Data Frame
Overview
A common lisp data frame is a collection of observations of sample variables that shares many of the properties of arrays and lists. By design it can be manipulated using the same mechanisms used to manipulate lisp arrays. This allow you to, for example, transform a data frame into an array and use array-operations to manipulate it, and then turn it into a data frame again to use in modeling or plotting.
Data frame is implemented as a two-dimensional common lisp data structure: a vector of vectors for data, and a hash table mapping variable names to column vectors. All columns are of equal length. This structure provides the flexibility required for column oriented manipulation, as well as speed for large data sets.
Note
In this document we refer to column and variable interchangeably. Likewise factor and category refer to a variable type. Where necessary we distinguish the terminology.Load/install
Data-frame is part of the Lisp-Stat package. It can be used independently if desired. Since the examples in this manual use Lisp-Stat functionality, we’ll use it from there rather than load independently.
(ql:quickload :lisp-stat)
Within the Lisp-Stat system, the LS-USER package is the package for
you to do statistics work. Type the following to change to that
package:
(in-package :ls-user)
Note
The examples assume that you are in package LS-USER. You should make a habit of always working from theLS-USER
package. All the samples may be copied to the clipboard using the
copy button in the upper-right corner of the sample code
box.
Naming conventions
Lisp-Stat has a few naming conventions you should be aware of. If you see a punctuation mark or the letter ‘p’ as the last letter of a function name, it indicates something about the function:
- ‘!’ indicates that the function is destructive. It will modify the data that you pass to it. Otherwise, it will return a copy that you will need to save in a variable.
- ‘p’, ‘-p’ or ‘?’ means the function is a predicate, that is returns a Boolean truth value.
Data frame environment
Although you can work with data frames bound to symbols (as would
happen if you used (defparameter ...), it is more convenient to
define them as part of an environment. When you do this, the system
defines a package of the same name as the data frame, and provides a
symbol for each variable. Let’s see how things work without an
environment:
First, we define a data frame as a parameter:
(defparameter mtcars (read-csv rdata:mtcars)
"Motor Trend Car Road Tests")
;; WARNING: Missing column name was filled in
;; MTCARS2
Now if we want a column, we can say:
(column mtcars 'mpg)
Now let’s define an environment using defdf:
(defdf mtcars (read-csv rdata:mtcars)
"Motor Trend Car Road Tests")
;; WARNING: Missing column name was filled in
;; #<DATA-FRAME (32 observations of 12 variables)
;; Motor Trend Car Road Tests>
Now we can access the same variable with:
mtcars:mpg
defdf does a lot more than this, and you should probably use defdf to set up an environment instead of defparameter. We mention it here because there’s an important bit about maintaining the environment to be aware of:
Note
Destructive functions (those ending in ‘!’), will automatically update the environment for you. Functions that return a copy of the data will not.defdf
The defdf macro is conceptually equivalent to the Common
Lisp defparameter, but with some additional functionality that makes
working with data frames easier. You use it the same way you’d use
defparameter, for example:
(defdf foo <any-function returning a data frame> )
We’ll use both ways of defining data frames in this manual. The access
methods that are defined by defdf are described in the
access data section.
Data types
It is important to note that there are two ’types’ in Lisp-Stat: the
implementation type and the ‘statistical’ type. Sometimes these are
the same, such as in the case of reals; in other situations they are
not. A good example of this can be seen in the mtcars data set. The
hp (horsepower), gear and carb are all of type integer from an
implementation perspective. However only horsepower is a continuous
variable. You can have an additional 0.5 horsepower, but you cannot
add an additional 0.5 gears or carburetors.
Data types are one kind of property that can be set on a variable.
As part of the recoding and data cleansing process, you will want to add
properties to your variables. In Common Lisp, these are plists that
reside on the variable symbols, e.g. mtcars:mpg. In R they are
known as attributes. By default, there are three properties for
each variable: type, unit and label (documentation). When you load
from external formats, like CSV, these properties are all nil; when
you load from a lisp file, they will have been saved along with the
data (if you set them).
There are seven data types in Lisp-Stat:
- string
- integer
- double-float
- single-float
- categorical (
factorin R) - temporal
- bit (Boolean)
Numeric
Numeric types, double-float, single-float and integer are all
essentially similar. The vector versions have type definitions (from
the numeric-utilities package) of:
- simple-double-float-vector
- simple-single-float-vector
- simple-fixnum-vector
As an example, let’s look at mtcars:mpg, where we have a variable of
type float, but a few integer values mixed in.
The values may be equivalent, but the types are not. The CSV
loader has no way of knowing, so loads the column as a mixture of
integers and floats. Let’s start by reloading mtcars from the CSV
file:
(undef 'mtcars)
(defdf mtcars (read-csv rdata:mtcars))
and look at the mpg variable:
LS-USER> mtcars:mpg
#(21 21 22.8d0 21.4d0 18.7d0 18.1d0 14.3d0 24.4d0 22.8d0 19.2d0 17.8d0 16.4d0
17.3d0 15.2d0 10.4d0 10.4d0 14.7d0 32.4d0 30.4d0 33.9d0 21.5d0 15.5d0 15.2d0
13.3d0 19.2d0 27.3d0 26 30.4d0 15.8d0 19.7d0 15 21.4d0)
LS-USER> (type-of *)
(SIMPLE-VECTOR 32)
Notice that the first two entries in the vector are integers, and the
remainder floats. To fix this manually, you will need to coerce each
element of the column to type double-float (you could use
single-float in this case; as a matter of habit we usually use
double-float) and then change the type of the vector to a
specialised float vector.
You can use the heuristicate-types function to guess the statistical
types for you. For reals and strings, heuristicate-types works
fine, however because integers and bits can be used to encode
categorical or numeric values, you will have to indicate the type
using set-properties. We see this below with gear and carb,
although implemented as integer, they are actually type
categorical. The next sections describes how to set them.
Using describe, we can view the
types of all the variables that heuristicate-types set:
LS-USER> (heuristicate-types mtcars)
LS-USER> (describe mtcars)
MTCARS
A data-frame with 32 observations of 12 variables
Variable | Type | Unit | Label
-------- | ---- | ---- | -----------
X8 | STRING | NIL | NIL
MPG | DOUBLE-FLOAT | NIL | NIL
CYL | INTEGER | NIL | NIL
DISP | DOUBLE-FLOAT | NIL | NIL
HP | INTEGER | NIL | NIL
DRAT | DOUBLE-FLOAT | NIL | NIL
WT | DOUBLE-FLOAT | NIL | NIL
QSEC | DOUBLE-FLOAT | NIL | NIL
VS | BIT | NIL | NIL
AM | BIT | NIL | NIL
GEAR | INTEGER | NIL | NIL
CARB | INTEGER | NIL | NIL
Notice the system correctly typed vs and am as Boolean (bit)
(correct in a mathematical sense)
Strings
Unlike in R, strings are not considered categorical variables by default. Ordering of strings varies according to locale, so it’s not a good idea to rely on the strings. Nevertheless, they do work well if you are working in a single locale.
Categorical
Categorical variables have a fixed and known set of possible values.
In mtcars, gear, carb vs and am are categorical variables,
but heuristicate-types can’t distinguish categorical types, so
we’ll set them:
(set-properties mtcars :type '(:vs :categorical
:am :categorical
:gear :categorical
:carb :categorical))
Temporal
Dates and times can be surprisingly complicated. To make working with
them simpler, Lisp-Stat uses vectors of
localtime objects to
represent dates & times. You can set a temporal type with
set-properties as well using the keyword :temporal.
Units & labels
To add units or labels to the data frame, use the set-properties
function. This function takes a plist of variable/value pairs, so to
set the units and labels:
(set-properties mtcars :unit '(:mpg m/g
:cyl :NA
:disp in³
:hp hp
:drat :NA
:wt lb
:qsec s
:vs :NA
:am :NA
:gear :NA
:carb :NA))
(set-properties mtcars :label '(:mpg "Miles/(US) gallon"
:cyl "Number of cylinders"
:disp "Displacement (cu.in.)"
:hp "Gross horsepower"
:drat "Rear axle ratio"
:wt "Weight (1000 lbs)"
:qsec "1/4 mile time"
:vs "Engine (0=v-shaped, 1=straight)"
:am "Transmission (0=automatic, 1=manual)"
:gear "Number of forward gears"
:carb "Number of carburetors"))
Now look at the description again:
LS-USER> (describe mtcars)
MTCARS
A data-frame with 32 observations of 12 variables
Variable | Type | Unit | Label
-------- | ---- | ---- | -----------
X8 | STRING | NIL | NIL
MPG | DOUBLE-FLOAT | M/G | Miles/(US) gallon
CYL | INTEGER | NA | Number of cylinders
DISP | DOUBLE-FLOAT | IN3 | Displacement (cu.in.)
HP | INTEGER | HP | Gross horsepower
DRAT | DOUBLE-FLOAT | NA | Rear axle ratio
WT | DOUBLE-FLOAT | LB | Weight (1000 lbs)
QSEC | DOUBLE-FLOAT | S | 1/4 mile time
VS | BIT | NA | Engine (0=v-shaped, 1=straight)
AM | BIT | NA | Transmission (0=automatic, 1=manual)
GEAR | INTEGER | NA | Number of forward gears
CARB | INTEGER | NA | Number of carburetors
You can set your own properties with this command too. To make your
custom properties appear in the describe command and be saved
automatically, override the describe and write-df methods, or use
:after methods.
Create data-frames
A data frame can be created from a Common Lisp array, alist,
plist, individual data vectors, another data frame or a vector-of
vectors. In this section we’ll describe creating a data frame from each of these.
Data frame columns represent sample set variables, and its rows are observations (or cases).
Note
For these examples we are going to install a modified version of the Lisp-Stat data-frame print-object function. This will cause the REPL to display the data-frame at creation, and save us from having to type (print-data data-frame) in each example. If you’d like to install it as we have, execute the code below at the REPL.(defmethod print-object ((df data-frame) stream)
"Print the first six rows of DATA-FRAME"
(let ((*print-lines* 6))
(df:print-data df stream nil)))
(set-pprint-dispatch 'df:data-frame
#'(lambda (s df) (df:print-data df s nil)))
You can ignore the warning that you’ll receive after executing the code above.
Let’s create a simple data frame. First we’ll setup some variables (columns) to represent our sample domain:
(defparameter v #(1 2 3 4)) ; vector
(defparameter b #*0110) ; bits
(defparameter s #(a b c d)) ; symbols
(defparameter plist `(:vector ,v :symbols ,s)) ;only v & s
Let’s print plist. Just type the name in at the REPL prompt.
plist
(:VECTOR #(1 2 3 4) :SYMBOLS #(A B C D))
From p/a-lists
Now suppose we want to create a data frame from a plist
(apply #'df plist)
;; VECTOR SYMBOLS
;; 1 A
;; 2 B
;; 3 C
;; 4 D
We could also have used the plist-df function:
(plist-df plist)
;; VECTOR SYMBOLS
;; 1 A
;; 2 B
;; 3 C
;; 4 D
and to demonstrate the same thing using an alist, we’ll use the
alexandria:plist-alist function to convert the plist into an
alist:
(alist-df (plist-alist plist))
;; VECTOR SYMBOLS
;; 1 A
;; 2 B
;; 3 C
;; 4 D
From vectors
You can use make-df to create a data frame from keys and a list of
vectors. Each vector becomes a column in the data-frame.
(make-df '(:a :b) ; the keys
'(#(1 2 3) #(10 20 30))) ; the columns
;; A B
;; 1 10
;; 2 20
;; 3 30
This is useful if you’ve started working with variables defined with
defparameter or defvar and want to combine them into a data frame.
From arrays
matrix-df converts a matrix (array) to a data-frame with the given
keys.
(matrix-df #(:a :b) #2A((1 2)
(3 4)))
;#<DATA-FRAME (2 observations of 2 variables)>
This is useful if you need to do a lot of numeric number-crunching on
a data set as an array, perhaps with BLAS or array-operations then
want to add categorical variables and continue processing as a
data-frame.
Example datasets
Vincent Arel-Bundock maintains a library of over 1700 R
datasets that is a
consolidation of example data from various R packages. You can load
one of these by specifying the url to the raw data to the read-csv
function. For example to load the
iris
data set, use:
(defdf iris
(read-csv "https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/master/csv/datasets/iris.csv")
"Edgar Anderson's Iris Data")
Default datasets
To make the examples and tutorials easier, Lisp-Stat includes the URLs
for the R built in data sets. You can see these by viewing the
rdata:*r-default-datasets* variable:
LS-USER? rdata:*r-default-datasets*
(RDATA:AIRPASSENGERS RDATA:ABILITY.COV RDATA:AIRMILES RDATA:AIRQUALITY
RDATA:ANSCOMBE RDATA:ATTENU RDATA:ATTITUDE RDATA:AUSTRES RDATA:BJSALES
RDATA:BOD RDATA:CARS RDATA:CHICKWEIGHT RDATA:CHICKWTS RDATA:CO2-1 RDATA:CO2-2
RDATA:CRIMTAB RDATA:DISCOVERIES RDATA:DNASE RDATA:ESOPH RDATA:EURO
RDATA:EUSTOCKMARKETS RDATA:FAITHFUL RDATA:FORMALDEHYDE RDATA:FREENY
RDATA:HAIREYECOLOR RDATA:HARMAN23.COR RDATA:HARMAN74.COR RDATA:INDOMETH
RDATA:INFERT RDATA:INSECTSPRAYS RDATA:IRIS RDATA:IRIS3 RDATA:ISLANDS
RDATA:JOHNSONJOHNSON RDATA:LAKEHURON RDATA:LH RDATA:LIFECYCLESAVINGS
RDATA:LOBLOLLY RDATA:LONGLEY RDATA:LYNX RDATA:MORLEY RDATA:MTCARS RDATA:NHTEMP
RDATA:NILE RDATA:NOTTEM RDATA:NPK RDATA:OCCUPATIONALSTATUS RDATA:ORANGE
RDATA:ORCHARDSPRAYS RDATA:PLANTGROWTH RDATA:PRECIP RDATA:PRESIDENTS
RDATA:PRESSURE RDATA:PUROMYCIN RDATA:QUAKES RDATA:RANDU RDATA:RIVERS
RDATA:ROCK RDATA:SEATBELTS RDATA::STUDENT-SLEEP RDATA:STACKLOSS
RDATA:SUNSPOT.MONTH RDATA:SUNSPOT.YEAR RDATA:SUNSPOTS RDATA:SWISS RDATA:THEOPH
RDATA:TITANIC RDATA:TOOTHGROWTH RDATA:TREERING RDATA:TREES RDATA:UCBADMISSIONS
RDATA:UKDRIVERDEATHS RDATA:UKGAS RDATA:USACCDEATHS RDATA:USARRESTS
RDATA:USJUDGERATINGS RDATA:USPERSONALEXPENDITURE RDATA:USPOP RDATA:VADEATHS
RDATA:VOLCANO RDATA:WARPBREAKS RDATA:WOMEN RDATA:WORLDPHONES RDATA:WWWUSAGE)
To load one of these, you can use the name of the data set. For example to load mtcars:
(defdf mtcars
(read-csv rdata:mtcars))
If you want to load all of the default R data sets, use the
rdata:load-r-default-datasets command. All the data sets included in
base R will now be loaded into your environment. This is useful if you
are following a R tutorial, but using Lisp-Stat for the analysis
software.
You may also want to save the default R data sets in order to augment
the data with labels, units, types, etc. To save all of the default R
data sets to the LS:DATA;R directory, use the
(rdata:save-r-default-datasets) command if the default data sets
have already been loaded, or save-r-data if they have not. This
saves the data in lisp format.
Install R datasets
To work with all of the R data sets, we recommend you use git to
download the repository to your hard drive. For example I downloaded the
example data to the s: drive like this:
cd s:
git clone https://github.com/vincentarelbundock/Rdatasets.git
and setup a logical host in my ls-init.lisp file like so:
;;; Define logical hosts for external data sets
(setf (logical-pathname-translations "RDATA")
`(("**;*.*.*" ,(merge-pathnames "csv/**/*.*" "s:/Rdatasets/"))))
Now you can access any of the datasets using the logical
pathname. Here’s an example of creating a data frame using the
ggplot mpg data set:
(defdf mpg (read-csv #P"RDATA:ggplot2;mpg.csv"))
Searching the examples
With so many data sets, it’s helpful to load the index into a data
frame so you can search for specific examples. You can do this by
loading the rdata:index into a data frame:
(defdf rindex (read-csv rdata:index))
I find it easiest to use the SQL-DF system to query this data. For example if you wanted to find the data sets with the largest number of observations:
(ql:quickload :sqldf)
(print-data
(sqldf:sqldf "select item, title, rows, cols from rindex order by rows desc limit 10"))
;; ITEM TITLE ROWS COLS
;; 0 military US Military Demographics 1414593 6
;; 1 Birthdays US Births in 1969 - 1988 372864 7
;; 2 wvs_justifbribe Attitudes about the Justifiability of Bribe-Taking in the ... 348532 6
;; 3 flights Flights data 336776 19
;; 4 wvs_immig Attitudes about Immigration in the World Values Survey 310388 6
;; 5 Fertility Fertility and Women's Labor Supply 254654 8
;; 6 avandia Cardiovascular problems for two types of Diabetes medicines 227571 2
;; 7 AthleteGrad Athletic Participation, Race, and Graduation 214555 3
;; 8 mortgages Data from "How do Mortgage Subsidies Affect Home Ownership? ..." 214144 6
;; 9 mammogram Experiment with Mammogram Randomized
Export data frames
These next few functions are the reverse of the ones above used to create them. These are useful when you want to use foreign libraries or common lisp functions to process the data.
For this section of the manual, we are going to work with a subset of
the mtcars data set from above. We’ll use the
select package to take the first 5 rows so that
the data transformations are easier to see.
(defparameter mtcars-small (select mtcars (range 0 5) t))
The next three functions convert a data-frame to and from standard
common lisp data structures. This is useful if you’ve got data in
Common Lisp format and want to work with it in a data frame, or if
you’ve got a data frame and want to apply Common Lisp operators on it
that don’t exist in df.
as-alist
Just like it says on the tin, as-alist takes a data frame and
returns an alist version of it (formatted here for clearer output –
a pretty printer that outputs an alist in this format would be a
welcome addition to Lisp-Stat)
(as-alist mtcars-small)
;; ((MTCARS:X1 . #("Mazda RX4" "Mazda RX4 Wag" "Datsun 710" "Hornet 4 Drive" "Hornet Sportabout"))
;; (MTCARS:MPG . #(21 21 22.8d0 21.4d0 18.7d0))
;; (MTCARS:CYL . #(6 6 4 6 8))
;; (MTCARS:DISP . #(160 160 108 258 360))
;; (MTCARS:HP . #(110 110 93 110 175))
;; (MTCARS:DRAT . #(3.9d0 3.9d0 3.85d0 3.08d0 3.15d0))
;; (MTCARS:WT . #(2.62d0 2.875d0 2.32d0 3.215d0 3.44d0))
;; (MTCARS:QSEC . #(16.46d0 17.02d0 18.61d0 19.44d0 17.02d0))
;; (MTCARS:VS . #*00110)
;; (MTCARS:AM . #*11100)
;; (MTCARS:GEAR . #(4 4 4 3 3))
;; (MTCARS:CARB . #(4 4 1 1 2)))
as-plist
Similarly, as-plist will return a plist:
(as-plist mtcars-small)
;; (MTCARS:X1 #("Mazda RX4" "Mazda RX4 Wag" "Datsun 710" "Hornet 4 Drive" "Hornet Sportabout")
;; MTCARS:MPG #(21 21 22.8d0 21.4d0 18.7d0)
;; MTCARS:CYL #(6 6 4 6 8)
;; MTCARS:DISP #(160 160 108 258 360)
;; MTCARS:HP #(110 110 93 110 175)
;; MTCARS:DRAT #(3.9d0 3.9d0 3.85d0 3.08d0 3.15d0)
;; MTCARS:WT #(2.62d0 2.875d0 2.32d0 3.215d0 3.44d0)
;; MTCARS:QSEC #(16.46d0 17.02d0 18.61d0 19.44d0 17.02d0)
;; MTCARS:VS #*00110
;; MTCARS:AM #*11100
;; MTCARS:GEAR #(4 4 4 3 3)
;; MTCARS:CARB #(4 4 1 1 2))
as-array
as-array returns the data frame as a row-major two dimensional lisp
array. You’ll want to save the variable names using the
keys function to make it easy to
convert back (see matrix-df). One of the reasons you
might want to use this function is to manipulate the data-frame using
array-operations. This is
particularly useful when you have data frames of all numeric values.
(defparameter mtcars-keys (keys mtcars)) ; we'll use later
(defparameter mtcars-small-array (as-array mtcars-small))
mtcars-small-array
;; 0 Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
;; 1 Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
;; 2 Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
;; 3 Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
;; 4 Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
Our abbreviated mtcars data frame is now a two dimensional Common
Lisp array. It may not look like one because Lisp-Stat will ‘print
pretty’ arrays. You can inspect it with the describe command to make
sure:
LS-USER> (describe mtcars-small-array)
...
Type: (SIMPLE-ARRAY T (5 12))
Class: #<BUILT-IN-CLASS SIMPLE-ARRAY>
Element type: T
Rank: 2
Physical size: 60
vectors
The columns function returns the variables of the data frame as a vector of
vectors:
(columns mtcars-small)
; #(#("Mazda RX4" "Mazda RX4 Wag" "Datsun 710" "Hornet 4 Drive" "Hornet Sportabout")
; #(21 21 22.8d0 21.4d0 18.7d0)
; #(6 6 4 6 8)
; #(160 160 108 258 360)
; #(110 110 93 110 175)
; #(3.9d0 3.9d0 3.85d0 3.08d0 3.15d0)
; #(2.62d0 2.875d0 2.32d0 3.215d0 3.44d0)
; #(16.46d0 17.02d0 18.61d0 19.44d0 17.02d0)
; #*00110
; #*11100
; #(4 4 4 3 3)
; #(4 4 1 1 2))
This is a column-major lisp array.
You can also pass a selection to the columns function to return
specific columns:
(columns mtcars-small 'mpg)
; #(21 21 22.8d0 21.4d0 18.7d0)
The functions in array-operations are
helpful in further dealing with data frames as vectors and arrays. For
example you could convert a data frame to a transposed array by using
aops:combine with the
columns function:
(combine (columns mtcars-small))
;; 0 Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive Hornet Sportabout
;; 1 21.00 21.000 22.80 21.400 18.70
;; 2 6.00 6.000 4.00 6.000 8.00
;; 3 160.00 160.000 108.00 258.000 360.00
;; 4 110.00 110.000 93.00 110.000 175.00
;; 5 3.90 3.900 3.85 3.080 3.15
;; 6 2.62 2.875 2.32 3.215 3.44
;; 7 16.46 17.020 18.61 19.440 17.02
;; 8 0.00 0.000 1.00 1.000 0.00
;; 9 1.00 1.000 1.00 0.000 0.00
;; 10 4.00 4.000 4.00 3.000 3.00
;; 11 4.00 4.000 1.00 1.000 2.00
Load data
There are two functions for loading data. The first data makes
loading from logical pathnames convenient. The other, read-csv
works with the file system or URLs. Although the name read-csv
implies only CSV (comma separated values), it can actually read with
other delimiters, such as the tab character. See the DFIO API
reference for more information.
The data command
For built in Lisp-Stat data sets, you can load with just the data set
name. For example to load mtcars:
(data :mtcars)
If you’ve installed the R data
sets, and want to load
the antigua data set from the daag package, you could do it like
this:
(data :antigua :system :rdata :directory :daag :type :csv)
If the file type is not lisp (say it’s TSV or CSV), you need to
specify the type parameter.
From strings
Here is a short demonstration of reading from strings:
(defparameter *d*
(read-csv
(format nil "Gender,Age,Height~@
\"Male\",30,180.~@
\"Male\",31,182.7~@
\"Female\",32,1.65e2")))
dfio tries to hard to decipher the various number formats sometimes
encountered in CSV files:
(select (dfio:read-csv
(format nil "\"All kinds of wacky number formats\"~%.7~%19.~%.7f2"))
t 'all-kinds-of-wacky-number-formats)
; => #(0.7d0 19.0d0 70.0)
From delimited files
We saw above that dfio can read from strings, so one easy way to
read from a file is to use the uiop system function
read-file-string. We can read one of the example data files
included with Lisp-Stat like this:
(read-csv
(uiop:read-file-string #P"LS:DATA;absorbtion.csv"))
;; IRON ALUMINUM ABSORPTION
;; 0 61 13 4
;; 1 175 21 18
;; 2 111 24 14
;; 3 124 23 18
;; 4 130 64 26
;; 5 173 38 26 ..
That example just illustrates reading from a file to a string. In practice you’re better off just reading the file in directly and avoid reading into a string first:
(read-csv #P"LS:DATA;absorbtion.csv")
;; IRON ALUMINUM ABSORPTION
;; 0 61 13 4
;; 1 175 21 18
;; 2 111 24 14
;; 3 124 23 18
;; 4 130 64 26
;; 5 173 38 26 ..
From parquet files
You can use the duckdb system to load data from parquet files:
(ql:quickload :duckdb) ; see duckdb repo for installation instructions
(ddb:query "INSTALL httpfs;" nil) ; loading via http
(ddb:initialize-default-connection)
(defdf yellow-taxis
(let ((q (ddb:query "SELECT * FROM read_parquet('https://d37ci6vzurychx.cloudfront.net/trip-data/yellow_tripdata_2023-01.parquet') LIMIT 10" nil)))
(make-df (mapcar #'dfio:string-to-symbol (alist-keys q))
(alist-values q))))
Now we can find the average fare:
(mean yellow-taxis:fare-amount)
11.120000000000001d0
From URLs
dfio can also read from Common Lisp
streams.
Stream operations can be network or file based. Here is an example
of how to read the classic Iris data set over the network:
(read-csv
"https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/master/csv/datasets/iris.csv")
;; X27 SEPAL-LENGTH SEPAL-WIDTH PETAL-LENGTH PETAL-WIDTH SPECIES
;; 0 1 5.1 3.5 1.4 0.2 setosa
;; 1 2 4.9 3.0 1.4 0.2 setosa
;; 2 3 4.7 3.2 1.3 0.2 setosa
;; 3 4 4.6 3.1 1.5 0.2 setosa
;; 4 5 5.0 3.6 1.4 0.2 setosa
;; 5 6 5.4 3.9 1.7 0.4 setosa ..
From a database
You can load data from a SQLite table using the
read-table
command. Here’s an example of reading the iris data frame from a
SQLite table:
(asdf:load-system :sqldf)
(defdf iris
(sqldf:read-table
(sqlite:connect #P"S:\\src\\lisp-stat\\data\\iris.db3")
"iris"))
Note that sqlite:connect does not take a logical pathname; use a
system path appropriate for your computer. One reason you might want
to do this is for speed in loading CSV. The CSV loader for SQLite is
10-15 times faster than the fastest Common Lisp CSV parser, and it is
often quicker to load to SQLite first, then load into Lisp.
Save data
Data frames can be saved into any delimited text format supported by fare-csv, or several flavors of JSON, such as Vega-Lite.
As CSV
To save the mtcars data frame to disk, you could use:
(write-csv mtcars
#P"LS:DATA;mtcars.csv"
:add-first-row t) ; add column headers
to save it as CSV, or to save it to tab-separated values:
(write-csv mtcars
#P"LS:DATA;mtcars.tsv"
:separator #\tab
:add-first-row t) ; add column headers
As Lisp
For the most part, you will want to save your data frames as lisp. Doing so is both faster in loading, but more importantly it preserves any variable attributes that may have been given.
To save a data frame, use the save command:
(save 'mtcars #P"LS:DATA;mtcars-example")
Note that in this case you are passing the symbol to the function, not the value (thus the quote (’) before the name of the data frame). Also note that the system will add the ’lisp’ suffix for you.
To a database
The write-table function can be used to save a data frame to a SQLite database. Each take a connection to a database, which may be file or memory based, a table name and a data frame. Multiple data frames, with different table names, may be written to a single SQLite file this way.
Access data
This section describes various way to access data variables.
Define a data-frame
Let’s use defdf to define the iris data
frame. We’ll use both of these data frames in the examples below.
(defdf iris
(read-csv rdata:iris))
;WARNING: Missing column name was filled in
We now have a global
variable
named iris that represents the data frame. Let’s look at the first
part of this data:
(head iris)
;; X29 SEPAL-LENGTH SEPAL-WIDTH PETAL-LENGTH PETAL-WIDTH SPECIES
;; 0 1 5.1 3.5 1.4 0.2 setosa
;; 1 2 4.9 3.0 1.4 0.2 setosa
;; 2 3 4.7 3.2 1.3 0.2 setosa
;; 3 4 4.6 3.1 1.5 0.2 setosa
;; 4 5 5.0 3.6 1.4 0.2 setosa
;; 5 6 5.4 3.9 1.7 0.4 setosa
Notice a couple of things. First, there is a column X29. In fact if
you look back at previous data frame output in this tutorial you will
notice various columns named X followed by some number. This is
because the column was not given a name in the data set, so a name was
generated for it. X starts at 1 and increased by 1 each time an
unnamed variable is encountered during your Lisp-Stat session. The
next time you start Lisp-Stat, numbering will begin from 1 again.
We will see how to clean this up this data frame in the next sections.
The second thing to note is the row numbers on the far left side. When Lisp-Stat prints a data frame it automatically adds row numbers. Row and column numbering in Lisp-Stat start at 0. In R they start with 1. Row numbers make it convenient to select data sections from a data frame, but they are not part of the data and cannot be selected or manipulated themselves. They only appear when a data frame is printed.
Access a variable
The defdf macro also defines symbol macros that allow you to refer
to a variable by name, for example to refer to the mpg column of
mtcars, you can refer to it by the the name data-frame:variable
convention.
mtcars:mpg
; #(21 21 22.8D0 21.4D0 18.7D0 18.1D0 14.3D0 24.4D0 22.8D0 19.2D0 17.8D0 16.4D0
17.3D0 15.2D0 10.4D0 10.4D0 14.7D0 32.4D0 30.4D0 33.9D0 21.5D0 15.5D0 15.2D0
13.3D0 19.2D0 27.3D0 26 30.4D0 15.8D0 19.7D0 15 21.4D0)
There is a point of distinction to be made here: the values of mpg
and the column mpg. For example to obtain the same vector using
the selection/sub-setting package select we must refer to the
column:
(select mtcars t 'mpg)
; #(21 21 22.8D0 21.4D0 18.7D0 18.1D0 14.3D0 24.4D0 22.8D0 19.2D0 17.8D0 16.4D0
17.3D0 15.2D0 10.4D0 10.4D0 14.7D0 32.4D0 30.4D0 33.9D0 21.5D0 15.5D0 15.2D0
13.3D0 19.2D0 27.3D0 26 30.4D0 15.8D0 19.7D0 15 21.4D0)
Note that with select we passed the symbol 'mpg (you can
tell it’s a symbol because of the quote in front of it).
So, the rule here is: if you want the value refer to it directly,
e.g. mtcars:mpg. If you are referring to the column, use the
symbol. Data frame operations sometimes require the symbol, where as
Common Lisp and other packages that take vectors use the direct access
form.
Data-frame operations
These functions operate on data-frames as a whole.
copy
copy returns a newly allocated data-frame with the same values as
the original:
(copy mtcars-small)
;; X1 MPG CYL DISP HP DRAT WT QSEC VS AM GEAR CARB
;; 0 Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
;; 1 Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
;; 2 Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
;; 3 Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
;; 4 Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
By default only the keys are copied and the original data remains the
same, i.e. a shallow copy. For a deep copy, use the copy-array
function as the key:
(copy mtcars-small :key #'copy-array)
;; X1 MPG CYL DISP HP DRAT WT QSEC VS AM GEAR CARB
;; 0 Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
;; 1 Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
;; 2 Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
;; 3 Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
;; 4 Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
Useful when applying destructive operations to the data-frame.
keys
Returns a vector of the variables in the data frame. The keys are symbols. Symbol properties describe the variable, for example units.
(keys mtcars)
; #(X45 MPG CYL DISP HP DRAT WT QSEC VS AM GEAR CARB)
Recall the earlier discussion of X1 for the column name.
map-df
map-df transforms one data-frame into another, row-by-row. Its
function signature is:
(map-df data-frame keys function result-keys) ...
It applies function to each row, and returns a data frame with the
result-keys as the column (variable) names. keys is a list.
You can also specify the type of the new variables in the
result-keys list.
The goal for this example is to transform df1:
(defparameter df1 (make-df '(:a :b) '(#(2 3 5)
#(7 11 13))))
into a data-frame that consists of the product of :a and :b, and a
bit mask of the columns that indicate where the value is <= 30. First
we’ll need a helper for the bit mask:
(defun predicate-bit (a b)
"Return 1 if a*b <= 30, 0 otherwise"
(if (<= 30 (* a b))
1
0))
Now we can transform df1 into our new data-frame, df2, with:
(defparameter df2 (map-df df1
'(:a :b)
(lambda (a b)
(vector (* a b) (predicate-bit a b)))
'((:p fixnum) (:m bit))))
Since it was a parameter assignment, we have to view it manually:
(print-df df2)
;; P M
;; 0 14 0
;; 1 33 1
;; 2 65 1
Note how we specified both the new key names and their type. Here’s
an example that transforms the units of mtcars from imperial to metric:
(map-df mtcars '(x1 mpg disp hp wt)
(lambda (model mpg disp hp wt)
(vector model ;no transformation for model (X1), return as-is
(/ 235.214583 mpg)
(/ disp 61.024)
(* hp 1.01387)
(/ (* wt 1000) 2.2046)))
'(:model (:100km/l float) (:disp float) (:hp float) (:kg float)))
;; MODEL 100KM/L DISP HP KG
;; 0 Mazda RX4 11.2007 2.6219 111.5257 1188.4242
;; 1 Mazda RX4 Wag 11.2007 2.6219 111.5257 1304.0914
;; 2 Datsun 710 10.3164 1.7698 94.2899 1052.3451
;; 3 Hornet 4 Drive 10.9913 4.2278 111.5257 1458.3144
;; 4 Hornet Sportabout 12.5783 5.8993 177.4272 1560.3737
;; 5 Valiant 12.9953 3.6871 106.4564 1569.4456 ..
Note that you may have to adjust the X column name to suit your
current environment.
You might be wondering how we were able to refer to the columns without the ’ (quote); in fact we did, at the beginning of the list. The lisp reader then reads the contents of the list as symbols.
The print-data command will print a data frame in a nicely formatted
way, respecting the pretty printing row/column length variables:
(print-data mtcars)
;; MODEL MPG CYL DISP HP DRAT WT QSEC VS AM GEAR CARB
;; Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
;; Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
;; Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
;; Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
...
;; Output elided for brevity
rows
rows returns the rows of a data frame as a vector of vectors:
(rows mtcars-small)
;#(#("Mazda RX4" 21 6 160 110 3.9d0 2.62d0 16.46d0 0 1 4 4)
; #("Mazda RX4 Wag" 21 6 160 110 3.9d0 2.875d0 17.02d0 0 1 4 4)
; #("Datsun 710" 22.8d0 4 108 93 3.85d0 2.32d0 18.61d0 1 1 4 1)
; #("Hornet 4 Drive" 21.4d0 6 258 110 3.08d0 3.215d0 19.44d0 1 0 3 1)
; #("Hornet Sportabout" 18.7d0 8 360 175 3.15d0 3.44d0 17.02d0 0 0 3 2))
remove duplicates
The df-remove-duplicates function will remove duplicate rows. Let’s
create a data-frame with duplicates:
(defparameter dup (make-df '(a b c) '(#(a1 a1 a3)
#(a1 a1 b3)
#(a1 a1 c3))))
;DUP
;; A B C
;; 0 A1 A1 A1
;; 1 A1 A1 A1
;; 2 A3 B3 C3
Now remove duplicate rows 0 and 1:
(df-remove-duplicates dup)
;; A B C
;; A1 A1 A1
;; A3 B3 C3
remove data-frame
If you are working with large data sets, you may wish to remove a data
frame from your environment to save memory. The undef command does
this:
LS-USER> (undef 'tooth-growth)
(TOOTH-GROWTH)
You can check that it was removed with the show-data-frames
function, or by viewing the list df::*data-frames*.
list data-frames
To list the data frames in your environment, use the
show-data-frames function. Here is an example of what is currently
loaded into the authors environment. The data frames listed may be
different for you, depending on what you have loaded.
To see this output, you’ll have to change to the standard
print-object method, using this code:
(defmethod print-object ((df data-frame) stream)
"Print DATA-FRAME dimensions and type
After defining this method it is permanently associated with data-frame objects"
(print-unreadable-object (df stream :type t)
(let ((description (and (slot-boundp df 'name)
(documentation (find-symbol (name df)) 'variable))))
(format stream
"(~d observations of ~d variables)"
(aops:nrow df)
(aops:ncol df))
(when description
(format stream "~&~A" (short-string description))))))
Now, to see all the data frames in your environment:
LS-USER> (show-data-frames)
#<DATA-FRAME AQ (153 observations of 7 variables)>
#<DATA-FRAME MTCARS (32 observations of 12 variables)
Motor Trend Car Road Tests>
#<DATA-FRAME USARRESTS (50 observations of 5 variables)
Violent Crime Rates by US State>
#<DATA-FRAME PLANTGROWTH (30 observations of 3 variables)
Results from an Experiment on Plant Growth>
#<DATA-FRAME TOOTHGROWTH (60 observations of 4 variables)
The Effect of Vitamin C on Tooth Growth in Guinea Pigs>
with the :head t option, show-data-frames will print the first
five rows of the data frame, similar to the head command:
LS-USER> (show-data-frames :head t)
AQ
;; X5 OZONE SOLAR-R WIND TEMP MONTH DAY
;; 1 41.0000 190 7.4 67 5 1
;; 2 36.0000 118 8.0 72 5 2
;; 3 12.0000 149 12.6 74 5 3
;; 4 18.0000 313 11.5 62 5 4
;; 5 42.1293 NA 14.3 56 5 5
;; 6 28.0000 NA 14.9 66 5 6 ..
MTCARS
;; MODEL MPG CYL DISP HP DRAT WT QSEC VS AM GEAR CARB
;; Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
;; Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
;; Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
;; Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
;; Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
;; Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1 ..
;; Output elided for brevity
You, of course, may see different output depending on what data frames you currently have loaded.
Let’s change the print-object back to our convenience method.
(defmethod print-object ((df data-frame) stream)
"Print the first six rows of DATA-FRAME"
(let ((*print-lines* 6))
(df:print-data df stream nil)))
stacking
Stacking is done with the array-operations stacking functions. Since these functions operate on both arrays and data frames, we can use them to stack data frames, arrays, or a mixture of both, providing they have a rank of 2. Here’s an example using the mtcars data frame:
(defparameter boss-mustang
#("Boss Mustang" 12.7d0 8 302 405 4.11d0 2.77d0 12.5d0 0 1 4 4))
and now stack it onto the mtcars data set (load it with (data :mtcars) if you haven’t already done so):
(matrix-df
(keys mtcars)
(stack-rows mtcars boss-mustang))
This is the functional equivalent of R’s rbind function. You can also add columns with the stack-cols function.
An often asked question is: why don’t you have a dedicated stack-rows function? Well, if you want one it might look like this:
(defun stack-rows (df &rest objects)
"Stack rows that works on matrices and/or data frames."
(matrix-df
(keys df)
(apply #'aops:stack-rows (cons df objects))))
But now the data frame must be the first parameter passed to the function. Or perhaps you want to rename the columns? Or you have matrices as your starting point? For all those reasons, it makes more sense to pass in the column keys than a data frame:
(defun stack-rows (col-names &rest objects)
"Stack rows that works on matrices and/or data frames."
(matrix-df
(keys col-names)
(stack-rows objects)))
However this means we have two stack-rows functions, and you don’t really gain anything except an extra function call. So use the above definition if you like; we use the first example and call matrix-df and stack-rows to stack data frames.
Column operations
You have seen some of these functions before, and for completeness we repeat them here.
To obtain a variable (column) from a data frame, use the column
function. Using the mtcars-small data frame, defined in export data
frames above:
(column mtcars-small 'mpg)
;; #(21 21 22.8d0 21.4d0 18.7d0)
To get all the columns as a vector, use the columns function:
(columns mtcars-small)
; #(#("Mazda RX4" "Mazda RX4 Wag" "Datsun 710" "Hornet 4 Drive" "Hornet Sportabout")
; #(21 21 22.8d0 21.4d0 18.7d0)
; #(6 6 4 6 8)
; #(160 160 108 258 360)
; #(110 110 93 110 175)
; #(3.9d0 3.9d0 3.85d0 3.08d0 3.15d0)
; #(2.62d0 2.875d0 2.32d0 3.215d0 3.44d0)
; #(16.46d0 17.02d0 18.61d0 19.44d0 17.02d0)
; #*00110
; #*11100
; #(4 4 4 3 3)
; #(4 4 1 1 2))
You can also return a subset of the columns by passing in a selection:
(columns mtcars-small '(mpg wt))
;; #(#(21 21 22.8d0 21.4d0 18.7d0) #(2.62d0 2.875d0 2.32d0 3.215d0 3.44d0))
Add columns
There are two ‘flavors’ of add functions, destructive and non-destructive. The latter return a new data frame as the result, and the destructive versions modify the data frame passed as a parameter. The destructive versions are denoted with a ‘!’ at the end of the function name.
The columns to be added can be in several formats:
- plist
- alist
- (plist)
- (alist)
- (data-frame)
To add a single column to a data frame, use the add-column!
function. We’ll use a data frame similar to the one used in our
reading data-frames from a string example to illustrate column
operations.
Create the data frame:
(defparameter *d* (read-csv
(format nil "Gender,Age,Height
\"Male\",30,180
\"Male\",31,182
\"Female\",32,165
\"Male\",22,167
\"Female\",45,170")))
and print it:
(head *d*)
;; GENDER AGE HEIGHT
;; 0 Male 30 180
;; 1 Male 31 182
;; 2 Female 32 165
;; 3 Male 22 167
;; 4 Female 45 170
and add a ‘weight’ column to it:
(add-column! *d* 'weight #(75.2 88.5 49.4 78.1 79.4))
;; GENDER AGE HEIGHT WEIGHT
;; 0 Male 30 180 75.2
;; 1 Male 31 182 88.5
;; 2 Female 32 165 49.4
;; 3 Male 22 167 78.1
;; 4 Female 45 170 79.4
now that we have weight, let’s add a BMI column to it to demonstrate using a function to compute the new column values:
(add-column! *d* 'bmi
(map-rows *d* '(height weight)
#'(lambda (h w) (/ w (square (/ h 100))))))
;; SEX AGE HEIGHT WEIGHT BMI
;; 0 Female 10 180 75.2 23.209875
;; 1 Female 15 182 88.5 26.717787
;; 2 Male 20 165 49.4 18.145086
;; 3 Female 25 167 78.1 28.003874
;; 4 Male 30 170 79.4 27.474049
Now let’s add multiple columns destructively using add-columns!
(add-columns! *d* 'a #(1 2 3 4 5) 'b #(foo bar baz qux quux))
;; GENDER AGE HEIGHT WEIGHT BMI A B
;; Male 30 180 75.2 23.2099 1 FOO
;; Male 31 182 88.5 26.7178 2 BAR
;; Female 32 165 49.4 18.1451 3 BAZ
;; Male 22 167 78.1 28.0039 4 QUX
;; Female 45 170 79.4 27.4740 5 QUUX
Remove columns
Let’s remove the columns a and b that we just added above with
the remove-columns function. Since it returns a new data frame,
we’ll need to assign the return value to *d*:
(setf *d* (remove-columns *d* '(a b bmi)))
;; GENDER AGE HEIGHT WEIGHT BMI
;; Male 30 180 75.2 23.2099
;; Male 31 182 88.5 26.7178
;; Female 32 165 49.4 18.1451
;; Male 22 167 78.1 28.0039
;; Female 45 170 79.4 27.4740
To remove columns destructively, meaning modifying the original data,
use the remove-column! or remove-columns! functions.
Rename columns
Sometimes data sources can have variable names that we want to change.
To do this, use the rename-column! function. This example will
rename the ‘gender’ variable to ‘sex’:
(rename-column! *d* 'sex 'gender)
;; SEX AGE HEIGHT WEIGHT
;; 0 Male 30 180 75.2
;; 1 Male 31 182 88.5
;; 2 Female 32 165 49.4
;; 3 Male 22 167 78.1
;; 4 Female 45 170 79.4
If you used defdf to create your data frame, and this is the
recommended way to define data frames, the variable references within
the data package will have been updated. This is true for all
destructive data frame operations. Let’s use this now to rename the
mtcars X1 variable to model. First a quick look at the first 2
rows as they are now:
(head mtcars 2)
;; X1 MPG CYL DISP HP DRAT WT QSEC VS AM GEAR CARB
;; 0 Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
;; 1 Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
Replace X1 with model:
(rename-column! mtcars 'model 'x1)
Note: check to see what value your version of mtcars has. In this
case, with a fresh start of Lisp-Stat, it has X1. It could have
X2, X3, etc.
Now check that it worked:
(head mtcars 2)
;; MODEL MPG CYL DISP HP DRAT WT QSEC VS AM GEAR CARB
;; 0 Mazda RX4 21 6 160 110 3.9 2.620 16.46 0 1 4 4
;; 1 Mazda RX4 Wag 21 6 160 110 3.9 2.875 17.02 0 1 4 4
We can now refer to mtcars:model
mtcars:model
#("Mazda RX4" "Mazda RX4 Wag" "Datsun 710" "Hornet 4 Drive" "Hornet Sportabout"
"Valiant" "Duster 360" "Merc 240D" "Merc 230" "Merc 280" "Merc 280C"
"Merc 450SE" "Merc 450SL" "Merc 450SLC" "Cadillac Fleetwood"
"Lincoln Continental" "Chrysler Imperial" "Fiat 128" "Honda Civic"
"Toyota Corolla" "Toyota Corona" "Dodge Challenger" "AMC Javelin"
"Camaro Z28" "Pontiac Firebird" "Fiat X1-9" "Porsche 914-2" "Lotus Europa"
"Ford Pantera L" "Ferrari Dino" "Maserati Bora" "Volvo 142E")
Replace columns
Columns are “setf-able” places and the simplest way to replace a
column is set the field to a new value. We’ll complement the sex
field of *d*:
(df::setf (df:column *d* 'sex) #("Female" "Female" "Male" "Female" "Male"))
;#("Female" "Female" "Male" "Female" "Male")
Note that df::setf is not exported. Use this with caution.
You can also replace a column using two functions specifically for this purpose. Here we’ll replace the ‘age’ column with new values:
(replace-column *d* 'age #(10 15 20 25 30))
;; SEX AGE HEIGHT WEIGHT
;; 0 Female 10 180 75.2
;; 1 Female 15 182 88.5
;; 2 Male 20 165 49.4
;; 3 Female 25 167 78.1
;; 4 Male 30 170 79.4
That was a non-destructive replacement, and since we didn’t reassign
the value of *d*, it is unchanged:
LS-USER> (print-data *d*)
;; SEX AGE HEIGHT WEIGHT
;; 0 Female 30 180 75.2
;; 1 Female 31 182 88.5
;; 2 Male 32 165 49.4
;; 3 Female 22 167 78.1
;; 4 Male 45 170 79.4
We can also use the destructive version to make a permanent change
instead of setf-ing *d*:
(replace-column! *d* 'age #(10 15 20 25 30))
;; SEX AGE HEIGHT WEIGHT
;; 0 Female 10 180 75.2
;; 1 Female 15 182 88.5
;; 2 Male 20 165 49.4
;; 3 Female 25 167 78.1
;; 4 Male 30 170 79.4
Transform columns
There are two functions for column transformations, replace-column
and map-columns.
replace-column
replace-column can be used to transform a column by applying a
function to each value. This example will add 20 to each row of the
age column:
(replace-column *d* 'age #'(lambda (x) (+ 20 x)))
;; SEX AGE HEIGHT WEIGHT
;; 0 Female 30 180 75.2
;; 1 Female 35 182 88.5
;; 2 Male 40 165 49.4
;; 3 Female 45 167 78.1
;; 4 Male 50 170 79.4
replace-column! can also apply functions to a column, destructively
modifying the column.
map-columns
The map-columns functions can be thought of as applying a function
on all the values of each variable/column as a vector, rather than the
individual rows as replace-column does. To see this, we’ll use
functions that operate on vectors, in this case nu:e+, which is the
vector addition function for Lisp-Stat. Let’s see this working first:
(nu:e+ #(1 1 1) #(2 3 4))
; => #(3 4 5)
observe how the vectors were added element-wise. We’ll demonstrate
map-columns by adding one to each of the numeric columns in the
example data frame:
(map-columns (select *d* t '(weight age height))
#'(lambda (x)
(nu:e+ 1 x)))
;; WEIGHT AGE HEIGHT
;; 0 76.2 11 181
;; 1 89.5 16 183
;; 2 50.4 21 166
;; 3 79.1 26 168
;; 4 80.4 31 171
recall that we used the non-destructive version of replace-column
above, so *d* has the original values. Also note the use of select
to get the numeric variables from the data frame; e+ can’t add
categorical values like gender/sex.
Row operations
As the name suggests, row operations operate on each row, or observation, of a data set.
count-rows
This function is used to determine how many rows meet a certain condition. For example if you want to know how many cars have a MPG (miles-per-galleon) rating greater than 20, you could use:
(count-rows mtcars 'mpg #'(lambda (x) (< 20 x)))
; => 14
do-rows
do-rows applies a function on selected variables. The function must
take the same number of arguments as variables supplied. It is
analogous to dotimes, but
iterating over data frame rows. No values are returned; it is purely
for side-effects. Let’s create a new data data-frame to
illustrate row operations:
LS-USER> (defparameter *d2*
(make-df '(a b) '(#(1 2 3) #(10 20 30))))
*D2*
LS-USER> *d2*
;; A B
;; 0 1 10
;; 1 2 20
;; 2 3 30
This example uses format to illustrate iterating using do-rows for
side effect:
(do-rows *d2* '(a b) #'(lambda (a b) (format t "~A " (+ a b))))
11 22 33
; No value
map-rows
Where map-columns can be thought of as working through the data
frame column-by-column, map-rows goes through row-by-row. Here we
add the values in each row of two columns:
(map-rows *d2* '(a b) #'+)
#(11 22 33)
Since the length of this vector will always be equal to the data-frame column length, we can add the results to the data frame as a new column. Let’s see this in a real-world pattern, subtracting the mean from a column:
(add-column! *d2* 'c
(map-rows *d2* 'b
#'(lambda (x) (- x (mean (select *d2* t 'b))))))
;; A B C
;; 0 1 10 -10.0
;; 1 2 20 0.0
;; 2 3 30 10.0
You could also have used replace-column! in a similar manner to
replace a column with normalize values.
mask-rows
mask-rows is similar to count-rows, except it returns a bit-vector
for rows matching the predicate. This is useful when you want to pass
the bit vector to another function, like select to retrieve only the
rows matching the predicate.
(mask-rows mtcars 'mpg #'(lambda (x) (< 20 x)))
; => #*11110001100000000111100001110001
filter-rows
The filter-rows function will return a data-frame whose rows match
the predicate. The function signature is:
(defun filter-rows (data body) ...
As an example, let’s filter mtcars to find all the cars whose fuel
consumption is greater than 20 mpg:
(filter-rows mtcars '(< 20 mpg))
;=> #<DATA-FRAME (14 observations of 12 variables)>
To view them we’ll need to call the print-data function directly instead
of using the print-object function we installed earlier. Otherwise,
we’ll only see the first 6.
(print-data *)
;; MODEL MPG CYL DISP HP DRAT WT QSEC VS AM GEAR CARB
;; 0 Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
;; 1 Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
;; 2 Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
;; 3 Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
;; 4 Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
;; 5 Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
;; 6 Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
;; 7 Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
;; 8 Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
;; 9 Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
;; 10 Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
;; 11 Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
;; 12 Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
;; 13 Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
Filter predicates can be more complex than this, here’s an example
filtering the Vega movies data set (which we call imdb):
(filter-rows imdb
'(and (not (eql imdb-rating :na))
(local-time:timestamp< release-date
(local-time:parse-timestring "2019-01-01"))))
You can refer to any of the column/variable names in the data-frame
directly when constructing the filter predicate. The predicate is
turned into a lambda function, so let, etc is also possible.
Summarising data
Often the first thing you’ll want to do with a data frame is get a quick summary. You can do that with these functions, and we’ve seen most of them used in this manual. For more information about these functions, see the data-frame api reference.
- nrow data-frame
- return the number of rows in data-frame
- ncol data-frame
- return the number of columns in data-frame
- dims data-frame
- return the dimensions of data-frame as a list in (rows columns) format
- keys data-frame
- return a vector of symbols representing column names
- column-names data-frame
- returns a list of strings of the column names in data-frames
- head data-frame &optional n
- displays the first n rows of data-frame. n defaults to 6.
- tail data-frame &optional n
- displays the last n rows of data-frame. n defaults to 6.
describe
- describe data-frame
- returns the meta-data for the variables in data-frame
describe is a common lisp function that describes an object. In
Lisp-Stat describe prints a description of the data frame and the
three ‘standard’ properties of the variables: type, unit and
description. It is similar to the str command in R. To see an
example use the augmented mtcars data set included in Lisp-Stat. In
this data set, we have added properties describing the variables.
This is a good illustration of why you should always save data frames
in lisp format; properties such as these are lost in CSV format.
(data :mtcars)
LS-USER> (describe mtcars)
MTCARS
Motor Trend Car Road Tests
A data-frame with 32 observations of 12 variables
Variable | Type | Unit | Label
-------- | ---- | ---- | -----------
MODEL | STRING | NIL | NIL
MPG | DOUBLE-FLOAT | M/G | Miles/(US) gallon
CYL | INTEGER | NA | Number of cylinders
DISP | DOUBLE-FLOAT | IN3 | Displacement (cu.in.)
HP | INTEGER | HP | Gross horsepower
DRAT | DOUBLE-FLOAT | NA | Rear axle ratio
WT | DOUBLE-FLOAT | LB | Weight (1000 lbs)
QSEC | DOUBLE-FLOAT | S | 1/4 mile time
VS | BIT | NA | Engine (0=v-shaped, 1=straight)
AM | BIT | NA | Transmission (0=automatic, 1=manual)
GEAR | INTEGER | NA | Number of forward gears
CARB | INTEGER | NA | Number of carburetors
summary
- summary data-frame
- returns a summary of the variables in data-frame
Summary functions are one of those things that tend to be use-case or application specific. Witness the number of R summary packages; there are at least half a dozen, including hmisc, stat.desc, psych describe, skim and summary tools. In short, there is no one-size-fits-all way to provide summaries, so Lisp-Stat provides the data structures upon which users can customise the summary output. The output you see below is a simple :print-function for each of the summary structure types (numeric, factor, bit and generic).
LS-USER> (summary mtcars)
(
MPG (Miles/(US) gallon)
n: 32
missing: 0
min=10.40
q25=15.40
q50=19.20
mean=20.09
q75=22.80
max=33.90
CYL (Number of cylinders)
14 (44%) x 8, 11 (34%) x 4, 7 (22%) x 6,
DISP (Displacement (cu.in.))
n: 32
missing: 0
min=71.10
q25=120.65
q50=205.87
mean=230.72
q75=334.00
max=472.00
HP (Gross horsepower)
n: 32
missing: 0
min=52
q25=96.00
q50=123
mean=146.69
q75=186.25
max=335
DRAT (Rear axle ratio)
n: 32
missing: 0
min=2.76
q25=3.08
q50=3.70
mean=3.60
q75=3.95
max=4.93
WT (Weight (1000 lbs))
n: 32
missing: 0
min=1.51
q25=2.54
q50=3.33
mean=3.22
q75=3.68
max=5.42
QSEC (1/4 mile time)
n: 32
missing: 0
min=14.50
q25=16.88
q50=17.71
mean=17.85
q75=18.90
max=22.90
VS (Engine (0=v-shaped, 1=straight))
ones: 14 (44%)
AM (Transmission (0=automatic, 1=manual))
ones: 13 (41%)
GEAR (Number of forward gears)
15 (47%) x 3, 12 (38%) x 4, 5 (16%) x 5,
CARB (Number of carburetors)
10 (31%) x 4, 10 (31%) x 2, 7 (22%) x 1, 3 (9%) x 3, 1 (3%) x 6, 1 (3%) x 8, )
Note that the model column, essentially row-name was deleted from
the output. The summary function, designed for human readable
output, removes variables with all unique values, and those with
monotonically increasing numbers (usually row numbers).
To build your own summary function, use the get-summaries function
to get a list of summary structures for the variables in the data
frame, and then print them as you wish.
columns
You can also describe or summarize individual columns:
LS-USER> (describe 'mtcars:mpg)
MTCARS:MPG
[symbol]
MPG names a symbol macro:
Expansion: (AREF (COLUMNS MTCARS) 1)
Symbol-plist:
:TYPE -> DOUBLE-FLOAT
:UNIT -> M/G
:LABEL -> "Miles/(US) gallon"
LS-USER> (summarize-column 'mtcars:mpg)
MPG (Miles/(US) gallon)
n: 32
missing: 0
min=10.40
q25=15.40
q50=19.20
mean=20.09
q75=22.80
max=33.90
Missing values
Data sets often contain missing values and we need to both understand
where and how many are missing, and how to transform or remove them
for downstream operations. In Lisp-Stat, missing values are
represented by the keyword symbol :na. You can control this
encoding during delimited text import by passing an a-list
containing the mapping. By default this is a keyword parameter
map-alist:
(map-alist '(("" . :na)
("NA" . :na)))
The default maps blank cells ("") and ones containing “NA” (not
available) to the keyword :na, which stands for missing.
Some systems encode missing values as numeric, e.g. 99; in this case
you can pass in a map-alist that includes this mapping:
(map-alist '(("" . :na)
("NA" . :na)
(99 . :na)))
We will use the R air-quality dataset to illustrate working with missing values. Let’s load it now:
(defdf aq
(read-csv rdata:airquality))
Examine
To see missing values we use the predicate missingp. This works on
sequences, arrays and data-frames. It returns a logical sequence,
array or data-frame indicating which values are missing. T
indicates a missing value, NIL means the value is present. Here’s
an example of using missingp on a vector:
(missingp #(1 2 3 4 5 6 :na 8 9 10))
;#(NIL NIL NIL NIL NIL NIL T NIL NIL NIL)
and on a data-frame:
(print-data (missingp aq))
;; X3 OZONE SOLAR-R WIND TEMP MONTH DAY
;; 0 NIL NIL NIL NIL NIL NIL NIL
;; 1 NIL NIL NIL NIL NIL NIL NIL
;; 2 NIL NIL NIL NIL NIL NIL NIL
;; 3 NIL NIL NIL NIL NIL NIL NIL
;; 4 NIL T T NIL NIL NIL NIL
;; 5 NIL NIL T NIL NIL NIL NIL
;; 6 NIL NIL NIL NIL NIL NIL NIL
;; 7 NIL NIL NIL NIL NIL NIL NIL
;; 8 NIL NIL NIL NIL NIL NIL NIL
;; 9 NIL T NIL NIL NIL NIL NIL
;; 10 NIL NIL T NIL NIL NIL NIL
;; 11 NIL NIL NIL NIL NIL NIL NIL
;; 12 NIL NIL NIL NIL NIL NIL NIL
;; 13 NIL NIL NIL NIL NIL NIL NIL
;; 14 NIL NIL NIL NIL NIL NIL NIL
;; 15 NIL NIL NIL NIL NIL NIL NIL
;; 16 NIL NIL NIL NIL NIL NIL NIL
;; 17 NIL NIL NIL NIL NIL NIL NIL
;; 18 NIL NIL NIL NIL NIL NIL NIL
;; 19 NIL NIL NIL NIL NIL NIL NIL
;; 20 NIL NIL NIL NIL NIL NIL NIL
;; 21 NIL NIL NIL NIL NIL NIL NIL
;; 22 NIL NIL NIL NIL NIL NIL NIL
;; 23 NIL NIL NIL NIL NIL NIL NIL ..
We can see that the ozone variable contains some missing values. To
see which rows of ozone are missing, we can use the which
function:
(which aq:ozone :predicate #'missingp)
;#(4 9 24 25 26 31 32 33 34 35 36 38 41 42 44 45 51 52 53 54 55 56 57 58 59 60 64 71 74 82 83 101 102 106 114 118 149)
and to get a count, use the length function on this vector:
(length *) ; => 37
It’s often convenient to use the summary function to get an overview
of missing values. We can do this because the missingp function is
a transformation of a data-frame that yields another data-frame of
boolean values:
LS-USER> (summary (missingp aq))
X4: 153 (100%) x NIL,
OZONE: 116 (76%) x NIL, 37 (24%) x T,
SOLAR-R: 146 (95%) x NIL, 7 (5%) x T,
WIND: 153 (100%) x NIL,
TEMP: 153 (100%) x NIL,
MONTH: 153 (100%) x NIL,
DAY: 153 (100%) x NIL,
we can see that ozone is missing 37 values, 24% of the total, and
solar-r is missing 7 values.
Exclude
To exclude missing values from a single column, use the Common Lisp
remove function:
(remove :na aq:ozone)
;#(41 36 12 18 28 23 19 8 7 16 11 14 18 14 34 6 30 11 1 11 4 32 ...
To ensure that our data-frame includes only complete observations, we
exclude any row with a missing value. To do this use the
drop-missing function:
(head (drop-missing aq))
;; X3 OZONE SOLAR-R WIND TEMP MONTH DAY
;; 0 1 41 190 7.4 67 5 1
;; 1 2 36 118 8.0 72 5 2
;; 2 3 12 149 12.6 74 5 3
;; 3 4 18 313 11.5 62 5 4
;; 4 7 23 299 8.6 65 5 7
;; 5 8 19 99 13.8 59 5 8
Replace
To replace missing values we can use the transformation functions.
For example we can recode the missing values in ozone by the mean.
Let’s look at the first six rows of the air quality data-frame:
(head aq)
;; X3 OZONE SOLAR-R WIND TEMP MONTH DAY
;; 0 1 41 190 7.4 67 5 1
;; 1 2 36 118 8.0 72 5 2
;; 2 3 12 149 12.6 74 5 3
;; 3 4 18 313 11.5 62 5 4
;; 4 5 NA NA 14.3 56 5 5
;; 5 6 28 NA 14.9 66 5 6
Now replace ozone with the mean using the common lisp function
nsubstitute:
(nsubstitute (mean (remove :na aq:ozone)) :na aq:ozone)
and look at head again:
(head aq)
;; X3 OZONE SOLAR-R WIND TEMP MONTH DAY
;; 0 1 41.0000 190 7.4 67 5 1
;; 1 2 36.0000 118 8.0 72 5 2
;; 2 3 12.0000 149 12.6 74 5 3
;; 3 4 18.0000 313 11.5 62 5 4
;; 4 5 42.1293 NA 14.3 56 5 5
;; 5 6 28.0000 NA 14.9 66 5 6
You could have used the non-destructive substitute if you wanted to
create a new data-frame and leave the original aq untouched.
Normally we’d round mean to be consistent from a type perspective,
but did not here so you can see the values that were replaced.
Sampling
You can take a random sample of the rows of a data-frame with the select:sample function:
LS-USER> mtcars
#<DATA-FRAME (32 observations of 12 variables)
Motor Trend Car Road Tests>
LS-USER> (sample mtcars 3 :skip-unselected t)
#<DATA-FRAME (3 observations of 12 variables)>
LS-USER> (print-data *)
;; MODEL MPG CYL DISP HP DRAT WT QSEC VS AM GEAR CARB
;; 0 Hornet Sportabout 18.7 8 360.0 175 3.15 3.44 17.02 0 0 3 2
;; 1 Duster 360 14.3 8 360.0 245 3.21 3.57 15.84 0 0 3 4
;; 2 Merc 230 22.8 4 140.8 95 3.92 3.15 22.90 1 0 4 2
You can also take random samples from CL sequences and arrays, with or without replacement and in various proportions. For further information see sampling in the select system manual.
Uses Vitter’s Algorithm
D to
efficiently select the rows. Sometimes you may want to use the
algorithm at a lower level. If you don’t want the sample itself, say you
only want the indices, you can directly use map-random-below, which
simply calls a provided function on each index.
This is an enhancement and port to standard common lisp of ruricolist’s random-sample. It also removes the dependency on Trivia, which has a restrictive license (LLGPL).
Dates & Times
Lisp-Stat uses localtime to
represent dates. This works well, but the system is a bit strict on
input formats, and real-world data can be quite messy at times. For
these cases chronicity
and
cl-date-time-parser
can be helpful. Chronicity returns local-time timestamp objects,
and is particularly easy to work with.
For example, if you have a variable with dates encoded like: ‘Jan 7
1995’, you can recode the column like we did for the vega movies
data set:
(replace-column! imdb 'release-date #'(lambda (x)
(local-time:universal-to-timestamp
(date-time-parser:parse-date-time x))))
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