Numerical Analysis & Statistics: MATLAB, R, NumPy, Julia

a side-by-side reference sheet

sheet one: grammar and invocation | variables and expressions | arithmetic and logic | strings | regexes | dates and time | tuples | arrays | arithmetic sequences | 2d arrays | 3d arrays | dictionaries | functions | execution control | file handles | directories | processes and environment | libraries and namespaces | reflection

sheet two: tables | import and export | relational algebra | aggregation

vectors | matrices | sparse matrices | optimization | polynomials | descriptive statistics | distributions | linear regression | statistical tests | time series | fast fourier transform | clustering

univariate charts | bivariate charts | multivariate charts

matlabrnumpyjulia
version usedMATLAB 8.3

Octave 3.8
3.1Python 2.7
NumPy 1.7
SciPy 0.13
Pandas 0.12
Matplotlib 1.3
0.4
show version$ matlab -nojvm -nodisplay -r 'exit'

$ octave --version
$ R --versionsys.version
np.__version__
sp.__version__
mpl.__version__
$ julia --version
implicit prologuenoneimport sys, os, re, math
import numpy as np
import scipy as sp
import scipy.stats as stats
import pandas as pd
import matplotlib as mpl
import matplotlib.pyplot as plt
grammar and invocation
matlabrnumpyjulia
interpreter
 
$ cat >>foo.m
1 + 1
exit

$ matlab -nojvm -nodisplay -r "run('foo.m')"

$ octave foo.m
$ cat >>foo.r
1 + 1

$ Rscript foo.r

$ R -f foo.r
$ cat >>foo.py
print(1 + 1)

$ python foo.py
$ cat >>foo.jl
println(1 + 1)

$ julia foo.jl
repl
 
$ matlab -nojvm -nodisplay

$ octave
$ R$ python$ julia
command line program$ matlab -nojvm -nodisplay -r 'disp(1 + 1); exit'

$ octave --silent --eval '1 + 1'
$ Rscript -e 'print("hi")'python -c 'print("hi")'$ julia -e 'println("hi")'
block delimitersfunction end
if elseif else end
while end
for end
{ }offside rule
statement separator; or newline

Newlines not separators after three dots: ...

Output is suppressed when lines end with a semicolon.
; or sometimes newline

Newlines not separators inside (), [], {}, '', "", or after binary operator.
newline or ;

Newlines not separators inside (), [], {}, triple quote literals, or after backslash: \
end-of-line comment
 
1 + 1 % addition1 + 1 # addition1 + 1 # addition1 + 1 # addition
variables and expressions
matlabrnumpyjulia
assignmenti = 3i = 3
i <- 3
3 -> i
assign("i", 3)
i = 3i = 3
parallel assignment
swap
compound assignment
arithmetic, string, logical
nonenone# do not return values:
+= -= *= /= //= %= **=
+= *=
&= |= ^=
null% Only used in place of numeric values:
NaN
NA NULLNone np.nan

# None cannot be stored in a numpy array;
# np.nan can if dtype is float64.
# Only used in place of float values:
NaN
null testisnan(v)

% true for '', []:
isempty(v)
is.na(v)
is.null(v)
v == None
v is None

np.isnan(np.nan)
# np.nan == np.nan is False
isnan(v)
conditional expressionnone(if (x > 0) x else -x)
ifelse(x > 0, x, -x)
x if x > 0 else -xx > 0 ? x : -x
arithmetic and logic
matlabrnumpyjulia
true and false
 
1 0 true falseTRUE FALSE T FTrue Falsetrue false
falsehoodsfalse 0 0.0
matrices evaluate to false unless nonempty and all entries evaluate to true
FALSE F 0 0.0
matrices evaluate to value of first entry; string in boolean context causes error
False None 0 0.0 '' [] {}false
logical operators~true | (true & false)

% short-circuit operators:
&& ||
!TRUE | (TRUE & FALSE)
short-circuit operators:
&& ||

& and | can operate on and return vectors, but && and || return scalars
and or not&& || !
relational operators
 
== ~= > < >= <=== != > < >= <=== != > < >= <=== != > < >= <=
integer typeInt8 Int16 Int32 Int64 Int128

Int is either 32 or 64 bits, depending on WORD_SIZE
unsigned typeUInt8 UInt16 UInt32 UInt64 UInt128

UInt is either 32 or 64 bits, depending on WORD_SIZE
float type
 
Float16 Float32 Float64
arithmetic operators
add, sub, mult, div, quot, rem
+ - * / none mod(n, divisor)+ - * / %/% %%+ - * / // %+ - * / div(n, divisor) rem(n, divisor)

# always non-negative:
mod(n, divisor)
integer division
 
fix(13 / 5)13 %/% 5
as.integer(13 / 5)
13 // 5div(13, 5)
integer division by zero
 
Inf NaN or -Infresult of converting Inf or NaN to an integer with as.integer:
NA
raises ZeroDivisionErrorraises DivideError
float division
 
13 / 513 / 5float(13) / 513 / 5
5 \ 13
float division by zero
dividend is positive, zero, negative
these values are literals:
Inf
NaN
-Inf
these values are literals:
Inf
NaN
-Inf
raises ZeroDivisionErrorthese values are literals:
Inf
NaN
-Inf
power2 ^ 162 ^ 16
2 ** 16
2 ** 162 ^ 16
sqrt
 
sqrt(2)sqrt(2)math.sqrt(2)sqrt(2)
sqrt -1% returns 0 + 1i:
sqrt(-1)
# returns NaN:
sqrt(-1)

# returns 0+1i:
sqrt(-1+0i)
# raises ValueError:
math.sqrt(-1)

# returns 1.41421j:
import cmath
cmath.sqrt(-1)
# raises DomainError:
sqrt(-1)

# returns 0.0 + 1.0im:
sqrt(-1 + 0im)
transcendental functionsexp log sin cos tan asin acos atan atan2exp log sin cos tan asin acos atan atan2math.exp math.log math.sin math.cos math.tan math.asin math.acos math.atan math.atan2exp log sin cos tan asin acos atan atan2
transcendental constantspi epi exp(1)math.pi math.epi e
float truncation
round towards zero, to nearest integer, down, up
fix(x)
round(x)
floor(x)
ceil(x)
as.integer(x)
round(x)
floor(x)
ceiling(x)
int(x)
int(round(x))
math.floor(x)
math.ceil(x)
Int(trunc(x))
Int(round(x))
Int(floor(x))
Int(ceil(x))

# trunc() and other functions return floats.
# Int() raises InexactError if float argument has
# nonzero fractional portion.
absolute value
and signum
abs signabs signabs(-3.7)
math.copysign(1, -3.7)
abs(-3.7)
sign(-3.7)
integer overflowbecomes float; largest representable integer in the variable intmaxbecomes float; largest representable integer in the variable .Machine$integer.maxbecomes arbitrary length integer of type long
float overflow
 
InfInfraises OverflowError
float limits
 
eps
realmax
realmin
.Machine$double.eps
.Machine$double.xmax
.Machine$double.xmin
np.finfo(np.float64).eps
np.finfo(np.float64).max
np.finfo(np.float64).min
rational construction22 // 7
rational decompositionnum(22 // 7)
den(22 // 7)
complex construction
 
1 + 3i1 + 3i1 + 3j1 + 3im
complex(1, 3)
complex decompositionreal imag
abs arg
conj
Re Im
abs Arg
Conj
import cmath

z.real
z.imag
cmath.polar(z)[1]
real(1 + 3im)
imag(1 + 3im)
abs(1 + 3im)
angle(1 + 3im)
conj(1 + 3im)
random number
uniform integer, uniform float
floor(100 * rand)
rand
floor(100 * runif(1))
runif(1)
np.random.randint(0, 100)
np.random.rand()
rand(1:100)
rand()
random seed
set, get, and restore
rand('state', 17)
sd = rand('state')
rand('state', sd)
set.seed(17)
sd = .Random.seed
none
np.random.seed(17)
sd = np.random.get_state()
np.random.set_state(sd)
bit operatorsbitshift(100, 3)
bitshift(100, -3)
bitand(1, 2)
bitor(1, 2)
bitxor(1, 2)
% MATLAB:
bitcmp(1, 'uint16')
% Octave:
bitcmp(1, 16)
none100 << 3
100 >> 3
1 & 2
1 | 2
1 ^ 2
~1
binary, octal, and hex literals0b101010
0o52
0x2a
radix
convert integer to and from string with radix
base(7, 42)
parse(Int, "60", 7)
strings
matlabrnumpyjulia
literal'don''t say "no"'

% Octave only:
"don't say \"no\""
"don't say \"no\""
'don\'t say "no"'
'don\'t say "no"'
"don't say \"no\""
r"don't " r'say "no"'
"don't say \"no\""
newline in literal
 
noyesnoyes
literal escapes% Octave double quote only:
\\ \" \' \0 \a \b \f \n \r \t \v
\\ \" \' \a \b \f \n \r \t \v \ooo# single and double quoted:
\newline \\ \' \" \a \b \f \n \r \t \v \ooo \xhh
\\ \" \' \a \b \f \n \t \r \v
\ooo \xhh \uhhhh \Uhhhhhhhh
variable interpolationcount = 3
item = "ball"
println("$count $(item)s")
expression interpolation
 
"1 + 1 = $(1 + 1)"
concatenatestrcat('one ', 'two ', 'three')paste("one", "two", "three", sep=" ")'one ' + 'two ' + 'three'
literals, but not variables, can be concatenated with juxtaposition:
'one ' "two " 'three'
"one " * "two " * "three"

string("one ", "two ", "three")
replicate
 
hbar = repmat('-', 1, 80)hbar = paste(rep('-', 80), collapse='')hbar = '-' * 80hbar = "-" ^ 80

hbar = repeat("-", 80)
index of substring% returns array of one-indexed
% locations

strfind('hello', 'el')
counts from one, returns
-1 if not found

regexpr("el", "hello")
# Counts from zero; raises ValueError if not found:
'hello'.index('el')
# returns UnitRange:
search("hello", "el")
extract substring
 
s = 'hello'
% syntax error: 'hello'(1:4)
s(1:4)
substr("hello", 1, 4)'hello'[0:4]"hello"[1:4]
split% returns cell array:
strsplit('foo,bar,baz', ',')
strsplit('foo,bar,baz', ',')'foo,bar,baz'.split(',')split("foo,bar,baz", ",")
join% takes cell array as arg:
strjoin({'foo', 'bar', 'baz'}, ',')
paste("foo", "bar", "baz", sep=",")
paste(c('foo', 'bar', 'baz'),
  collapse=',')
','.join(['foo', 'bar', 'baz'])join(["foo", "bar", "baz"], ",")
trim
both sides, left, right
strtrim(' foo ')
none
deblank('foo ')
gsub("(^[\n\t ]+|[\n\t ]+$)",
  "",
  " foo ")
sub("^[\n\t ]+", "", " foo")
sub("[\n\t ]+$", "", "foo ")
' foo '.strip()
' foo'.lstrip()
'foo '.rstrip()
pad
on right, on left, centered
s = repmat(' ', 1, 10)
s(1:5) = 'lorem'
strjust(s, 'left')
strjust(s, 'right')
strjust(s, 'center')
sprintf("%-10s", "lorem")
sprintf("%10s", "lorem")
none
'lorem'.ljust(10)
'lorem'.rjust(10)
'lorem'.center(10)
number to string
 
strcat('value: ', num2str(8))paste("value: ", toString("8"))'value: ' + str(8)
string to number7 + str2num('12')
73.9 + str2num('.037')
7 + as.integer("12")
73.9 + as.double(".037")
7 + int('12')
73.9 + float('.037')
7 + parse(Int, "12")
73.9 + parse(Float64, ".037")
translate caselower('FOO')
upper('foo')
tolower("FOO")
toupper("foo")
'foo'.upper()
'FOO'.lower()
uppercase("foo")
lowercase("FOO")
sprintf
 
sprintf('%s: %.3f %d', 'foo', 2.2, 7)sprintf("%s: %.3f %d", "foo", 2.2, 7)'%s: %.3f %d' % ('foo', 2.2, 7)@sprintf("%s: %.2f %d", "foo", 2.2, 7)
length
 
length('hello')nchar("hello")len('hello')length("hello")

# index of first byte of last char:
endof("hello")
character access
 
s = 'hello'
% syntax error: 'hello'(1)
s(1)
substr("hello", 1, 1)'hello'[0]"hello"[1]

# index must be byte-index of the first byte of a
# character. Raises BoundsErrror if no such byte,
# and UnicodeError if byte not first in char.
chr and ordchar(65)
double('A')
intToUtf8(65)
utf8ToInt("A")
chr(65)
ord('A')
Char(65)
Int('A')
regular expressions
matlabrnumpyjulia
character class abbreviations. \d \D \s \S \w \W

% also C-string style backslash escapes:
\a \b \f \n \r \t \v
# escape backslash in strings by doubling:
. \d \D \s \S \w \W
. \d \D \s \S \w \W. \d \D \h \H \s \S \v \V \w \W
anchors
 
^ $ \< \># escape backslash in strings by doubling:
^ $ \< \> \b \B
^ $ \A \b \B \Z^ $ \A \b \B \z \Z
match testregexp('hello', '^[a-z]+$')
regexp('hello', '^\S+$')
regexpr("^[a-z]+$", "hello") > 0
regexpr('^\\S+$', "hello") > 0
re.search(r'^[a-z]+$', 'hello')
re.search(r'^\S+$', 'hello')
ismatch(r"^[a-z]+$", "hello")
case insensitive match testregexpi('Lorem Ipsum', 'lorem')regexpr('(?i)lorem', "Lorem Ipsum") > 0re.search(r'lorem', 'Lorem Ipsum', re.I)ismatch(r"lorem"i, "Lorem Ipsum")
modifiers
 
none(?i) (?m) (?s) (?x)re.I re.M re.S re.Xi m s x
substitution
first match, all matches
s = 'do re mi mi mi'
regexprep(s, 'ma', 'once')
regexprep(s, 'mi', 'ma')
sub('mi', 'ma', 'do re mi mi mi')
gsub('mi', 'ma', 'do re mi mi mi')
rx = re.compile(r'mi')
s = rx.sub('ma', 'do re mi mi mi', 1)
s2 = rx.sub('ma', 'do re mi mi mi')
replace("do re mi mi mi", r"mi", s"ma", 1)
replace("do re mi mi mi", r"mi", s"ma")
backreference in match and substitutionregexp('do do', '(\w+) \1')
regexprep('do re', '(\w+) (\w+)', '$2 $1')
regexpr('(\\w+) \\1', 'do do') > 0
sub('(\\w+) (\\w+)', '\\2 \\1', 'do re')
none

rx = re.compile(r'(\w+) (\w+)')
rx.sub(r'\2 \1', 'do re')
ismatch(r"(\w+) \1", "do do")
group capturerx = '(\d{4})-(\d{2})-(\d{2})'
m = re.search(rx, '2010-06-03')
yr, mo, dy = m.groups()
rx = r"(\d{4})-(\d{2})-(\d{2})"
m = match(rx, "2010-06-03")
yr, mn, dy = m.captures
dates and time
matlabrnumpyjulia
current date/time
 
t = nowt = as.POSIXlt(Sys.time())import datetime

t = datetime.datetime.now()
t = now()
date/time typefloating point number representing days since year 0 in the Gregorian calendarPOSIXltdatettimeDateTime
date/time difference typefloating point number representing daysa difftime object which behaves like a floating point number representing secondstimedelta, which can be converted to float value in seconds via total_seconds() methodBase.Dates.Millisecond
get date partsdv = datevec(t)
dv(1)
dv(2)
dv(3)
% syntax error: datevec(t)(1)
t$year + 1900
t$mon + 1
t$mday
t.year
t.month
t.day
Dates.year(t)
Dates.month(t)
Dates.day(t)
get time partsdv = datevec(t)
dv(4)
dv(5)
dv(6)
t$hour
t$min
t$sec
t.hour
t.minute
t.second
Dates.hour(t)
Dates.minute(t)
Dates.second(t)
build date/time from partst = datenum([2011 9 20 23 1 2])t = as.POSIXlt(Sys.time())
t$year = 2011 - 1900
t$mon = 9 - 1
t$mday = 20
t$hour = 23
t$min = 1
t$sec = 2
import datetime

t = datetime.datetime(2011, 9, 20, 23, 1, 2)
t = DateTime(2011, 9, 20, 23, 1, 2)
convert to string
 
datestr(t)print(t)str(t)"$t"
parse datetimes = '2011-09-20 23:01:02'
fmt = 'yyyy-mm-dd HH:MM:SS'
t = datenum(s, fmt)
t = strptime('2011-09-20 23:01:02',
  '%Y-%m-%d %H:%M:%S')
import datetime

s = '2011-05-03 10:00:00'
fmt = '%Y-%m-%d %H:%M:%S'
t = datetime.datetime.strptime(s, fmt)
fmt = "yyyy-mm-dd HH:MM:SS"
t = DateTime("2011-05-03 10:00:00", fmt)

# fmt string can be compiled:
df = Dates.DateFormat(fmt)
t2 = DateTime("2011-05-03 10:00:00", df)
format datetime
 
datestr(t, 'yyyy-mm-dd HH:MM:SS')format(t, format='%Y-%m-%d %H:%M:%S')t.strftime('%Y-%m-%d %H:%M:%S')Dates.format(t, "yyyy-mm-dd HH:MM:SS")
sleeppause(0.5)Sys.sleep(0.5)import time

time.sleep(0.5)
sleep(0.5)
tuples
matlabrnumpyjulia
type
 
celllisttupleTuple{T[, ...]}
literal
 
tup = {1.7, 'hello', [1 2 3]}tup = list(1.7, "hello", c(1, 2, 3))tup = (1.7, "hello", [1,2,3])tup = (1.7, "foo", [1, 2, 3])
lookup element
 
% indices start at one:
tup{1}
# indices start at one:
tup[[1]]
# indices start at zero:
tup[0]
# indices start at one:
tup[1]
update element
 
tup{1} = 2.7tup[[1]] = 2.7tuples are immutabletuples are immutable
length
 
length(tup)length(tup)len(tup)length(tup)
arrays
matlabrnumpyjulia
element typealways numeric# "numeric":
class(c(1, 2, 3))

# arrays can also have "boolean" or "string" elements
# values can have different types:
[type(x) for x in a]
a = [1, 2, 3]

# Array{Int64, 2}:
typeof(a)
# Int64:
typeof(a[1])
literal
 
a = [1, 2, 3, 4]

% commas are optional:
a = [1 2 3 4]
# use c() constructor:
a = c(1, 2, 3, 4)
a = [1, 2, 3, 4]a = [1, 2, 3, 4]
size
 
length(a)length(a)len(a)length(a)
empty test
 
length(a) == 0

% An array used in a conditional test is
% false unless nonempty and all entries evaluate
% as true.
length(a) == 0not aisempty(a)
lookup
 
% Indices start at one:
a(1)
# Indices start at one:
a[1]
# Indices start at zero:
a[0]
# Indices start at one:
a[1]
update
 
a(1) = -1a[1] = -1a[0] = -1a[1] = -1
out-of-bounds behaviora = []

% error:
a(1)

% increases array size to 10;
% zero-fills slots 1 through 9:

a(10) = 10
a = c()
# evaluates as NA:
a[10]
# increases array size to 10:
a[10] = "lorem"
a = []
# raises IndexError:
a[10]
# raises IndexError:
a[10] = 'lorem'
a = []

# raises BoundsError:
a[10]
# raises BoundsError:
a[10] = "lorem"
index of elementa = [7 8 9 10 8]

% returns [2 5]:
find(a == 8)

% returns 2:
find(a == 8, 1, 'first')
a = c('x', 'y', 'z', 'w', 'y')

# c(2, 5):
which(a == 'y')
a = ['x', 'y', 'z', 'w', 'y']

a.index('y')   # 1
a.rindex('y')  # 4
a = ["x", "y", "z", "w", "y"]

# 2:
findfirst(a, "y")
# 5:
julia> findlast(a, "y")
slice
by endpoints
a = ['a' 'b' 'c' 'd' 'e']

% ['c' 'd']:
a(3:4)
a = c("a", "b", "c", "d", "e")

# c("c", "d"):
a[seq(3, 4)]
a = ['a', 'b', 'c', 'd', 'e']

# ['c', 'd']:
a[2:4]
a = ["a", "b", "c", "d", "e"]

# ["c", "d"]:
a[3:4]
slice to end
 
a = ['a' 'b' 'c' 'd' 'e']

% ['c' 'd' 'e']:
a(3:end)
a = c("a", "b", "c", "d", "e")

# both return c("c", "d", "e"):
tail(a, n=length(a) - 2)
a[-1:-2]
a = ['a', 'b', 'c', 'd', 'e']

# ['c', 'd', 'e']:
a[2:]
a = ["a", "b", "c", "d", "e"]

# ["c", "d", "e"]:
a[3:end]
integer array as index[7 8 9]([1 3 3])c(7, 8, 9)[c(1, 3, 3)]np.array([7, 8, 9])[[0, 2, 2]]# [7, 9, 9]:
[7, 8, 9][[1, 3, 3]]
logical array as index[7 8 9]([true false true])c(7, 8, 9)[c(T, F, T)]np.array([7, 8, 9])[[True, False, True]]# [7, 9]:
[7, 8, 9][[true, false, true]]
concatenatea = [1 2 3]
a2 = [a [4 5 6]]
a = [a [4 5 6]]
% or:
a = horzcat(a, a2)
a = c(1, 2, 3)
a2 = append(a, c(4, 5, 6))
a = append(a, c(4, 5, 6))
a = [1, 2, 3]
a2 = a + [4, 5, 6]
a.extend([4, 5, 6])
a = [1, 2, 3]
a2 = vcat(a, [4, 5, 6])
a = vcat(a, [4, 5, 6])
replicatea = repmat(NA, 1, 10)a = rep(NA, 10)

# 30 a's, 50 b's, and 90 c's:
rep(c("a", "b", "c"), c(30, 50, 90))
a = [None] * 10
a = [None for i in range(0, 10)]
fill(NaN, 10)
copy
address copy, shallow copy, deep copy
There is no address copy. Because arrays cannot be nested, there is no distinction between shallow copy and deep copy. Assignment and passing an array to a function can be regarded as performing a shallow or deep copy, though MATLAB does not allocate memory for a 2nd array until one of the arrays is modified.Arrays in R behave like arrays in MATLAB.import copy

a = [1, 2, [3, 4]]

a2 = a
a3 = list(a)
a4 = copy.deepcopy(a)
a = Any[1, 2, [3, 4]]

a2 = a
a3 = copy(a)
a4 = deepcopy(a)
iteration
 
a = [9 7 3]
for i = 1:numel(a)
  x = a(i)
  disp(x)
end
for (x in c(9, 7, 3)) {
  print(x)
}
for i in [9, 7, 3]:
  print(i)
for i = [9, 7, 3]
  println(i)
end
indexed iterationfor (i in seq_along(a)) {
  cat(sprintf("%s at index %d\n", i, a[i]))
}
a = ['do', 're', 'mi', 'fa']
for i, s in enumerate(a):
  print('%s at index %d' % (s, i))
a = ["do", "re", "mi", "fa"]
for (i, s) in enumerate(a)
  println(i, " ", s)
end
reversea = [1 2 3]
a2 = fliplr(a)
a = fliplr(a)
a = c(1, 2, 3)
a2 = rev(a)
a = rev(a)
a = [1, 2, 3]
a2 = a[::-1]
a.reverse()
a = [1, 2, 3]
a2 = reverse(a)
reverse!(a)
sorta = [3 1 4 2]
a = sort(a)
a = c('b', 'A', 'a', 'B')
a2 = sort(a)
a = sort(a)
a = ['b', 'A', 'a', 'B']
sorted(a)
a.sort()
a.sort(key=str.lower)
a = [3, 1, 4, 2]
a2 = sort(a)
sort!(a)
dedupea = [1 2 2 3]
a2 = unique(a)
a = c(1, 2, 2, 3)
a2 = unique(a)
a = [1, 2, 2, 3]
a2 = list(set(a)))
a = unique([1, 2, 2, 3])
membership
 
ismember(7, a)7 %in% a
is.element(7, a)
7 in a7 in a
7 ∈ a
a ∋ 7
intersection
 
intersect([1 2], [2 3 4])intersect(c(1, 2), c(2, 3, 4)){1, 2} & {2, 3, 4}intersection([1, 2], [2, 3, 4])
∩([1, 2], [2, 3, 4])
union
 
union([1 2], [2 3 4])union(c(1, 2), c(2, 3, 4)){1, 2} | {2, 3, 4}union([1, 2], [2, 3, 4])
∪([1, 2], [2, 3, 4])
relative complement, symmetric differencesetdiff([1 2 3], [2])

a1 = [1 2]
a2 = [2 3 4]
union(setdiff(a1, a2), setdiff(a2, a1))
setdiff(c(1, 2, 3), c(2))

union(setdiff(c(1, 2), c(2, 3, 4)),
  setdiff(c(2, 3, 4), c(1, 2)))
{1, 2, 3} - {2}

{1, 2} ^ {2, 3, 4}
setdiff([1, 2, 3], [2])
symdiff([1, 2], [2, 3, 4])
map
 
arrayfun( @(x) x*x, [1 2 3])sapply(c(1,2,3), function (x) { x * x})map(lambda x: x * x, [1, 2, 3])
# or use list comprehension:
[x * x for x in [1, 2, 3]]
filter
 
a = [1 2 3]
a(a > 2)
a = c(1, 2, 3)
a[a > 2]

Filter(function(x) { x > 2}, a)
filter(lambda x: x > 1, [1, 2, 3])
# or use list comprehension:
[x for x in [1, 2, 3] if x > 1]
reduce
 
Reduce(function(x, y) { x + y }, c(1, 2, 3), 0)reduce(lambda x, y: x + y, [1 ,2, 3], 0)reduce(+, [1, 2, 3])
foldl(-, 0, [1, 2, 3])
foldr(-, 0, [1, 2, 3])
universal and existential tests
 
all(mod([1 2 3 4], 2) == 0)
any(mod([1 2 3 4]) == 0)
all(c(1, 2, 3, 4) %% 2 == 0)
any(c(1, 2, 3, 4) %% 2 == 0)
all(i % 2 == 0 for i in [1, 2, 3, 4])
any(i % 2 == 0 for i in [1, 2, 3, 4])
all([x % 2 == 0 for x in [1, 2, 3, 4]])
any([x % 2 == 0 for x in [1, 2, 3, 4]])
shuffle and samplea = c(1, 1, 2, 3, 9, 28)
sample(a, 3)
a[sample.int(length(a))]
from random import shuffle, sample

a = [1, 2, 3, 4]
shuffle(a)
sample(a, 2)
zip
 
none; MATLAB arrays can't be nested# R arrays can't be nested.
# One approximation of zip is a 2d array:

a = rbind(c(1, 2, 3), c('a', 'b', 'c'))

# To prevent data type coercion, use a data frame:
df = data.frame(numbers=c(1, 2, 3),
  letters=c('a', 'b', 'c'))
# array of 3 pairs:
a = zip([1, 2, 3], ['a', 'b', 'c'])
arithmetic sequences
matlabrnumpyjulia
unit difference1:100# type integer:
1:100
seq(1, 100)

# type double:
seq(1, 100, 1)
range(1, 101)1:100
difference of 100:10:100# type double:
seq(0, 100, 10)
range(0, 101, 10)0:10:100
difference of 0.10:0.1:10seq(0, 10, 0.1)[0.1 * x for x in range(0, 101)]

# 3rd arg is length of sequence, not step size:
sp.linspace(0, 10, 100)
0:0.1:10
iterate over arithmetic sequence# range replaces xrange in Python 3:
n = 0
for i in xrange(1, 1000001):
  n += i
n = 0
for i in 1:1000000
  n += i
end
convert arithmetic sequence to arraya = range(1, 11)
# Python 3:
a = list(range(1, 11))
a = Array(1:10)
two dimensional arrays
matlabrnumpyjulia
element typealways numericA = array(c(1, 2, 3))

# "array":
class(A)

# "boolean", "numeric", or "string":
class(c(A))
np.array([1, 2, 3]).dtype

# possible values: np.bool, np.int64, np.float64,
# np.complex128, ...
literal[1, 2; 3, 4]

% commas optional; newlines can replace semicolons::
[1 2
 3 4]
nonenone
construct from sequencereshape([1 2 3 4], 2, 2)array(c(1, 2, 3, 4), dim=c(2, 2))np.array([1, 2, 3, 4]).reshape(2, 2)
construct from rowsrow1 = [1 2 3]
row2 = [4 5 6]

A = [row1; row2]
rbind(c(1, 2, 3), c(4, 5, 6))np.vstack((np.array([1, 2, 3]), np.array([4, 5, 6])))

np.array([[1, 2], [3, 4]])
construct from columnscol1 = [1; 4]
col2 = [2; 5]
col3 = [3; 6]

% commas are optional:
A = [col1, col2, col3]
cbind(c(1, 4), c(2, 5), c(3, 6))cols = (
  np.array([1, 4]),
  np.array([2, 5]),
  np.array([3, 6])
)
np.vstack(cols).transpose()
construct from subarraysA = [1 3; 2 4]

A4_by_2 = [A; A]
A2_by_4 = [A A]
A = matrix(c(1, 2, 3, 4), nrow=2)
A4_by_2 = rbind(A, A)
A2_by_4 = cbind(A, A)
A = np.array([[1, 2], [3, 4]])
A2_by_4 = np.hstack([A, A])
A4_by_2 = np.vstack([A, A])
size
number of elements, number of dimensions, dimension lengths
numel(A)
ndims(A)
size(A)

% length of 1st dimension (i.e. # of rows):
size(A, 1)

% length of longest dimension:
length(A)
length(A)
length(dim(A))
dim(A)
A.size
A.ndim
A.shape

# number of rows:
len(A)
length(A)
ndims(A)
size(A)
lookup% indices start at one:
[1 2; 3 4](1, 1)
# indices start at one:
A = array(c(1, 2, 3, 4), dim=c(2, 2)

A[1, 1]
# indices start at zero:
A = np.array([[1, 2], [3, 4]])

A[0][0] or
A[0, 0]
1d lookupA = [2 4; 6 8]
% returns 8:
A(4)

% convert to column vector of length 4:
A2 = A(:)
A = array(c(2, 4, 6, 8), dim=c(2, 2))

# returns 8:
A[4]
A = np.array([[2, 4], [6, 8]])

# returns np.array([6, 8]):
A[1]

# returns 8:
A.reshape(4)[3]
lookup row or columnA = [1 2 3; 4 5 6; 7 8 9]

% 2nd row:
A(2, :)

% 2nd column:
A(:, 2)
A = t(array(1:9, dim=c(3, 3)))

# 2nd row:
A[2, ]

# 2nd column:
A[, 2]
A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# 2nd row:
A[1, :]

# 2nd column:
A[:, 1]
updateA = [2 4; 6 8]
A(1, 1) = 3
A = array(c(2, 4, 6, 8), dim=c(2, 2))
A[1, 1] = 3
A = np.array([[2, 4], [6, 8]])
A[0, 0] = 3
update row or columnA = [1 2; 3 4]

% [2 1; 3 4]:
A(1, :) = [2 1]

% [3 1; 2 4]:
A(:, 1) = [3 2]
A = t(array(1:4, dim=c(2, 2)))

A[1, ] = c(2, 1)
A[, 1] = c(3, 2)
A = np.array([[1, 2], [3, 4]])

A[0, :] = [2, 1]
# or
A[0] = [2, 1]

A[:, 0] = [3, 2]
update subarrayA = ones(3, 3)
A(1:2, 1:2) = 2 * ones(2, 2)
% or just:
A(1:2, 1:2) = 2
A = array(1, dim=c(3, 3))
A[1:2, 1:2] = array(2, dim=c(2, 2))
# or just:
A[1:2, 1:2] = 2
A = np.ones([3, 3])
A[0:2, 0:2] = 2 * np.ones([2, 2])
out-of-bounds behaviorA = [2 4; 6 8]

% error:
x = A(3, 1)

% becomes 3x2 array with zero at (3, 2):
A(3, 1) = 9
Lookups and updates both cause subscript out of bounds error.Lookups and updates both raise an IndexError exception.
slice subarrayA = reshape(1:16, 4, 4)'

% top left 2x2 subarray:
A(1:2, 1:2)

% bottom right 2x2 subarray:
A(end-1:end, end-1:end)

% 2x2 array containing corners:
A([1 4], [1 4])
A([1 end], [1 end])
A = t(array(1:16, dim=c(4, 4)))

# top left 2x2 subarray:
A[1:2, 1:2]

# bottom right 2x2 subarray:
A[-1:-2, -1:-2]

# 2x2 array containing corners:
A[c(1, 4), c(1, 4)]
A = np.array(range(1, 17)).reshape(4, 4)

# top left 2x2 subarray:
A[0:2, 0:2]

# bottom right 2x2 subarray:
A[2:, 2:]
transposeA = [1 2; 3 4]

A'
transpose(A)
A = array(c(1, 2, 3, 4), dim=c(2, 2))
t(A)
A = np.array([[1, 2], [3, 4]])
A.transpose()
A.T
flip% [ 2 1; 4 3]:
fliplr([1 2; 3 4])

% [3 4; 1 2]:
flipud([1 2; 3 4])
# install.packages('pracma'):
require(pracma)

A = t(array(1:4, dim=c(2, 2)))

fliplr(A)
flipud(A)
A = np.array([[1, 2], [3, 4]])

np.fliplr(A)
np.flipud(A)
circular shift

along columns, along rows
A = [1 2; 3, 4]

% [3 4; 1 2]:
circshift(A, 1)

% [2 1; 4 3]:
circshift(A, 1, 2)

% The 2nd argument can be any integer; negative values shift
% in the opposite direction.
# install.packages('pracma'):
require(pracma)

A = t(array(1:4, dim=c(2, 2)))

circshift(A, c(1, 0))
circshift(A, c(0, 1))
A = np.array([[1, 2], [3, 4]])

np.roll(A, 1, axis=0)
np.roll(A, 1, axis=1)
rotate
clockwise, counter-clockwise
A = [1 2; 3 4]

% [3 1; 4 2]:
rot90(A, -1)

% [2 4; 1 3]:
rot90(A)

% set 2nd arg to 2 for 180 degree rotation
# install.packages('pracma'):
require(pracma)

A = t(array(1:4, dim=c(2, 2)))

rot90(A)
rot90(A, -1)
rot90(A, 2)
A = np.array([[1, 2], [3, 4]])

np.rot90(A)
np.rot90(A, -1)
np.rot90(A, 2)
reduce
rows, columns
M = [1 2; 3 4]

% sum each row:
cellfun(@sum, num2cell(M, 2))

% sum each column:
cellfun(@sum, num2cell(M, 1))

% sum(M, 2) and sum(M, 1) also sum rows and columns
M = matrix(c(1, 2, 3, 4), nrow=2)

# sum each row:
apply(M, 1, sum)

# sum each column:
apply(M, 2, sum)
M = np.array([[1, 2], [3, 4]])

np.add.reduce(A, 1)

np.add.reduce(A, 0)

# np.add is a built-in universal function. All universal functions have a reduce method.

# np.sum(A, 1,) and np.sum(A, 0) also sum rows and columns
three dimensional arrays
matlabrnumpyjulia
construct from sequencereshape([1 2 3 4 5 6 7 8], 2, 2, 2)array(c(1, 2, 3, 4, 5, 6, 7, 8), dim=c(2, 2, 2))np.array([1, 2, 3, 4, 5, 6, 7, 8]).reshape(2, 2, 2)
construct from nested sequencesnonenonenp.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
construct 3d array from 2d arraysA = [1, 2; 3, 4]
A(:,:,2) = [5, 6; 7, 8]
permute axesA = reshape([1 2 3 4 5 6 7 8], 2, 2, 2)

% swap 2nd and 3rd axes:
permute(A, [1 3 2])
A = array(1:8, dim=c(2, 2, 2))

# swap 2nd and 3rd axes:
aperm(A, perm=c(1, 3, 2))
A = np.array(range(1, 9)).reshape(2, 2, 2)

# swap 2nd and 3rd axes:
A.transpose((0, 2, 1))
flipA = reshape([1 2 3 4 5 6 7 8], 2, 2, 2)

flipdim(A, 3)
nonenone
circular shiftA = reshape([1 2 3 4 5 6 7 8], 2, 2, 2)

% 3rd arg specifies axis:
circshift(A, 1, 3)
noneA = np.array([1, 2, 3, 4, 5, 6, 7, 8]).reshape(2, 2, 2)

np.roll(A, 1, axis=2)
dictionaries
matlabrnumpyjulia
literal
 
% no literal; use constructor:
d = struct('n', 10, 'avg', 3.7, 'sd', 0.4)

% or build from two cell arrays:
d = cell2struct({10 3.7 0.4}, {'n' 'avg' 'sd'}, 2)
# keys are 'n', 'avg', and 'sd':
d = list(n=10, avg=3.7, sd=0.4)

# keys are 1, 2, and 3:
d2 = list('do', 're', 'mi')
d = {'n': 10, 'avg': 3.7, 'sd': 0.4}d = Dict("n"=>10.0, "avg"=>3.7, "sd"=>0.4)
size
 
length(fieldnames(d))length(d)len(d)length(d)
lookup
 
d.n
getfield(d, 'n')
d[['n']]

# if 'n' is a key:
d$n
d['n']
update
 
d.var = d.sd**2d$var = d$sd**2d['var'] = d['sd']**2
missing key behavior
 
errorNULLraises KeyError
is key present
 
isfield(d, 'var')is.null(d$var)'var' in dhaskey(d, "var")
delete
 
d = rmfield(d, 'sd')d$sd = NULLdel(d['sd'])
iteratefor i = 1:numel(fieldnames(d))
  k = fieldnames(d){i}
  v = d.(k)
  code
end
for (k in names(d)) {
  v = d[[k]]
  code
}
for k, v in d.iteritems():
  code
keys and values as arrays% these return cell arrays:
fieldnames(d)
struct2cell(d)
names(d)
unlist(d, use.names=F)
d.keys()
d.values()
mergenoned1 = list(a=1, b=2)
d2 = list(b=3, c=4)
# values of first dictionary take precedence:
d3 = c(d1, d2)
d1 = {'a':1, 'b':2}
d2 = {'b':3, 'c':4}
d1.update(d2)
functions
matlabrnumpyjulia
define functionfunction add(x, y)
  x + y
end
add = function(x, y) {x + y}function add(x,y)
  x + y
end

# optional syntax when body is an expression:
add(x, y) = x + y
invoke function
 
add(3, 7)add(3, 7)add(3, 7)
nested functionfunction ret1 = add3(x, y, z)
  function ret2 = add2(x, y)
    ret2 = x + y;
  end

  ret1 = add2(x, y) + z;
end
add3 = function(x, y, z) {
  add2 = function(x, y) { x + y }
  add2(x, y) + z
}
function add3(x, y, z)
  function add2(x2, y2)
    x2 + y2
  end
  add2(x, y) + z
end
missing argument behaviorraises error if code with the parameter that is missing an argument is executedraises errorraises MethodError
extra argument behavior
 
ignoredraises errorraises MethodError
default argumentfunction mylog(x, base=10)
  log(x) / log(base)
end
mylog = function(x,base=10) {
  log(x) / log(base)
}
variadic functionfunction s = add(varargin)
  if nargin == 0
    s = 0
  else
    r = add(varargin{2:nargin})
    s = varargin{1} + r
  end
end
add = function (...) {
  a = list(...)
  if (length(a) == 0)
    return(0)
  s = 0
  for(i in 1:length(a)) {
    s = s + a[[i]]
  }
  return(s)
}
return valuefunction ret = add(x, y)
  ret = x + y;
end

% If a return variable is declared, the value assigned
% to it is returned. Otherwise the value of the last
% statement will be used if it does not end with a
% semicolon.
return argument or last expression evaluated. NULL if return called without an argument.return argument or last expression evaluated. Void if return called without an argument.
multiple return valuesfunction [x, y] = first_two(a)
  x = a(1);
  y = a(2);
end

% sets first to 7; second to 8:
[first, second] = first_two([7 8 9])
function first_two(a)
  a[1], a[2]
end

x, y = first_two([1, 2, 3])
anonymous function literal% body must be an expression:
@(x, y) x + y
function(x, y) {x + y}add = (x, y) -> x + y

add = function(x, y)
  x + y
end
invoke anonymous functionadd(1, 2)
closuremake_counter = function() {
  i = 0
  function() {
    i <<- i + 1
    i
  }
}
function as value
 
@addaddadd
overload operator
call operator like function`+`(3, 7)+(3, 7)
execution control
matlabrnumpyjulia
ifif (x > 0)
  disp('positive')
elseif (x < 0)
  disp('negative')
else
  disp('zero')
end
if (x > 0) {
  print('positive')
} else if (x < 0) {
  print('negative')
} else {
  print('zero')
}
if x > 0:
  print('positive')
elif x < 0:
  print('negative')
else:
  print('zero')
if x > 0
  println("positive")
elseif x < 0
  println("negative")
else
  println("zero")
end
whilei = 0
while (i < 10)
  i = i + 1
  disp(i)
end
while (i < 10) {
  i = i + 1
  print(i)
}
while i < 10:
  i += 1
  print(i)
i = 0
while i < 10
  i += 1
  println(i)
end
forfor i = 1:10
  disp(i)
end
for (i in 1:10) {
  print(i)
}
for i in range(1,11):
  print(i)
for i = 1:10
  println(i)
end
break/continue
 
break continuebreak nextbreak continuebreak continue
raise exception
 
error('%s', 'failed')stop('failed')raise Exception('failed')throw("failed")
handle exceptiontry
  error('failed')
catch err
  disp(err)
end
tryCatch(
  stop('failed'),
  error=function(e) print(message(e)))
try:
  raise Exception('failed')
except Exception as e:
  print(e)
file handles
matlabrnumpyjulia
standard file handles0 1 2

% Octave has predefined variables
% containing the above descriptors:

stdin stdout stderr
stdin() stdout() stderr()sys.stdin sys.stdout sys.stderrSTDIN STDOUT STDERR
read line from stdinline = input('', 's')line = readLines(n=1)line = sys.stdin.readline()line = readline()
write line to stdoutfprintf(1, 'hello\n')cat("hello\n")

writeLines("hello")
print('hello')println("hello")
write formatted string to stdoutfprintf(1, '%.2f\n', pi)cat(sprintf("%.2f\n", pi))import math

print('%.2f' % math.pi)
open file for readingf = fopen('/etc/hosts')
if (f == -1)
  error('failed to open file')
end
f = file("/etc/hosts", "r")f = open('/etc/hosts')f = open("/etc/hosts")
open file for writingif ((f = fopen('/tmp/test', 'w') == -1)
  error('failed to open file')
endif
f = file("/tmp/test", "w")f = open('/tmp/test', 'w')f = open("/etc/hosts", "w")
open file for appendingif ((f = fopen('/tmp/err.log', 'a') == -1)
  error('failed to open file')
endif
f = file("/tmp/err.log", "a")f = open('/tmp/err.log', 'a')f = open("/tmp/err.log", "a")
close filefclose(f)close(f)f.close()close(f)
i/o errorsfopen returns -1; fclose throws an errorraise IOError exception
read lineline = fgets(f)line = readLines(f, n=1)line = f.readline()line = readline(f)
iterate over file by linewhile(!feof(f))
  line = fgets(f)
  puts(line)
endwhile
for line in f:
  print(line)
read file into array of stringslines = readLines(f)lines = f.readlines()lines = readlines(f)
write stringfputs(f, 'lorem ipsum')cat("lorem ipsum", file=f)f.write('lorem ipsum')write(f, "lorem ipsum")
write linefputs(f, 'lorem ipsum\n')writeLines("lorem ipsum", con=f)f.write('lorem ipsum\n')
flush file handlefflush(f)flush(f)f.flush()
file handle position
get, set
ftell(f)

% 3rd arg can be SEEK_CUR or SEEK_END
fseek(f, 0, SEEK_SET)
seek(f)

# sets seek point to 12 bytes after start;
# origin can also be "current" or "end"

seek(f, where=0, origin="start")
f.tell()

f.seek(0)
redirect stdout to filesink("foo.txt")
write variables to fileA = [1 2; 3 4]
B = [4 3; 2 1]

save('data.mdata', 'A', 'B')
A = matrix(c(1, 3, 2, 4), nrow=2)
B = matrix(c(4, 2, 3, 1), nrow=2)

save(A, B, file='data.rdata')
A = np.matrix([[1, 2], [3, 4]])
B = np.matrix([[4, 3], [2, 1]])

# Data must be of type np.array;
# file will have .npz suffix:
np.savez('data', A=A, B=B)
read variables from file% puts A and B in scope:
load('data.mdata')

% puts just A in scope:
load('data.mdata', 'A')
# puts A and B in scope:
load('data.rdata')
data = np.load('data.npz')
A = data['A']
B = data['B']
write all variables in scope to filesave('data.txt')save.image('data.txt')
directories
matlabrnumpyjulia
working directory
get, set
pwd

cd('/tmp')
getwd()

setwd("/tmp")
os.path.abspath('.')

os.chdir('/tmp')
build pathnamefullfile('/etc', 'hosts')file.path("/etc", "hosts")os.path.join('/etc', 'hosts')
dirname and basename[dir, base] = fileparts('/etc/hosts')dirname("/etc/hosts")
basename("/etc/hosts")
os.path.dirname('/etc/hosts')
os.path.basename('/etc/hosts')
absolute pathnamenormalizePath("..")os.path.abspath('..')
iterate over directory by file% lists /etc:
ls('/etc')

% lists working directory:
ls()
# list.files() defaults to working directory
for (path in list.files('/etc')) {
  print(path)
}
for filename in os.listdir('/etc'):
  print(filename)
glob pathsglob('/etc/*')Sys.glob('/etc/*')import glob

glob.glob('/etc/*')
processes and environment
matlabrnumpyjulia
command line arguments% does not include interpreter name:
argv()
# first arg is name of interpreter:
commandArgs()

# arguments after --args only:
commandArgs(TRUE)
sys.argvARGS
environment variable
get, set
getenv('HOME')

setenv('PATH', '/bin')
Sys.getenv("HOME")

Sys.setenv(PATH="/bin")
os.getenv('HOME')

os.environ['PATH'] = '/bin'
ENV["HOME"]

ENV["PATH"] = "/bin"
exit
 
exit(0)quit(save="no", status=0)sys.exit(0)exit(0)
external commandif (shell_cmd('ls -l /tmp'))
  error('ls failed')
endif
if (system("ls -l /tmp")) {
  stop("ls failed")
}
if os.system('ls -l /tmp'):
  raise Exception('ls failed')
command substitutions = readall(‘ls`)
libraries and namespaces
matlabrnumpyjulia
load libraryWhen a function is invoked, MATLAB searches the library path for a file with the same name and a .m suffix. Other functions defined in the file are not visible outside the file.# quoting the name of the package is optional:
require("foo")
# or:
library("foo")

# if the package does not exist, require returns false, and library raises an error.
import fooinclude("foo.jl")
list loaded librariesnonesearch()dir()
library search pathpath()
addath(’~/foo')
rmpath('~/foo')
.libPaths()sys.path
source file
 
run('foo.m')source("foo.r")none
install package% Octave: how to install package
% downloaded from Octave-Forge:

pkg install foo-1.0.0.tar.gz
install.packages("ggplot2")$ pip install scipy
load package library% Octave:
pkg load foo
require("foo")
# or:
library("foo")
import foo
list installed packages% Octave:
pkg list
library()
installed.packages()
$ pip freeze
reflection
matlabrnumpyjulia
data typeclass(x)class(x)
# often more informative:
str(x)
type(x)typeof(x)
attributes% if x holds an object:
x
attributes(x)[m for m in dir(x)
  if not callable(getattr(o,m))]
fieldnames(x)
methods% if x holds an object:
methods(x)
none; objects are implemented by functions which dispatch based on type of first arg[m for m in dir(x)
  if callable(getattr(o,m))]
methods(x)
variables in scopewho()

% with size and type:
whos()
objects()
ls()

# with type and description:
ls.str()
dir()whos()
undefine variable
 
clear('x')rm(v)del(x)none
undefine all variablesclear -arm(list=objects())none
eval
 
eval('1 + 1')eval(parse(text='1 + 1'))eval('1 + 1')eval(parse("1 + 1"))
function documentationhelp tanhelp(tan)
?tan
math.tan.__doc__?tan
list library functionsnonels("package:moments")dir(stats)whos(Base)
search documentationdocsearch tan??tan$ pydoc -k tanapropos("tan")
________________________________________________________________________________________________________________________________________________________________________________________________________

tables | import and export | relational algebra | aggregation

vectors | matrices | sparse matrices | optimization | polynomials | descriptive statistics | distributions | linear regression | statistical tests | time series | fast fourier transform | clustering

univariate charts | bivariate charts | multivariate charts

General

version used

The version of software used to check the examples in the reference sheet.

show version

How to determine the version of an installation.

implicit prologue

Code which examples in the sheet assume to have already been executed.

r:

The ggplot2 library must be installed and loaded to use the plotting functions qplot and ggplot.

Grammar and Invocation

interpreter

How to invoke the interpreter on a script.

repl

How to launch a command line read-eval-print loop for the language.

r:

R installations come with a GUI REPL.

The shell zsh has a built-in command r which re-runs the last command. Shell built-ins take precedence over external commands, but one can invoke the R REPL with:

$ command r

command line program

How to pass the code to be executed to the interpreter as a command line argument.

environment variables

How to get and set an environment variable.

block delimiters

Punctuation or keywords which define blocks.

matlab:

The list of keywords which define blocks is not exhaustive. Blocks are also defined by

  • switch, case, otherwise, endswitch
  • unwind_protect, unwind_protect_cleanup, end_unwind_protect
  • try, catch, end_try_catch

statement separator

How statements are separated.

matlab:

Semicolons are used at the end of lines to suppress output. Output echoes the assignment performed by a statement; if the statement is not an assignment the value of the statement is assigned to the special variable ans.

In Octave, but not MATLAB, newlines are not separators when preceded by a backslash.

end-of-line comment

Character used to start a comment that goes to the end of the line.

octave:

Octave, but not MATLAB, also supports shell-style comments which start with #.

Variables and Expressions

assignment

r:

Traditionally <- was used in R for assignment. Using an = for assignment was introduced in version 1.4.0 sometime before 2002. -> can also be used for assignment:

3 -> x

compound assignment

The compound assignment operators.

octave:

Octave, but not MATLAB, has compound assignment operators for arithmetic and bit operations:

+= -= *= /=  **=  ^=
&= |=

Octave, but not MATLAB, also has the C-stye increment and decrement operators ++ and --, which can be used in prefix and postfix position.

increment and decrement operator

The operator for incrementing the value in a variable; the operator for decrementing the value in a variable.

null

matlab:

NaN can be used for missing numerical values. Using a comparison operator on it always returns false, including NaN == NaN. Using a logical operator on NaN raises an error.

octave:

Octave, but not MATLAB, provides NA which is a synonym of NaN.

r:

Relational operators return NA when one of the arguments is NA. In particular NA == NA is NA. When acting on values that might be NA, the logical operators observe the rules of ternary logic, treating NA is the unknown value.

null test

How to test if a value is null.

octave:

Octave, but not MATLAB, has isna and isnull, which are synonyms of isnan and isempty.

conditional expression

A conditional expression.

Arithmetic and Logic

true and false

The boolean literals.

matlab:

true and false are functions which return matrices of ones and zeros of type logical. If no arguments are specified they return single entry matrices. If one argument is provided, a square matrix is returned. If two arguments are provided, they are the row and column dimensions.

falsehoods

Values which evaluate to false in a conditional test.

matlab:

When used in a conditional, matrices evaluate to false unless they are nonempty and all their entries evaluate to true. Because strings are matrices of characters, an empty string ('' or "") will evaluate to false. Most other strings will evaluate to true, but it is possible to create a nonempty string which evaluates to false by inserting a null character; e.g. "false\000".

r:

When used in a conditional, a vector evaluates to the boolean value of its first entry. Using a vector with more than one entry in a conditional results in a warning message. Using an empty vector in a conditional, c() or NULL, raises an error.

logical operators

The boolean operators.

octave:

Octave, but not MATLAB, also uses the exclamation point '!' for negation.

relational operators

The relational operators.

octave:

Octave, but not MATLAB, also uses != for an inequality test.

arithmetic operators

The arithmetic operators: addition, subtraction, multiplication, division, quotient, remainder.

matlab:

mod is a function and not an infix operator. mod returns a positive value if the first argument is positive, whereas rem returns a negative value.

integer division

How to compute the quotient of two integers.

integer division by zero

What happens when an integer is divided by zero.

float division

How to perform float division, even if the arguments are integers.

float division by zero

What happens when a float is divided by zero.

power

octave:

Octave, but not MATLAB, supports ** as a synonym of ^.

sqrt

The square root function.

sqrt(-1)

The result of taking the square root of a negative number.

transcendental functions

The standard transcendental functions.

transcendental constants

Constants for pi and e.

float truncation

Ways of converting a float to a nearby integer.

absolute value

The absolute value and signum of a number.

integer overflow

What happens when an expression evaluates to an integer which is too big to be represented.

float overflow

What happens when an expression evaluates to a float which is too big to be represented.

float limits

The machine epsilon; the largest representable float and the smallest (i.e. closest to negative infinity) representable float.

complex construction

Literals for complex numbers.

complex decomposition

How to decompose a complex number into its real and imaginary parts; how to decompose a complex number into its absolute value and argument; how to get the complex conjugate.

random number

How to generate a random integer from a uniform distribution; how to generate a random float from a uniform distribution.

random seed

How to set, get, and restore the seed used by the random number generator.

matlab:

At startup the random number generator is seeded using operating system entropy.

r:

At startup the random number generator is seeded using the current time.

numpy:

On Unix the random number generator is seeded at startup from /dev/random.

bit operators

The bit operators left shift, right shift, and, or , xor, and negation.

matlab/octave:

bitshift takes a second argument which is positive for left shift and negative for right shift.

bitcmp takes a second argument which is the size in bits of the integer being operated on. Octave is not compatible with MATLAB in how the integer size is indicated.

r:

There is a library on CRAN called bitops which provides bit operators.

Strings

literal

The syntax for a string literal.

newline in literal

Can a newline be included in a string literal? Equivalently, can a string literal span more than one line of source code?

octave:

Double quote strings are Octave specific.

A newline can be inserted into a double quote string using the backslash escape \n.

A double quote string can be continued on the next line by ending the line with a backslash. No newline is inserted into the string.

literal escapes

Escape sequences for including special characters in string literals.

matlab:

C-style backslash escapes are not recognized by string literals, but they are recognized by the IO system; the string 'foo\n' contains 5 characters, but emits 4 characters when written to standard output.

concatenate

How to concatenate strings.

replicate

How to create a string which consists of a character of substring repeated a fixed number of times.

index of substring

How to get the index of first occurrence of a substring.

extract substring

How to get the substring at a given index.

octave:

Octave supports indexing string literals directly: 'hello'(1:4).

split

How to split a string into an array of substrings. In the original string the substrings must be separated by a character, string, or regex pattern which will not appear in the array of substrings.

The split operation can be used to extract the fields from a field delimited record of data.

matlab:

Cell arrays, which are essentially tuples, are used to store variable-length strings.

A two dimensional array of characters can be used to store strings of the same length, one per row. Regular arrays cannot otherwise be used to store strings.

join

How to join an array of substrings into single string. The substrings can be separated by a specified character or string.

Joining is the inverse of splitting.

trim

How to remove whitespace from the beginning and the end of a string.

Trimming is often performed on user provided input.

pad

How to pad the edge of a string with spaces so that it is a prescribed length.

number to string

How to convert a number to a string.

string to number

How to convert a string to number.

translate case

How to put a string into all caps. How to put a string into all lower case letters.

sprintf

How to create a string using a printf style format.

length

How to get the number of characters in a string.

character access

How to get the character in a string at a given index.

octave:

Octave supports indexing string literals directly: 'hello'(1).

chr and ord

How to convert an ASCII code to a character; how to convert a character to its ASCII code.

Regular Expressions

character class abbreviations

The supported character class abbreviations.

A character class is a set of one or more characters. In regular expressions, an arbitrary character class can be specified by listing the characters inside square brackets. If the first character is a circumflex ^, the character class is all characters not in the list. A hyphen - can be used to list a range of characters.

matlab:

The C-style backslash escapes, which can be regarded as character classes which match a single character, are a feature of the regular expression engine and not string literals like in other languages.

anchors

The supported anchors.

The \< and \> anchors match the start and end of a word respectively.

match test

How to test whether a string matches a regular expression.

case insensitive match test

How to perform a case insensitive match test.

substitution

How to replace all substring which match a pattern with a specified string; how to replace the first substring which matches a pattern with a specified string.

backreference in match and substitution

How to use backreferences in a regex; how to use backreferences in the replacement string of substitution.

Date and Time

current date/time

How to get the current date and time.

r:

Sys.time() returns a value of type POSIXct.

date/time type

The data type used to hold a combined date and time value.

matlab:

The Gregorian calendar was introduced in 1582. The Proleptic Gregorian Calendar is sometimes used for earlier dates, but in the Proleptic Gregorian Calendar the year 1 CE is preceded by the year 1 BCE. The MATLAB epoch thus starts at the beginning of the year 1 BCE, but uses a zero to refer to this year.

date/time difference type

The data type used to hold the difference between two date/time types.

get date parts

How to get the year, the month as an integer from 1 through 12, and the day of the month from a date/time value.

octave:

In Octave, but not MATLAB, one can use index notation on the return value of a function:

t = now
datevec(t)(1)

get time parts

How to get the hour as an integer from 0 through 23, the minute, and the second from a date/time value.

build date/time from parts

How to build a date/time value from the year, month, day, hour, minute, and second as integers.

convert to string

How to convert a date value to a string using the default format for the locale.

parse datetime

How to parse a date/time value from a string in the manner of strptime from the C standard library.

format datetime

How to write a date/time value to a string in the manner of strftime from the C standard library.

Tuples

type

The name of the data type which implements tuples.

literal

How to create a tuple, which we define as a fixed length, inhomogeneous list.

lookup element

How to access an element of a tuple.

update element

How to change one of a tuple's elements.

length

How to get the number of elements in a tuple.

Arrays

This section covers one-dimensional arrays which map integers to values.

Multidimensional arrays are a generalization which map tuples of integers to values.

Vectors and matrices are one-dimensional and two-dimensional arrays respectively containing numeric values. They support additional operations including the dot product, matrix multiplication, and norms.

Here are the data types covered in each section:

sectionmatlabrnumpy
arraysmatrix (ndims = 1)vectorlist
multidimensional arraysmatrixarraynp.array
vectorsmatrix (ndims = 1)vectornp.array (ndim = 1)
matricesmatrix (ndims = 2)matrixnp.matrix

element type

How to get the type of the elements of an array.

permitted element types

Permitted data types for array elements.

matlab:

Arrays in Octave can only contain numeric elements.

Array literals can have a nested structure, but Octave will flatten them. The following literals create the same array:

[ 1 2 3 [ 4 5 6] ]
[ 1 2 3 4 5 6 ]

Logical values can be put into an array because true and false are synonyms for 1 and 0. Thus the following literals create the same arrays:

[ true false false ]
[ 1 0 0 ]

If a string is encountered in an array literal, the string is treated as an array of ASCII values and it is concatenated with other ASCII values to produce as string. The following literals all create the same string:

[ 'foo', 98, 97, 114]
[ 'foo', 'bar' ]
'foobar'

If the other numeric values in an array literal that includes a string are not integer values that fit into a ASCII byte, then they are converted to byte sized values.

r:

Array literals can have a nested structure, but R will flatten them. The following literals produce the same array of 6 elements:

c(1,2,3,c(4,5,6))
c(1,2,3,4,5,6)

If an array literal contains a mixture of booleans and numbers, then the boolean literals will be converted to 1 (for TRUE and T) and 0 (for FALSE and F).

If an array literal contains strings and either booleans or numbers, then the booleans and numbers will be converted to their string representations. For the booleans the string representations are "TRUE'" and "FALSE".

literal

The syntax, if any, for an array literal.

matlab:

The array literal

[1,'foo',3]

will create an array with 5 elements of class char.

r:

The array literal

c(1,'foo',3)

will create an array of 3 elements of class character, which is the R string type.

size

How to get the number of values in an array.

empty test

lookup

update

out-of-bounds behavior

index of element

slice

slice to end

concatenate

replicate

copy

How to make an address copy, a shallow copy, and a deep copy of an array.

After an address copy is made, modifications to the copy also modify the original array.

After a shallow copy is made, the addition, removal, or replacement of elements in the copy does not modify of the original array. However, if elements in the copy are modified, those elements are also modified in the original array.

A deep copy is a recursive copy. The original array is copied and a deep copy is performed on all elements of the array. No change to the contents of the copy will modify the contents of the original array.

Arithmetic Sequences

An arithmetic sequence is a sequence of numeric values in which consecutive terms have a constant difference.

unit difference

An arithmetic sequence with a difference of 1.

difference of 10

An arithmetic sequence with a difference of 10.

difference of 0.1

An arithmetic sequence with a difference of 0.1.

iterate

How to iterate over an arithmetic sequence.

convert to array

How to convert an arithmetic sequence to an array.


Multidimensional Arrays

Multidimensional arrays are a generalization of arrays which map tuples of integers to values. All tuples in the domain of a multidimensional array have the same length; this length is the dimension of the array.

The multidimensional arrays described in this sheet are homogeneous, meaning that the values are all of the same type. This restriction allows the implementation to store the values of the multidimensional array in a contiguous region of memory without the use of references or points.

Multidimensional arrays should be contrasted with nested arrays. When arrays are nested, the innermost nested arrays contain the values and the other arrays contain references to arrays. The syntax for looking up a value is usually different:

# nested:
a[1][2]

# multidimensional:
a[1, 2]

element type

How to get the type of the values stored in a multidimensional array.

r:

literal—1d

literal—2d

construct from sequence—2d

construct from sequence—3d

construct from nested sequences—2d

construct from nested sequences—3d

construct from rows—2d

construct from columns—2d

construct from subarrays—2d

construct 3d array from 2d arrays

size

lookup—1d

lookup—2d

1d lookup on 2d array

update—2d

out-of-bounds behavior

slice

slice to end

slice subarray

transpose

permute axes

flip—2d

flip—3d

circular shift—2d

rotate—2d

apply function element-wise

apply function to linear subarrays

Dictionaries

literal

The syntax for a dictionary literal.

size

How to get the number of keys in a dictionary.

lookup

How to use a key to lookup a value in a dictionary.

update

How to add or key-value pair or change the value for an existing key.

missing key behavior

What happens when looking up a key that isn't in the dictionary.

delete

How to delete a key-value pair from a dictionary.

iterate

How to iterate over the key-value pairs.

keys and values as arrays

How to get an array containing the keys; how to get an array containing the values.

merge

How to merge two dictionaries.

Functions

define function

How to define a function.

invoke function

How to invoke a function.

nested function

missing argument behavior

What happens when a function is invoked with too few arguments.

extra argument behavior

What happens when a function is invoked with too many arguments.

default argument

How to assign a default argument to a parameter.

variadic function

How to define a function which accepts a variable number of arguments.

return value

How the return value of a function is determined.

multiple return values

How to return multiple values from a function.

anonymous function literal

The syntax for an anonymous function.

invoke anonymous function

closure

function as value

How to store a function in a variable.

Execution Control

if

How to write a branch statement.

while

How to write a conditional loop.

for

How to write a C-style for statement.

break/continue

How to break out of a loop. How to jump to the next iteration of a loop.

raise exception

How to raise an exception.

handle exception

How to handle an exception.

File Handles

standard file handles

Standard input, standard output, and standard error.

read line from stdin

write line to stdout

How to write a line to stdout.

matlab:

The backslash escape sequence \n is stored as two characters in the string and interpreted as a newline by the IO system.

write formatted string to stdout

open file for reading

open file for writing

open file for appending

close file

i/o errors

read line

iterate over file by line

read file into array of strings

write string

write line

flush file handle

file handle position

redirect stdout to file

Directories

working directory

How to get and set the working directory.

Processes and Environment

command line arguments

How to get the command line arguments.

environment variables

How to get and set and environment variable.

Libraries and Namespaces

load library

How to load a library.

list loaded libraries

Show the list of libraries which have been loaded.

library search path

The list of directories the interpreter will search looking for a library to load.

source file

How to source a file.

r:

When sourcing a file, the suffix if any must be specified, unlike when loading library. Also, a library may contain a shared object, but a sourced file must consist of just R source code.

install package

How to install a package.

list installed packages

How to list the packages which have been installed.

Reflection

data type

How to get the data type of a value.

r:

For vectors class returns the mode of the vector which is the type of data contained in it. The possible modes are

  • numeric
  • complex
  • logical
  • character
  • raw

Some of the more common class types for non-vector entities are:

  • matrix
  • array
  • list
  • factor
  • data.frame

attributes

How to get the attributes for an object.

r:

Arrays and vectors do not have attributes.

methods

How to get the methods for an object.

variables in scope

How to list the variables in scope.

undefine variable

How to undefine a variable.

undefine all variables

How to undefine all variables.

eval

How to interpret a string as source code and execute it.

function documentation

How to get the documentation for a function.

list library functions

How to list the functions and other definitions in a library.

search documentation

How to search the documentation by keyword.

MATLAB

Octave Manual
MATLAB Documentation
Differences between Octave and MATLAB
Octave-Forge Packages

The basic data type of MATLAB is a matrix of floats. There is no distinction between a scalar and a 1x1 matrix, and functions that work on scalars typically work on matrices as well by performing the scalar function on each entry in the matrix and returning the results in a matrix with the same dimensions. Operators such as the logical operators ('&' '|' '!'), relational operators ('==', '!=', '<', '>'), and arithmetic operators ('+', '-') all work this way. However the multiplication '*' and division '/' operators perform matrix multiplication and matrix division, respectively. The .* and ./ operators are available if entry-wise multiplication or division is desired.

Floats are by default double precision; single precision can be specified with the single constructor. MATLAB has convenient matrix literal notation: commas or spaces can be used to separate row entries, and semicolons or newlines can be used to separate rows.

Arrays and vectors are implemented as single-row (1xn) matrices. As a result an n-element vector must be transposed before it can be multiplied on the right of a mxn matrix.

Numeric literals that lack a decimal point such as 17 and -34 create floats, in contrast to most other programming languages. To create an integer, an integer constructor which specifies the size such as int8 and uint16 must be used. Matrices of integers are supported, but the entries in a given matrix must all have the same numeric type.

Strings are implemented as single-row (1xn) matrices of characters. Matrices cannot contain strings. If a string is put in matrix literal, each character in the string becomes an entry in the resulting matrix. This is consistent with how matrices are treated if they are nested inside another matrix. The following literals all yield the same string or 1xn matrix of characters:

'foo'
[ 'f' 'o' 'o' ]
[ 'foo' ]
[ [ 'f' 'o' 'o' ] ]

true and false are functions which return matrices of ones and zeros. The ones and zeros have type logical instead of double, which is created by the literals 1 and 0. Other than having a different class, the 0 and 1 of type logical behave the same as the 0 and 1 of type double.

MATLAB has a tuple type (in MATLAB terminology, a cell array) which can be used to hold multiple strings. It can also hold values with different types.

R

An Introduction to R
Advanced R Programming
The Comprehensive R Archive Network

The primitive data types of R are vectors of floats, vectors of strings, and vectors of booleans. There is no distinction between a scalar and a vector with one entry in it. Functions and operators which accept a scalar argument will typically accept a vector argument, returning a vector of the same size with the scalar operation performed on each the entries of the original vector.

The scalars in a vector must all be of the same type, but R also provides a list data type which can be used as a tuple (entries accessed by index), record (entries accessed by name), or even as a dictionary.

In addition R provides a data frame type which is a list (in R terminology) of vectors all of the same length. Data frames are equivalent to the data sets of other statistical analysis packages.

NumPy

NumPy and SciPy Documentation
matplotlib intro
NumPy for Matlab Users
Pandas Documentation
Pandas Method/Attribute Index

NumPy is a Python library which provides a data type called array. It differs from the Python list data type in the following ways:

  • N-dimensional. Although the list type can be nested to hold higher dimension data, the array can hold higher dimension data in a space efficient manner without using indirection.
  • homogeneous. The elements of an array are restricted to be of a specified type. The NumPy library introduces new primitive types not available in vanilla Python. However, the element type of an array can be object which permits storing anything in the array.

In the reference sheet the array section covers the vanilla Python list and the multidimensional array section covers the NumPy array.

List the NumPy primitive types

SciPy, Matplotlib, and Pandas are libraries which depend on Numpy.

Julia

http://julialang.org/

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