= R Built-in Functions =

Several '''functions''' are built into the core R distribution.

<<TableOfContents>>

----



== Mathematical Functions ==

Most built-in functions operate on [[R/DataTypes#Numeric|numeric]] [[R/Vectors|vectors]] by applying the function element-wise. These include:

||'''Name''' ||'''Meaning'''                     ||'''Notes'''||
||`abs`      ||absolute value                    || ||
||`all.equal`||Approximate equality of two values||Useful for floating point numbers, but note that it never returns `FALSE`||
||`ceiling`  ||round toward positive infinity    || ||
||`floor`    ||round toward negative infinity    || ||
||`is.na`    ||checks if value is `NA`           || ||
||`isFALSE`  ||checks if value is `FALSE`        || ||
||`isTRUE`   ||checks if value is `TRUE`         || ||
||`log`      ||natural logarithm                 ||try `log(x, b) for a different base `b`; input of zero gives `-Inf` while input of a negative number gives `NaN`||
||`log1p`    ||natural logarithm of `1 + x`      || ||
||`log2`     ||base-2 logarithm                  || ||
||`log10`    ||base-10 logarithm                 || ||
||`round`    ||round to nearest integer          ||try `round(x,n)` to round to `n` digits||
||`sqrt`     ||square root                       || ||
||`trunc`    ||round to 0                        || ||

----



== Trigonometric Functions ==

See [[Calculus/Trigonometry#Functions|here]].

||'''Name'''||'''Meaning'''  ||
||`sin`     ||sine           ||
||`cos`     ||cosine         ||
||`tan`     ||tangent        ||
||`asin`    ||inverse sine   ||
||`acos`    ||inverse cosine ||
||`atan`    ||inverse tangent||

There is also an `atan2` function; `atan2(y, x)` calculates the angle (in radians) between the x-axis and the vector ''[x y]''.

----



== Statistical Functions ==

These functions take a (or, at least one) vector that represents observations and return a computed statistic.

`NA` values cause most of these functions to also return `NA`. Pass the `na.rm = TRUE` option to ignore these values instead.

||'''Example'''||'''Meaning'''             ||'''Notes'''||
||`cor(a,b)`   ||correlation of `a` and `b`|| ||
||`cov(a,b)`   ||covariance of `a` and `b `|| ||
||`density(a)` ||kernel density            ||return value is a list||
||`mad(a)`     ||median absolute deviation ||by default, use average of two candidates when number of observations is even; see `low` and `high` options for alternative strategies||
||`mean(a)`    ||mean                      || ||
||`median(a)`  ||median                    || ||
||`sd(a)`      ||standard deviation        || ||
||`var(a)`     ||variance                  || ||

The `sample` function is used as:

{{{
> samp.without.replacement <- sample(a, size=5)
> samp.with.replacement <- sample(a, size=10, replace=TRUE)
> weighted.samp <- sample(a, size=5, prob=b) # b must be same length as a
}}}

If the `size` option is not passed, then the result is the same size as the input, effectively just performing a randomized sort.

Also note that if the input to the `sample` function is a scalar positive integer `n`, then the sample is actually run on the sequence `1:n`.

These functions take a (or at least one) matrix where the columns represent vectors of observations.

||'''Name'''||'''Meaning'''                       ||
||`cor(a)`  ||correlation matrix of columns in `a`||
||`cov(a)`  ||covariance matrix of columns in `a` ||

----



== Distribution Functions ==

Some of these functions take an output size argument (i.e., `n`). Others take an input that can be a scalar or a vector. The return value matches this input.

For the [[Analysis/UniformDistribution|uniform distribution]] from `min` to `max` (defaulting to 0 and 1 respectively):

||'''Example'''               ||'''Description'''                                       ||
||`runif(n, min = 0, max = 1)`||`n` random values                                       ||
||`dunif(x, min = 0, max = 1)`||density at a given `x` value; `1/(max-min)`             ||
||`punif(q, min = 0, max = 1)`||cumulative probability for a given `q` value            ||
||`qunif(p, min = 0, max = 1)`||inverse of `punif`; takes a cumulative probability (`p`)||

For the [[Analysis/NormalDistribution|normal distribution]] (defaulting to the standard normal distribution):

||'''Example'''               ||'''Description'''                                       ||
||`rnorm(n, mean = 0, sd = 1)`||`n` random values                                       ||
||`dnorm(x, mean = 0, sd = 1)`||density at a given `x` value                            ||
||`pnorm(q, mean = 0, sd = 1)`||cumulative probability for a given `q` value            ||
||`qnorm(p, mean = 0, sd = 1)`||inverse of `pnorm`; takes a cumulative probability (`p`)||

For [[Analysis/StudentsTDistribution|Student's t distribution]] with `df` degrees of freedom:

||'''Example'''||'''Description'''                                       ||
||`rt(n, df)`  ||`n` random values                                       ||
||`dt(x, df)`  ||density at a given `x` value                            ||
||`pt(q, df)`  ||cumulative probability for a given `q` value            ||
||`qt(p, df)`  ||inverse of `pnorm`; takes a cumulative probability (`p`)||

For the [[Analysis/BinomialDistribution|binomial distribution]] with a given `size` and event probability `prob`:

||'''Example'''          ||'''Description'''                                                                        ||
||`rbinom(n, size, prob)`||`n` random values                                                                        ||
||`dbinom(x, size, prob)`||density at a given `x` value; the probability of `x` event successes                     ||
||`pbinom(q, size, prob)`||cumulative probability for a given `q` value; the probability at most `q` event successes||
||`qbinom(p, size, prob)`||inverse of `pbinom`; takes a cumulative probability (`p`)                                ||

R does not support functions relating to the [[Analysis/BernoulliDistribution|Bernoulli distribution]]. Instead use the above binomial distribution functions with a size of 1.

{{{
rbinom(10, size = 1, prob = 0.7)
}}}

For the [[Analysis/PoissonDistribution|Poisson distribution]] with a given `lambda` parameter:

||'''Example'''     ||'''Description'''                                       ||
||`rpois(n, lambda)`||`n` random values                                       ||
||`dpois(x, lambda)`||density at a given `x` value                            ||
||`ppois(q, lambda)`||cumulative probability for a given `q` value            ||
||`qpois(p, lambda` ||inverse of `ppois`; takes a cumulative probability (`p`)||

For the [[Analysis/ChiSquaredDistribution|Chi-squared distribution]] with `df` degrees of freedom:

||'''Example'''  ||'''Description'''                                       ||
||`rchisq(n, df)`||`n` random values                                       ||
||`dchisq(x, df)`||density at a given `x` value                            ||
||`pchisq(q, df)`||cumulative probability for a given `q` value            ||
||`qchisq(p, df` ||inverse of `ppois`; takes a cumulative probability (`p`)||

Set the random number generator's seed to ensure that random values are reproducible.

{{{
set.seed(123)
}}}

----



== String Functions ==

Most built-in functions operate on [[R/DataTypes#Character|character]] [[R/Vectors|vectors]] by applying the function element-wise. These include:

||'''Example'''                 ||'''Description'''                                                       ||
||`grepl(pattern,x)`            ||Checks if `x` matches                                                   ||
||`paste(x,y,sep=" ")`          ||Concatenate two strings with a separator                                ||
||`paste0(x,y)`                 ||Concatenate two strings with no separator                               ||
||`strsplit(x,split)`           ||Split a string by a regular expression `split` into a list of substrings||
||`strsplit(x,split,fixed=TRUE)`||Split a string by a literal delimiter `split`                           ||
||`substr(x,start,stop)`        ||Extract a substring                                                     ||
||`toupper(x)`                  ||Convert to uppercase                                                    ||
||`tolower(x)`                  ||Convert to lowercase                                                    ||

Functions that notably do not treat vectors in that manner:
 * `cat` concatenates and prints the vector
 * `print` prints the vector
 * If the `collapse=" "` option is passed on `paste`, then it takes the vectorized output and concatenates into a single string

The `sprintf` function provides [[C/StringFormatting|C-style string formatting]]. The format string must be a scalar. The substitution variables can be scalars or vectors, in which case the scalars are recycled as necessary. If multiple substitution variables are vectors, they must be the same length.

The `glue` library adds a vectorized function of the same name that supports Python f-string-style interpolation.

{{{
library(glue)

glue("file_{1:3}.txt") # "file_1.txt" "file_2.txt" "file_3.txt"
}}}

It also adds a function intended for composing human-readable messages:

{{{
glue_collapse(c("foo", "bar", "baz"), sep = ", ", last = ", and ") # "foo, bar, and baz"
}}}

----



== Modeling functions ==

See the [[R/BuiltinFunctions/Lm|lm]] function.

A model once fit can be summarized using the `summary` function.

The estimated coefficients of a model can be extracted by the `coef` function.

The design matrix of a model can be extracted by the `model.matrix` function.

A [[Statistics/AnalysisOfVariance|one-way ANOVA]] can be estimated as:

{{{
aov(y ~ x, data=df)

# If a linear model is already fit:
anova(mod)
}}}

----



== Plotting functions ==

See the [[R/BuiltinFunctions/Plot|plot]] function.

To create a Q-Q plot of any variable, try:

{{{
qqnorm(x, main="Normal Probability Plot of x")
}}}

To create a histogram from data, use the `hist` function.

To create a boxplot from data, try:

{{{
boxplot(x)
boxplot(x ~ y) # split by levels of y
}}}

To create a bar chart from statistics, try:

{{{
x <- c(3,2,1)
names(x) <- c("foo", "bar", "baz")
barplot(x)
}}}

To set two plots side-by-side, try:

{{{
par(mfrow=c(1,2))
plot(x,y)
plot(x,z)
}}}

The `par` function can be used this way to create a panel of plots in any arrangement.

----



== Vector Functions ==

These functions operate on a vector and return a scalar:

||'''Name'''||'''Meaning'''||
||`length`  ||vector length||

These functions operate on a vector and have some side effect, like printing something to the screen, rather than returning a value:

||'''Name'''||'''Meaning'''                ||
||`head`    ||prints the first 6 rows      ||
||`sort`    ||In-place sort a vector       ||
||`summary` ||prints descriptive statistics||

These functions are useful for working with logical vectors:

||'''Name'''||'''Meaning'''                       ||'''Notes'''||
||`all`     ||check if every member is `TRUE`     ||returns `NA` if any `NA` values present; pass the `na.rm = TRUE` option to ignore the `NA` values||
||`any`     ||check if a member is `TRUE`         ||returns `NA` if any `NA` values present; pass the `na.rm = TRUE` option to ignore the `NA` values||
||`which`   ||collects the indices that are `TRUE`|| ||

To recast other data types, especially lists (which can feature nesting), into vectors, use the `unlist` function.



=== Equality Testing ===

Testing for equality of two vectors is tricky. The `all.equal` function does evaluate to `TRUE` in the case that two vectors are equal. If they are not equal however, it evaluates to a text description of the differences, and inconveniently this is a truthy value.

Always use the `identical` function to test for equality.



=== Sequence Generation ===

The `seq` function has a number of overloaded parameterizations.

{{{
seq(start,finish)  #equivalent to seq(start,finish,1)
seq(finish,start)  #equivalent to seq(finish,start,-1)
seq(finish)        #equivalent to seq(1,finish,1)

seq(start, finish, by=0.1)          #custom step size
seq(start, finish, 0.1)             #shorthand, same as above
seq(start, finish, length.out=100)  #automatically calculates step size
}}}

The `rep` function also has a number of parameterizations.

{{{
rep(1:3, times=2)               #1 2 3 1 2 3
rep(1:3, length.out=7)          #1 2 3 1 2 3 1
rep(1:3, each=2)                #1 1 2 2 3 3
rep(1:3, each=2, length.out=7)  #1 1 2 2 3 3 1
}}}



=== Sorting ===

The `sort` function has a few options.
 * To sort descending instead of ascending, pass `decreasing = TRUE`.
 * To retain `NA` values and sort them to the end, pass `na.last = TRUE`. Or to retain them and sort them to the beginning, set as `FALSE`. The default is for `NA` values to be removed.

----



== Matrix functions ==

The `replicate` function collects the results of a repeated command into a matrix. For example, to generate 10 samples of 100 observations each from the standard normal distribution, with each sample becoming a column, try:

{{{
replicate(10, rnorm(100))
}}}

The `apply` function applies a function to a rows and/or columns of a matrix.

{{{
row_sums <- apply(x, MARGIN=1, FUN=sum)
col_sums <- apply(x, MARGIN=2, FUN=sum)
all_sums <- apply(x, MARGIN=c(1,2), FUN=sum)
}}}

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== See also ==

[[https://www.rdocumentation.org/packages/base|R documentation on functions in the base package]]

[[https://www.rdocumentation.org/packages/stats|R documentation on functions in the stats package]]

[[https://www.rdocumentation.org/packages/graphics|R documentation on functions in the graphics package]]



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