ways of subsetting;


 


Outcomes

After working through this unit you ...

  • ... can create vectors by assignment from sequences or using the c();
  • ... are familar with subsetting by index, name, and boolean vectors;
  • ... can subset elements, ranges, and slices from vectors and matrices;
  • ... can combine objects with c(), rbind(), or cbind().


 


Deliverables

  • Time management: Before you begin, estimate how long it will take you to complete this unit. Then, record in your course journal: the number of hours you estimated, the number of hours you worked on the unit, and the amount of time that passed between start and completion of this unit.
  • Journal: Document your progress in your Course Journal. Some tasks may ask you to include specific items in your journal. Don't overlook these.
  • Insights: If you find something particularly noteworthy about this unit, make a note in your insights! page.


 


Evaluation

Evaluation: NA

This unit is not evaluated for course marks.


 


Contents

Data items

R objects can be composed of different kinds of data according to the type and number of "atomic" values they contain:

  • Scalar items are single values;
  • Vectors are ordered sequences of scalars, they must all have the same "data type" (e.g. numeric, logical, character ...);
  • Matrices are vectors for which one or more "dimension(s)" have been defined;
  • "Dataframes"" are spreadsheet-like objects, their columns are like vectors and all columns must have the same length, but within one dataframe, columns can have different data types;
  • Lists are the most general collection of data items, the can contain items of any type and kind, including matrices, functions, dataframes, and lists.


 

Scalar data

Scalars are single numbers, the "atomic" parts of more complex datatypes. Of course we can work with single numbers in R, but under the hood they are actually vectors of length 1. (More on vectors in the next section). To create a scalar object, simply assign some value to its name.

x <- pi       # define a scalar by assignment
x             # its value is ...
length(x)     # its length is ...
x[1]          # it is actually a vector, and its first element is ...
x[2]          # a second element does not exist NA: Not Available


Here are some remarks on the types of scalars R uses, and on coercion between types, i.e. casting one datatype into another. The following scalar types are supported:

  • Boolean constants: TRUE and FALSE. This type has the "mode" logical";
  • Integers, floats (floating point numbers) and complex numbers. These types have the mode numeric;
  • Strings. These have the mode character.

Other modes exist, such as list, function and expression, all of which can be combined into complex objects.

The function mode() returns the mode of an object and typeof() returns its type. Also class() tells you what class it belongs to.

typeof(TRUE)
class(3L)
mode(print)

I have combined these information functions into a single function, objectInfo() which gets loaded and defined when you execute the init() function of the BasicSetup project, so you can explore objects in more detail. We can use objectInfo() to explore how R objects are made up, by handing various expressions as arguments to the function. Many of these you may not yet recognize ... bear with it though:

Task:

  • Load the R-Exercise_BasicSetup project in R studio if you don't still have it open.
  • Type init() as instructed when the project loads.
  • Continue below.


#Let's have a brief look at the function itself: typing a function name without its parentheses returns the source code for the function:
objectInfo

# Various objects:

#Scalars:
objectInfo( 3.0 )    # Double precision floating point number
objectInfo( 3.0e0 )  # Same value, exponential notation

objectInfo( 3 )   # Note: integers are double precision floats by default.
objectInfo( 3L )  # If we really want an integer, we must use R's
                  # special integer notation ...
objectInfo( as.integer(3) )  # or explicitly "coerce" to type integer...

# Coercions: For each of these, first think what result you would expect:
objectInfo( as.character(3) )  # Forcing the number to be interpreted as a character.
objectInfo( as.numeric("3") )   # character as numeric
objectInfo( as.numeric("3.141592653") )  # string as numeric. Where do the
                                         # non-zero digits at the end come from?
objectInfo( as.numeric(pi) )    # not a string, but a predefined constant
objectInfo( as.numeric("pi") )  # another string as numeric ... Ooops -
                                # why the warning?
objectInfo( as.complex(1) )

objectInfo( as.logical(0) )
objectInfo( as.logical(1) )
objectInfo( as.logical(-1) )
objectInfo( as.logical(pi) )      # any non-zero number is TRUE ...
objectInfo( as.logical("pie") )   # ... but not non-numeric types.
                                  # NA means "Not Available".
objectInfo( as.character(pi) )    # Interesting: the conversion eats digits.

objectInfo( Inf )                # Larger than the largest representable number
objectInfo( -Inf )               # ... or smaller
objectInfo( NaN )                # "Not a Number" is numeric
objectInfo( NA )                 # "Not Available" - i.e. missing value is
                                 # logical

# NULL
objectInfo( NULL )  # NULL is nothing. Not 0, not NaN,
                    # not FALSE - nothing. NULL is the value that is returned
                    # by expressions or functions when the result is
                    # undefined and nothing more can be said about it.

objectInfo( as.factor("M") )     # factor
objectInfo( Sys.time() )         # time
objectInfo( letters )            # inbuilt
objectInfo( 1:4 )                # numeric vector
objectInfo( matrix(1:4, nrow=2)) # numeric matrix
objectInfo( data.frame(arabic = 1:3,                           # dataframe
                       roman = c("I", "II", "III"),
                       stringsAsFactors = FALSE))
objectInfo( list(arabic = 1:7, roman = c("I", "II", "III")))   # list

# Expressions:
objectInfo( 3 > 5 ) # Note: any combination of variables via the logical
                    # operators ! == != > < >= <= | || & and && is a
                    # logical expression, with values TRUE or FALSE.
objectInfo( 3 < 5 )
objectInfo( 1:6 > 4 )

objectInfo( a ~ b )              # a formula
objectInfo( objectInfo )         # the function itself


 

Sometimes (but rarely) you may run into a distinction that R makes regarding integers and floating point numbers. By default, if you specify e.g. the number 2 in your code, it is stored as a floating point number. But if the numbers are generated e.g. from a range operator as in 1:2 they are integers! This can give rise to confusion as in the following example:


a <- 7
b <- 6:7
str(a)             # num 7
str(b)             # int [1:2] 6 7
a == b[2]          # TRUE
identical(b[2], a) # FALSE ! Not identical! Why?
                   # (see the str() results above.)

# If you need to be sure that a number is an
# integer, write it with an "L" after the number:
c <- 7L
str(c)             # int 7
identical(b[2], c) # TRUE


 

Vectors

Since we (almost) never do statistics on scalars, R obviously needs ways to handle collections of data items. In its simplest form such a collection is a vector: an ordered list of items of the same type. Vectors are created from scratch with the c() function which concatenates individual items into a list, or with various sequencing functions. Vectors have properties, such as length; individual items in vectors can be combined in useful ways. All elements of a vector must be of the same type. If they are not, they are coerced silently to the most general type (which is often character). (The actual hierarchy for coercion is raw < logical < integer < double < complex < character < list ).

# The c() function concatenates elements into a vector
c(2, 4, 6)


#Create a vector and list its contents and length:
f <- c(1, 1, 3, 5, 8, 13, 21)
f
length(f)

# Often, for teaching code, I want to demonstrate the contents of an object after
# assigning it. I can simply wrap the assignment into parentheses to achieve that.
# Parentheses return the value of whatever they enclose. So ...
a <- 17
# ... assigns 17 to the variable "a". But this happens silently. However ...
( a <- 17 )
# ... returns the result of the assignment. I will use this idiom often.

( f <- c(1, 1, 3, 5, 8, 13, 21, 34, 55, 89) )


# Coercion:
# all elements of vectors must be of the same mode
c(1, 2.0, "3", TRUE)  # trying to get a vector with mixed modes ...
[1] "1"    "2"    "3"    "TRUE"

# ... shows that all elements are silently being coerced
# to character mode. The emphasis is on _silently_. This might
# be unexpected, for example if you are reading numeric data
# from a text-file into a vector but someone has entered a " " for a missing
# value ... then everything is characterified. Nasty.


There are various ways to subset (retrieve) specific values from a vector; this is important.

Subsetting by index

# Extracting by index ...
f[1]         # "1" is first element, not 0.
head(f, 1)   # same thing

f[length(f)] # length() is the index of the last element.
tail(f, 1)   # same thing


# With a vector of indices ...
1:4 # This is the range operator
f[1:4] # using the range operator (it generates a sequence and returns it in a vector)
f[4:1] # same thing, backwards
seq(from=2, to=6, by=2) # The seq() function is a flexible, generic way to generate sequences
seq(2, 6, 2) # Same thing: arguments in default order
f[seq(2, 6, 2)]

# since a scalar is a vector of length 1, does this work?
5[1]


# ...using an index vector with positive indices
a <- c(1, 3, 4, 1) # the elements of index vectors must be
                   # valid indices of the target vector.
                   # The index vector can be of any length.
f[a] # In this case, four elements are retrieved from f[]


 

Excluding itwms with negative indexes

# Negative indices omit elements ...
# ...using an index vector with negative indices

# If elements of index vectors are negative integers,
# the corresponding elements are excluded.
( a <- -(1:4) ) # Note that this is NOT the same as -1:4

f[a] # Here, the first four elements are omitted from f[]

f[-((length(f)-3):length(f))] # Here, the last four elements are omitted


 

Subsetting by boolean vectors

f > 4 # A logical expression operating on the target vector
      # returns a vector of logical elements. It has the
      # same length as the target vector.
f[f > 4]; # We can use this logical vector to extract only
          # elements for which the logical expression evaluates as TRUE.
          # This is also called "filtering".
# Note: the logical vector is aligned with the elements of the original
# vector. You can't retrieve elements more than once, as you could
# with index vectors. If the logical vector is shorter than its target
# it is "recycled" to the full length.

(1:20)[c(TRUE, FALSE)]  # odd numbers, but how and why?


 


Subsetting by name

# If the vector has named elements, vectors of names can be used exactly like
# index vectors:

summary(f)["Median"]
summary(f)[c("Max", "Min")]  # Oooops - I mistyped. But you can fix the expression, right?


 

"[" is an operator

# Some more thoughts about "["
# "[" is not just a special character, it is an operator. It
# operates on whatever it is attached to on the left.

?"["   # help is available ...

# We have attached "[" to vectors above,
# but we can also attach it directly to functions or other expressions.
# For example, the summary() function returns some basic statistics of a vector:

summary(f)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
   1.00    5.00   21.00   75.69   89.00  377.00

# This is a vector of six numbers:
length(summary(f))

# We can extract e.g. the median like so:
summary(f)[3]

# ... or the boundaries of the interquartile range:
summary(f)[c(2, 5)]

# Note that the elements that summary() returns are "named".
# "Names" are attributes.
objectInfo(summary(f))

# The names() function can retrieve (or set) names:
names(summary(f))

# ... which brings us to yet another way to extract elements from Vectors:
# subsetting by name:


 

Extending vectors

# Vectors are not immutable. They can grow and shrink as required.
( x <- 1:3 )
length(x)
x[4] <- 4; x
length(x)
x[7] <- 7; x
length(x)
( x <- x[-(5:6)] )
length(x)

# Example: extending the Fibonacci series for three steps.
# Think: How does this work? What numbers are we adding here and why does the result end up in the vector?
( f <- c(f, f[length(f)-1] + f[length(f)]) )
( f <- c(f, f[length(f)-1] + f[length(f)]) )
( f <- c(f, f[length(f)-1] + f[length(f)]) )


 

Vectorized operations

Many operations on vectors are by default performed for every element of the vector, and '''R''' computes them '''very''' efficiently. These are called "vectorized" operations and definitely should be used whenever possible, rather than loops or other explicit iterations.

<source lang="rsplus">
f
f + 1
f * 2

# computing with two vectors of same length
f  # the Fibonacci numbers you have defined above
( a <- f[-1] )  # like f, but omitting the first element
( b <- f[1:(length(f)-1)] ) # like f, but shortened by the least element
c <- a / b # the "golden ratio", phi (~1.61803 or (1+sqrt(5))/2 ),
           # an irrational number, is approximated by the ratio of
           # two consecutive Fibonacci numbers.
c
abs(c - ((1+sqrt(5))/2)) # Calculating the error of the approximation, element by element


What could possibly go wrong?...


When a number is not a single number ...
One of the "warts" of R is that some functions substitute a range when they receive a vector of length one. Most everyone agrees this is pretty bad. This behaviour was introduced when someone sometime long ago thought it would be nifty to save two keystrokes. This has caused countless errors, hours of frustration and probably hundreds of undiscovered bugs instead. Today we wouldn't write code like that anymore (I hope), but the community believes that since it's been around for so long, it would probably break more things if it's changed. Two functions to watch out for are sample() and seq(); other functions include diag() and runif().
Consider:
x <- 8; sample(6:x)
x <- 7; sample(6:x)
x <- 6; sample(6:x)  # Oi!

# also consider
x <- 6:8; seq(x)
x <- 6:7; seq(x)
x <- 6:6; seq(x)    # Oi vay!
Wherever this misbehaviour is a possibility - i.e. when the number of elements to sample from is variable and could be just one, for example in some simulation code - you can write a replacement function like so...
safeSample <- function(x, size, ...) {
	# Replace the sample() function to ensure sampling from a single
	# value returns that value.
  # Respect additional arguments if present.
    if (length(x) == 1 && is.numeric(x) && x > 0) {
    	if (missing(size)) size <- 1
        return(rep(x, size))
    } else {
        return(sample(x, size, ...))
    }
}
Don't be discouraged though: such warts are rare in R.


 

Matrices and higher-dimensional objects

If we need to operate with several vectors, or multi-dimensional data, we make use of matrices or more generally k-dimensional arrays R. Matrix operations are very similar to vector operations, in fact a matrix actually is a vector for which the number of rows and columns have been defined. Thus matrices inherit the basic limitation of vectors: all elements have to be of the same type.

The most basic way to define matrix rows and columns is to use the dim() function and specify the size of each dimension. Consider:

( a <- 1:12 )
dim(a) <- c(2,6)
a
dim(a) <- c(4,3)
a
dim(a) <- c(2,2,3)
a

dim() also tells you the number of rows resp. columns a matrix has. For example:

dim(a)    # returns the dimensions of a in a vector
dim(a)[3]  # only the size of the third dimension of a

If you have a two-dimensional matrix, the function nrow() and ncol() will also give you the number of rows and columns, respectively. Obviously, dim(a)[1] is the same as nrow(a).

As an alternative to dim(), matrices can be defined using the matrix() or array() functions (see there), or "glued" together from vectors by rows or columns, using the rbind() or cbind() functions respectively:

( a  <- 1:4 )
( b  <- 5:8 )
( m1 <- rbind(a, b) )
( m2 <- cbind(a, b) )
( m  <- cbind(m2, c = 9:12) )  # naming a column "c" while cbind()'ing it

"Subsetting" (retrieving) individual elements or slices from matrices is simply done by specifying the appropriate indices, where a missing index indicates that the entire row or column is to be retrieved.

Explore how you extract rows or columns from a matrix by specifying them. Within the square brackets the order is [<rows>, <columns<]

m[1,] # first row
m[, 2] # second column
m[3, 2] # element at row == 3, column == 2
m[3:4, 1:2] # submatrix: rows 3 to 4 and columns 1 to 2

Note that R has numerous functions to compute with matrices, such as transposition, multiplication, inversion, calculating eigenvalues and eigenvectors and much more.


 


 


Further reading, links and resources

 


Notes


 


Self-evaluation

Question 1

Within the square brackets of a matrix the order is [<rows>, <columns<], but what about slices of a 3D matrix? Is it [<slices>, <rows>, <columns<] or [<rows>, <columns<, <slices>]?

Answer ...

Just try:

x <- 1:27
dim(x) <- c(3, 3, 3)
x
x[2, 1, 1]   # 2
x[1, 1, 2]   # 10

... and this means [<rows>, <columns<, <slices>] is correct.


 


 



 




 

If in doubt, ask! If anything about this learning unit is not clear to you, do not proceed blindly but ask for clarification. Post your question on the course mailing list: others are likely to have similar problems. Or send an email to your instructor.



 

About ...
 
Author:

Boris Steipe <boris.steipe@utoronto.ca>

Created:

2017-08-05

Modified:

2017-09-10

Version:

1.0

Version history:

  • 1.0 Completed to first live version
  • 0.1 Material collected from previous tutorial

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